Journal articles on the topic 'Physics Informed Neural Network (PINN)'
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Kenzhebek, Y., T. S. Imankulov, and D. Zh Akhmed-Zaki. "PREDICTION OF OIL PRODUCTION USING PHYSICS-INFORMED NEURAL NETWORKS." BULLETIN Series of Physics & Mathematical Sciences 76, no. 4 (December 15, 2021): 45–50. http://dx.doi.org/10.51889/2021-4.1728-7901.06.
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In recent years, modern information technologies have been actively used in various industries. The oil industry is no exception, since high-performance computing technologies, artificial intelligence algorithms, methods of collecting, processing and storing information are actively used to solve the problems of increasing oil recovery. Deep learning has made remarkable strides in a variety of applications, but its use for solving partial differential equations has only recently emerged. In particular, you can replace traditional numerical methods with a neural network that approximates the solution to a partial differential equation. Physically Informed Neural Networks (PINNs) embed partial differential equations into the neural network loss function using automatic differentiation. A numerical algorithm and PINN have been developed for solving the one-dimensional pressure equation from the Buckley-Leverett mathematical model. The results of numerical solution and prediction of the PINN neural network for solving the pressure equation are obtained.
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Ngo, Son Ich, and Young-Il Lim. "Solution and Parameter Identification of a Fixed-Bed Reactor Model for Catalytic CO2 Methanation Using Physics-Informed Neural Networks." Catalysts 11, no. 11 (October 28, 2021): 1304. http://dx.doi.org/10.3390/catal11111304.
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In this study, we develop physics-informed neural networks (PINNs) to solve an isothermal fixed-bed (IFB) model for catalytic CO2 methanation. The PINN includes a feed-forward artificial neural network (FF-ANN) and physics-informed constraints, such as governing equations, boundary conditions, and reaction kinetics. The most effective PINN structure consists of 5–7 hidden layers, 256 neurons per layer, and a hyperbolic tangent (tanh) activation function. The forward PINN model solves the plug-flow reactor model of the IFB, whereas the inverse PINN model reveals an unknown effectiveness factor involved in the reaction kinetics. The forward PINN shows excellent extrapolation performance with an accuracy of 88.1% when concentrations outside the training domain are predicted using only one-sixth of the entire domain. The inverse PINN model identifies an unknown effectiveness factor with an error of 0.3%, even for a small number of observation datasets (e.g., 20 sets). These results suggest that forward and inverse PINNs can be used in the solution and system identification of fixed-bed models with chemical reaction kinetics.
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Usama, Muhammad, Rui Ma, Jason Hart, and Mikaela Wojcik. "Physics-Informed Neural Networks (PINNs)-Based Traffic State Estimation: An Application to Traffic Network." Algorithms 15, no. 12 (November 27, 2022): 447. http://dx.doi.org/10.3390/a15120447.
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Traffic state estimation (TSE) is a critical component of the efficient intelligent transportation systems (ITS) operations. In the literature, TSE methods are divided into model-driven methods and data-driven methods. Each approach has its limitations. The physics information-based neural network (PINN) framework emerges to mitigate the limitations of the traditional TSE methods, while the state-of-art of such a framework has focused on single road segments but can hardly deal with traffic networks. This paper introduces a PINN framework that can effectively make use of a small amount of observational speed data to obtain high-quality TSEs for a traffic network. Both model-driven and data-driven components are incorporated into PINNs to combine the advantages of both approaches and to overcome their disadvantages. Simulation data of simple traffic networks are used for studying the highway network TSE. This paper demonstrates how to solve the popular LWR physical traffic flow model with a PINN for a traffic network. Experimental results confirm that the proposed approach is promising for estimating network traffic accurately.
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Tarkhov, Dmitriy, Tatiana Lazovskaya, and Galina Malykhina. "Constructing Physics-Informed Neural Networks with Architecture Based on Analytical Modification of Numerical Methods by Solving the Problem of Modelling Processes in a Chemical Reactor." Sensors 23, no. 2 (January 6, 2023): 663. http://dx.doi.org/10.3390/s23020663.
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A novel type of neural network with an architecture based on physics is proposed. The network structure builds on a body of analytical modifications of classical numerical methods. A feature of the constructed neural networks is defining parameters of the governing equations as trainable parameters. Constructing the network is carried out in three stages. In the first step, a neural network solution to an equation corresponding to a numerical scheme is constructed. It allows for forming an initial low-fidelity neural network solution to the original problem. At the second stage, the network with physics-based architecture (PBA) is further trained to solve the differential equation by minimising the loss function, as is typical in works devoted to physics-informed neural networks (PINNs). In the third stage, the physics-informed neural network with architecture based on physics (PBA-PINN) is trained on high-fidelity sensor data, parameters are identified, or another task of interest is solved. This approach makes it possible to solve insufficiently studied PINN problems: selecting neural network architecture and successfully initialising network weights corresponding to the problem being solved that ensure rapid convergence to the loss function minimum. It is advisable to use the devised PBA-PINNs in the problems of surrogate modelling and modelling real objects with multi-fidelity data. The effectiveness of the approach proposed is demonstrated using the problem of modelling processes in a chemical reactor. Experiments show that subsequent retraining of the initial low-fidelity PBA model based on a few high-accuracy data leads to the achievement of relatively high accuracy.
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Xu, Peng-Fei, Chen-Bo Han, Hong-Xia Cheng, Chen Cheng, and Tong Ge. "A Physics-Informed Neural Network for the Prediction of Unmanned Surface Vehicle Dynamics." Journal of Marine Science and Engineering 10, no. 2 (January 24, 2022): 148. http://dx.doi.org/10.3390/jmse10020148.
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A three-degrees-of-freedom model, including surge, sway and yaw motion, with differential thrusters is proposed to describe unmanned surface vehicle (USV) dynamics in this study. The experiment is carried out in the Qing Huai River and the data obtained from different zigzag trajectories are filtered by a Gaussian filtering method. A physics-informed neural network (PINN) is proposed to identify the dynamic models of the USV. PINNs combine the advantages of data-driven machine learning and physical models. They can also embed the speed and steering models into the loss function, which can significantly retain all types of information. Compared with traditional neural networks, the results show that the PINN has better generalization ability in predicting the surge and sway velocities and rotation speed with only limited training data.
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Lee, Jonghwan. "Physics-Informed Neural Network for High Frequency Noise Performance in Quasi-Ballistic MOSFETs." Electronics 10, no. 18 (September 10, 2021): 2219. http://dx.doi.org/10.3390/electronics10182219.
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A physics-informed neural network (PINN) model is presented to predict the nonlinear characteristics of high frequency (HF) noise performance in quasi-ballistic MOSFETs. The PINN model is formulated by combining the radial basis function-artificial neural networks (RBF-ANNs) with an improved noise equivalent circuit model, including all the noise sources. The RBF-ANNs are utilized to model the thermal channel noise, induced gate noise, correlation noise, as well as the shot noise, due to the gate and source-drain tunneling current through the potential barriers. By training a spatial distribution of the thermal channel noise and a Fano factor of the shot noise, underlying physical theories are naturally embedded into the PINN model as prior information. The PINN model shows good capability of predicting the noise performance at high frequencies.
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Kim, Jungeun, Kookjin Lee, Dongeun Lee, Sheo Yon Jhin, and Noseong Park. "DPM: A Novel Training Method for Physics-Informed Neural Networks in Extrapolation." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 9 (May 18, 2021): 8146–54. http://dx.doi.org/10.1609/aaai.v35i9.16992.
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We present a method for learning dynamics of complex physical processes described by time-dependent nonlinear partial differential equations (PDEs). Our particular interest lies in extrapolating solutions in time beyond the range of temporal domain used in training. Our choice for a baseline method is physics-informed neural network (PINN) because the method parameterizes not only the solutions, but also the equations that describe the dynamics of physical processes. We demonstrate that PINN performs poorly on extrapolation tasks in many benchmark problems. To address this, we propose a novel method for better training PINN and demonstrate that our newly enhanced PINNs can accurately extrapolate solutions in time. Our method shows up to 72% smaller errors than state-of-the-art methods in terms of the standard L2-norm metric.
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Huang, Yi, Zhiyu Zhang, and Xing Zhang. "A Direct-Forcing Immersed Boundary Method for Incompressible Flows Based on Physics-Informed Neural Network." Fluids 7, no. 2 (January 25, 2022): 56. http://dx.doi.org/10.3390/fluids7020056.
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The application of physics-informed neural networks (PINNs) to computational fluid dynamics simulations has recently attracted tremendous attention. In the simulations of PINNs, the collocation points are required to conform to the fluid–solid interface on which no-slip boundary condition is enforced. Here, a novel PINN that incorporates the direct-forcing immersed boundary (IB) method is developed. In the proposed IB-PINN, the boundary conforming requirement in arranging the collocation points is eliminated. Instead, velocity penalties at some marker points are added to the loss function to enforce no-slip condition at the fluid–solid interface. In addition, force penalties at some collocation points are also added to the loss function to ensure compact distribution of the volume force. The effectiveness of IB-PINN in solving incompressible Navier–Stokes equations is demonstrated through the simulation of laminar flow past a circular cylinder that is placed in a channel. The solution obtained using the IB-PINN is compared with two reference solutions obtained using a conventional mesh-based IB method and an ordinary body-fitted grid method. The comparison indicates that the three solutions are in excellent agreement with each other. The influences of some parameters, such as weights for different loss components, numbers of collocation and marker points, hyperparameters in the neural network, etc., on the performance of IB-PINN are also studied. In addition, a transfer learning experiment is conducted on solving Navier–Stokes equations with different Reynolds numbers.
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Prantikos, Konstantinos, Lefteri H. Tsoukalas, and Alexander Heifetz. "Physics-Informed Neural Network Solution of Point Kinetics Equations for a Nuclear Reactor Digital Twin." Energies 15, no. 20 (October 18, 2022): 7697. http://dx.doi.org/10.3390/en15207697.
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A digital twin (DT) for nuclear reactor monitoring can be implemented using either a differential equations-based physics model or a data-driven machine learning model. The challenge of a physics-model-based DT consists of achieving sufficient model fidelity to represent a complex experimental system, whereas the challenge of a data-driven DT consists of extensive training requirements and a potential lack of predictive ability. We investigate the performance of a hybrid approach, which is based on physics-informed neural networks (PINNs) that encode fundamental physical laws into the loss function of the neural network. We develop a PINN model to solve the point kinetic equations (PKEs), which are time-dependent, stiff, nonlinear, ordinary differential equations that constitute a nuclear reactor reduced-order model under the approximation of ignoring spatial dependence of the neutron flux. The PINN model solution of PKEs is developed to monitor the start-up transient of Purdue University Reactor Number One (PUR-1) using experimental parameters for the reactivity feedback schedule and the neutron source. The results demonstrate strong agreement between the PINN solution and finite difference numerical solution of PKEs. We investigate PINNs performance in both data interpolation and extrapolation. For the test cases considered, the extrapolation errors are comparable to those of interpolation predictions. Extrapolation accuracy decreases with increasing time interval.
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Hassanaly, Malik, Peter J. Weddle, Kandler Smith, Subhayan De, Alireza Doostan, and Ryan King. "Physics-Informed Neural Network Modeling of Li-Ion Batteries." ECS Meeting Abstracts MA2022-02, no. 3 (October 9, 2022): 174. http://dx.doi.org/10.1149/ma2022-023174mtgabs.
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Li-ion batteries (LIB) are a promising solution to enable the storage of intermittent energy sources due to their high energy density. However, LIBs are known to significantly degrade after about 1000 charge-discharge cycles. LIBs degrade following different degradation modes and at a rate that depends on the operating conditions (e.g., external temperature, load). To plan the installation of batteries, appropriate understanding and prediction capabilities of their lifecycle is needed. In particular, the LIB degradation model needs to be transferable to variable operating conditions throughout the LIB lifetime. To this end, degradation models of individual LIB battery properties are sought to allow for sufficient granularity in the degradation model. High-fidelity numerical models of LIBs such as the pseudo-two-dimensional (P2D) model have been shown to accurately represent the charge-discharge-cycle of an LIB if the physical parameters used in the model are accurately estimated. Given observations of battery charge-discharged cycles, the objective is to use the P2D model to infer the values of all the battery properties, throughout the battery life. To prevent overfitting and account for the sparse data availability, the overarching objective is to enable Bayesian calibration to solve the inverse problem. Given the number of physical parameters, and the number of cycles to simulate, adjusting parameters directly via P2D forward runs is computationally intractable. This work describes the development of a surrogate model that would replace numerical integration of the P2D equations to significantly reduce the cost of the forward runs. To capture parameter dependencies, a physics-informed neural network (PINN) is developed as a surrogate substitute for the P2D model. The inverse modeling approach is illustrated in the Figure (top). The PINN is advantageous as it needs little to no observational data, which avoids offsetting the reduced inference computational cost with an increased training data generation burden. However, PINNs are notoriously difficult to train in stiff dynamical systems such as the P2D equations. Here, we discuss the specific training procedure that is adopted to efficiently cover parameter space, handle model stiffness, enforce initial, boundary conditions, and treat variables of different magnitudes. Furthermore, a verification procedure akin to ones used in computational fluid dynamics is implemented to ensure that the right governing equations are implemented. An emphasis is placed on verifying the governing equation even in presence of numerical errors. The training procedure and loss convergence are described to highlight training instabilities encountered. In addition, the training cost is evaluated and put in perspective of the forward integration of the P2D equations. Through ablation studies, we discuss what model components are the most critical to appropriately capture P2D solutions. The trained PINN is validated against numerical solutions of the P2D model (sample results are shown in Figure, bottom). In particular, it is assessed whether the PINN can replicate numerical solutions for parameter values not represented in the training data which is key in ensuring that the surrogate can be used for parameter calibration. Figure 1
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Xiao, Chaohao, Xiaoqian Zhu, Fukang Yin, and Xiaoqun Cao. "Physics-informed neural network for solving coupled Korteweg-de Vries equations." Journal of Physics: Conference Series 2031, no. 1 (September 1, 2021): 012056. http://dx.doi.org/10.1088/1742-6596/2031/1/012056.
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Abstract The studies of coupled partial differential equations are focus of engineering and applied mathematics. Although traditional numerical methods have been widely used, researchers are still looking for new methods to solve coupled partial differential equations. In this paper, physical information neural network (PINN) is introduced to solve one-dimensional coupled Korteweg-de Vries (cKdV) equations. Compared with the traditional neural network, the innovation of PINN is to embed the physical constraints of the equations into the network loss function. Moreover, within the acceptable relative error range, the solution can take a longer single time step than the presently available. The results revealed that PINN can solve the cKdV equations with reasonable errors only by training a small amount of data.
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Molnar, Joseph P., and Samuel J. Grauer. "Flow field tomography with uncertainty quantification using a Bayesian physics-informed neural network." Measurement Science and Technology 33, no. 6 (March 18, 2022): 065305. http://dx.doi.org/10.1088/1361-6501/ac5437.
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Abstract We report a new approach to flow field tomography that uses the Navier–Stokes and advection–diffusion equations to regularize reconstructions. Tomography is increasingly employed to infer 2D or 3D fluid flow and combustion structures from a series of line-of-sight (LoS) integrated measurements using a wide array of imaging modalities. The high-dimensional flow field is reconstructed from low-dimensional measurements by inverting a projection model that comprises path integrals along each LoS through the region of interest. Regularization techniques are needed to obtain realistic estimates, but current methods rely on truncating an iterative solution or adding a penalty term that is incompatible with the flow physics to varying degrees. Physics-informed neural networks (PINNs) are new tools for inverse analysis that enable regularization of the flow field estimates using the governing physics. We demonstrate how a PINN can be leveraged to reconstruct a 2D flow field from sparse LoS-integrated measurements with no knowledge of the boundary conditions by incorporating the measurement model into the loss function used to train the network. The resulting reconstructions are remarkably superior to reconstructions produced by state-of-the-art algorithms, even when a PINN is used for post-processing. However, as with conventional iterative algorithms, our approach is susceptible to semi-convergence when there is a high level of noise. We address this issue through the use of a Bayesian PINN, which facilitates comprehensive uncertainty quantification of the reconstructions, enables the use of a more intuitive loss function, and reveals the source of semi-convergence.
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Lawal, Zaharaddeen Karami, Hayati Yassin, Daphne Teck Ching Lai, and Azam Che Idris. "Physics-Informed Neural Network (PINN) Evolution and Beyond: A Systematic Literature Review and Bibliometric Analysis." Big Data and Cognitive Computing 6, no. 4 (November 21, 2022): 140. http://dx.doi.org/10.3390/bdcc6040140.
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This research aims to study and assess state-of-the-art physics-informed neural networks (PINNs) from different researchers’ perspectives. The PRISMA framework was used for a systematic literature review, and 120 research articles from the computational sciences and engineering domain were specifically classified through a well-defined keyword search in Scopus and Web of Science databases. Through bibliometric analyses, we have identified journal sources with the most publications, authors with high citations, and countries with many publications on PINNs. Some newly improved techniques developed to enhance PINN performance and reduce high training costs and slowness, among other limitations, have been highlighted. Different approaches have been introduced to overcome the limitations of PINNs. In this review, we categorized the newly proposed PINN methods into Extended PINNs, Hybrid PINNs, and Minimized Loss techniques. Various potential future research directions are outlined based on the limitations of the proposed solutions.
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Sitte, Michael Philip, and Nguyen Anh Khoa Doan. "Velocity reconstruction in puffing pool fires with physics-informed neural networks." Physics of Fluids 34, no. 8 (August 2022): 087124. http://dx.doi.org/10.1063/5.0097496.
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Pool fires are canonical representations of many accidental fires which can exhibit an unstable unsteady behavior, known as puffing, which involves a strong coupling between the temperature and velocity fields. Despite their practical relevance to fire research, their experimental study can be limited due to the complexity of measuring relevant quantities in parallel. In this work, we analyze the use of a recent physics-informed machine learning approach, called hidden fluid mechanics (HFM), to reconstruct unmeasured quantities in a puffing pool fire from measured quantities. The HFM framework relies on a physics-informed neural network (PINN) for this task. A PINN is a neural network that uses both the available data, here the measured quantities, and the physical equations governing the system, here the reacting Navier–Stokes equations, to infer the full fluid dynamic state. This framework is used to infer the velocity field in a puffing pool fire from measurements of density, pressure, and temperature. In this work, the dataset used for this test was generated from numerical simulations. It is shown that the PINN is able to reconstruct the velocity field accurately and to infer most features of the velocity field. In addition, it is shown that the reconstruction accuracy is robust with respect to noisy data, and a reduction in the number of measured quantities is explored and discussed. This study opens up the possibility of using PINNs for the reconstruction of unmeasured quantities from measured ones, providing the potential groundwork for their use in experiments for fire research.
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Vashisth, Divakar, and Tapan Mukerji. "Direct estimation of porosity from seismic data using rock- and wave-physics-informed neural networks." Leading Edge 41, no. 12 (December 2022): 840–46. http://dx.doi.org/10.1190/tle41120840.1.
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Petrophysical inversion is an important aspect of reservoir modeling. However, due to the lack of a unique and straightforward relationship between seismic traces and rock properties, predicting petrophysical properties directly from seismic data is a complex task. Many studies have attempted to identify the direct end-to-end link using supervised machine learning techniques, but they face challenges such as lack of a large petrophysical training data set or estimates that may not conform with physics or depositional history of the rocks. We present a rock- and wave-physics-informed neural network (RW-PINN) model that can estimate porosity directly from seismic image traces with no wells or with a limited number of wells and with predictions that are consistent with rock physics and geologic knowledge of deposition. The RW-PINN takes advantage of auto-differentiation to compute the gradients across the rock- and wave-physics models. As an example, we use the uncemented-sand rock-physics model and normal-incidence wave physics to guide the learning of the RW-PINN to eventually get good estimates of porosities from normal-incidence seismic traces and limited well data. Training the RW-PINN with few wells (weakly supervised scenario) helps in tackling the problem of nonuniqueness as different porosity logs can give similar seismic traces. We use a weighted normalized root mean square error loss function to train the weakly supervised network and demonstrate the impact of different weights on porosity predictions. The RW-PINN's estimated porosities and seismic traces are compared to predictions from a completely supervised model, which gives slightly better porosity estimates but matches the seismic traces poorly and requires a large amount of labeled training data. We demonstrate the complete workflow for executing petrophysical inversion of seismic data using self-supervised or weakly supervised RW-PINNs.
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Ma, Yaoyao, Xiaoyu Xu, Shuai Yan, and Zhuoxiang Ren. "A Preliminary Study on the Resolution of Electro-Thermal Multi-Physics Coupling Problem Using Physics-Informed Neural Network (PINN)." Algorithms 15, no. 2 (February 1, 2022): 53. http://dx.doi.org/10.3390/a15020053.
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The problem of electro-thermal coupling is widely present in the integrated circuit (IC). The accuracy and efficiency of traditional solution methods, such as the finite element method (FEM), are tightly related to the quality and density of mesh construction. Recently, PINN (physics-informed neural network) was proposed as a method for solving differential equations. This method is mesh free and generalizes the process of solving PDEs regardless of the equations’ structure. Therefore, an experiment is conducted to explore the feasibility of PINN in solving electro-thermal coupling problems, which include the electrokinetic field and steady-state thermal field. We utilize two neural networks in the form of sequential training to approximate the electric field and the thermal field, respectively. The experimental results show that PINN provides good accuracy in solving electro-thermal coupling problems.
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Zhang, Wenjuan, and Mohammed Al Kobaisi. "On the Monotonicity and Positivity of Physics-Informed Neural Networks for Highly Anisotropic Diffusion Equations." Energies 15, no. 18 (September 18, 2022): 6823. http://dx.doi.org/10.3390/en15186823.
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Physics-informed neural network (PINN) models are developed in this work for solving highly anisotropic diffusion equations. Compared to traditional numerical discretization schemes such as the finite volume method and finite element method, PINN models are meshless and, therefore, have the advantage of imposing no constraint on the orientations of the diffusion tensors or the grid orthogonality conditions. To impose solution positivity, we tested PINN models with positivity-preserving activation functions for the last layer and found that the accuracy of the corresponding PINN solutions is quite poor compared to the vanilla PINN model. Therefore, to improve the monotonicity properties of PINN models, we propose a new loss function that incorporates additional terms which penalize negative solutions, in addition to the usual partial differential equation (PDE) residuals and boundary mismatch. Various numerical experiments show that the PINN models can accurately capture the tensorial effect of the diffusion tensor, and the PINN model utilizing the new loss function can reduce the degree of violations of monotonicity and improve the accuracy of solutions compared to the vanilla PINN model, while the computational expenses remain comparable. Moreover, we further developed PINN models that are composed of multiple neural networks to deal with discontinuous diffusion tensors. Pressure and flux continuity conditions on the discontinuity line are used to stitch the multiple networks into a single model by adding another loss term in the loss function. The resulting PINN models were shown to successfully solve the diffusion equation when the principal directions of the diffusion tensor change abruptly across the discontinuity line. The results demonstrate that the PINN models represent an attractive option for solving difficult anisotropic diffusion problems compared to traditional numerical discretization methods.
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Rafiq, Muhammad, Ghazala Rafiq, and Gyu Sang Choi. "DSFA-PINN: Deep Spectral Feature Aggregation Physics Informed Neural Network." IEEE Access 10 (2022): 22247–59. http://dx.doi.org/10.1109/access.2022.3153056.
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Ji, Weiqi, Weilun Qiu, Zhiyu Shi, Shaowu Pan, and Sili Deng. "Stiff-PINN: Physics-Informed Neural Network for Stiff Chemical Kinetics." Journal of Physical Chemistry A 125, no. 36 (August 31, 2021): 8098–106. http://dx.doi.org/10.1021/acs.jpca.1c05102.
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Garcia Inda, Adan Jafet, Shao Ying Huang, Nevrez İmamoğlu, Ruian Qin, Tianyi Yang, Tiao Chen, Zilong Yuan, and Wenwei Yu. "Physics Informed Neural Networks (PINN) for Low Snr Magnetic Resonance Electrical Properties Tomography (MREPT)." Diagnostics 12, no. 11 (October 29, 2022): 2627. http://dx.doi.org/10.3390/diagnostics12112627.
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Electrical properties (EPs) of tissues facilitate early detection of cancerous tissues. Magnetic resonance electrical properties tomography (MREPT) is a technique to non-invasively probe the EPs of tissues from MRI measurements. Most MREPT methods rely on numerical differentiation (ND) to solve partial differential Equations (PDEs) to reconstruct the EPs. However, they are not practical for clinical data because ND is noise sensitive and the MRI measurements for MREPT are noisy in nature. Recently, Physics informed neural networks (PINNs) have been introduced to solve PDEs by substituting ND with automatic differentiation (AD). To the best of our knowledge, it has not been applied to MREPT due to the challenges in using PINN on MREPT as (i) a PINN requires part of ground-truth EPs as collocation points to optimize the network’s AD, (ii) the noisy input data disrupts the optimization of PINNs despite the noise-filtering nature of NNs and additional denoising processes. In this work, we propose a PINN-MREPT model based on a canonical analytic MREPT model. A reference padding layer with known EPs was added to surround the region of interest for providing additive collocation points. Moreover, an optimizable diffusion coefficient was embedded in the analytic MREPT model used in the PINN-MREPT. The noise robustness of the proposed PINN-MREPT for single-sample reconstruction was tested by using numerical phantoms of human brain with extra tumor-like tissues at different noise levels. The results of numerical experiments show that PINN-MREPT outperforms two typical numerical MREPT methods in terms of reconstruction accuracy, sensitivity to the extra tissues, and the correlations of line profiles in the regions of interest. The advantage of the PINN-MREPT is shown by the results of an experiment on phantom measurement, too. Moreover, it is found that the diffusion term plays an important role to achieve a noise-robust PINN-MREPT. This is an important step moving forward to a clinical application of MREPT.
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Leung, Wing Tat, Guang Lin, and Zecheng Zhang. "NH-PINN: Neural homogenization-based physics-informed neural network for multiscale problems." Journal of Computational Physics 470 (December 2022): 111539. http://dx.doi.org/10.1016/j.jcp.2022.111539.
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Maddu, Suryanarayana, Dominik Sturm, Christian L. Müller, and Ivo F. Sbalzarini. "Inverse Dirichlet weighting enables reliable training of physics informed neural networks." Machine Learning: Science and Technology 3, no. 1 (February 15, 2022): 015026. http://dx.doi.org/10.1088/2632-2153/ac3712.
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Abstract We characterize and remedy a failure mode that may arise from multi-scale dynamics with scale imbalances during training of deep neural networks, such as physics informed neural networks (PINNs). PINNs are popular machine-learning templates that allow for seamless integration of physical equation models with data. Their training amounts to solving an optimization problem over a weighted sum of data-fidelity and equation-fidelity objectives. Conflicts between objectives can arise from scale imbalances, heteroscedasticity in the data, stiffness of the physical equation, or from catastrophic interference during sequential training. We explain the training pathology arising from this and propose a simple yet effective inverse Dirichlet weighting strategy to alleviate the issue. We compare with Sobolev training of neural networks, providing the baseline of analytically ε-optimal training. We demonstrate the effectiveness of inverse Dirichlet weighting in various applications, including a multi-scale model of active turbulence, where we show orders of magnitude improvement in accuracy and convergence over conventional PINN training. For inverse modeling using sequential training, we find that inverse Dirichlet weighting protects a PINN against catastrophic forgetting.
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Katsikis, Dimitrios, Aliki D. Muradova, and Georgios E. Stavroulakis. "A Gentle Introduction to Physics-Informed Neural Networks, with Applications in Static Rod and Beam Problems." Journal of Advances in Applied & Computational Mathematics 9 (May 31, 2022): 103–28. http://dx.doi.org/10.15377/2409-5761.2022.09.8.
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A modern approach to solving mathematical models involving differential equations, the so-called Physics-Informed Neural Network (PINN), is based on the techniques which include the use of artificial neural networks and the method of fitting the governing differential equations at collocation points. In this paper, training of the PINN with an application of optimization techniques is performed on simple one-dimensional mechanical problems of elasticity, namely rods and beams. Different boundary conditions are considered. Required computer algorithms are implemented using Python programming packages with the intention of creating neural networks. Numerical results are presented, and the efficiency of the proposed technique is investigated through numerical experiments with different numbers of epochs, batches, hidden layers, neurons, and collocation points. The paper provides useful skills for using a PINN for different problems of solid mechanics. The proposed methodology is a continuation of our intention of using PINNs for problems of the theory of elasticity. The objectives are to present simply the main steps of constructing PINN and an implementation of it. A detailed explanation of the Python programming code, based on the scientific software Tensorflow, built in the Keras library and optimizers, may help compose an effective code for complicated models in mechanics. PINNs are proposed in many recent publications to solve complicated direct and inverse problems. It seems to be a promising method that will play a central role in the development of computational mechanics in the near future. Nevertheless, the lack of educational material does not help new users to enter this scientific area. The present contribution describes the method for the solution of elementary rod and beam problems and gives computer codes that may help the reader to understand the method and to apply it to other problems.
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Muradova, Aliki D., and Georgios E. Stavroulakis. "PHYSICS-INFORMED NEURAL NETWORKS FOR ELASTIC PLATE PROBLEMS WITH BENDING AND WINKLER-TYPE CONTACT EFFECTS." Journal of the Serbian Society for Computational Mechanics 15, no. 2 (December 30, 2021): 46–55. http://dx.doi.org/10.24874/jsscm.2021.15.02.05.
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Kirchhoff plate bending and Winkler-type contact problems with different boundary conditions are solved with the use of physics-informed neural networks (PINN). The PINN is built on the base of mechanics laws and deep learning. The idea of the technique includes fitting the governing partial differential equations at collocation points and then training the neural network with the use of optimization techniques. Training of the neural network is performed by numerical optimization using Adam’s method and the L-BFGS (Limited- Broyden–Fletcher–Goldfarb–Shanno) algorithm. The error loss function and the computational error of the approximate solution (output of the neural network) of the bending problem and contact problem with Winkler type elastic foundation are shown on examples. The predictions of the NN are investigated for different values of the foundation’s constants. The effectiveness of the proposed framework is demonstrated through numerical experiments with different numbers of epochs, hidden layers, neurons and numbers of collocation points. The Tensorflow deep learning and scientific computing package of Python is used through a Jupyter Notebook.
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Voigt, Jorrit, and Michael Moeckel. "Modelling dynamic 3D heat transfer in laser material processing based on physics informed neural networks." EPJ Web of Conferences 266 (2022): 02010. http://dx.doi.org/10.1051/epjconf/202226602010.
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Machine learning algorithms make predictions by fitting highly parameterized nonlinear functions to massive amounts of data. Yet those models are not necessarily consistent with physical laws and offer limited interpretability. Extending machine learning models by introducing scientific knowledge in the optimization problem is known as physics-based and data-driven modelling. A promising development are physics informed neural networks (PINN) which ensure consistency to both physical laws and measured data. The aim of this research is to model the time-dependent temperature profile in bulk materials following the passage of a moving laser focus by a PINN. The results from the PINN agree essentially with finite element simulations, proving the suitability of the approach. New perspectives for applications in laser material processing arise when PINNs are integrated in monitoring systems or used for model predictive control.
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Almqvist, Andreas. "Fundamentals of Physics-Informed Neural Networks Applied to Solve the Reynolds Boundary Value Problem." Lubricants 9, no. 8 (August 19, 2021): 82. http://dx.doi.org/10.3390/lubricants9080082.
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This paper presents a complete derivation and design of a physics-informed neural network (PINN) applicable to solve initial and boundary value problems described by linear ordinary differential equations. The objective with this technical note is not to develop a numerical solution procedure which is more accurate and efficient than standard finite element- or finite difference-based methods, but to give a fully explicit mathematical description of a PINN and to present an application example in the context of hydrodynamic lubrication. It is, however, worth noticing that the PINN developed herein, contrary to FEM and FDM, is a meshless method and that training does not require big data which is typical in machine learning.
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Liu, Youqiong, Li Cai, Yaping Chen, and Bin Wang. "Physics-informed neural networks based on adaptive weighted loss functions for Hamilton-Jacobi equations." Mathematical Biosciences and Engineering 19, no. 12 (2022): 12866–96. http://dx.doi.org/10.3934/mbe.2022601.
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<abstract><p>Physics-informed neural networks (PINN) have lately become a research hotspot in the interdisciplinary field of machine learning and computational mathematics thanks to the flexibility in tackling forward and inverse problems. In this work, we explore the generality of the PINN training algorithm for solving Hamilton-Jacobi equations, and propose physics-informed neural networks based on adaptive weighted loss functions (AW-PINN) that is trained to solve unsupervised learning tasks with fewer training data while physical information constraints are imposed during the training process. To balance the contributions from different constrains automatically, the AW-PINN training algorithm adaptively update the weight coefficients of different loss terms by using the logarithmic mean to avoid additional hyperparameter. Moreover, the proposed AW-PINN algorithm imposes the periodicity requirement on the boundary condition and its gradient. The fully connected feedforward neural networks are considered and the optimizing procedure is taken as the Adam optimizer for some steps followed by the L-BFGS-B optimizer. The series of numerical experiments illustrate that the proposed algorithm effectively achieves noticeable improvements in predictive accuracy and the convergence rate of the total training error, and can approximate the solution even when the Hamiltonian is nonconvex. A comparison between the proposed algorithm and the original PINN algorithm for Hamilton-Jacobi equations indicates that the proposed AW-PINN algorithm can train the solutions more accurately with fewer iterations.</p></abstract>
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Jadhav, Vishal, Anirudh Deodhar, Ashit Gupta, and Venkataramana Runkana. "Physics Informed Neural Network for Health Monitoring of an Air Preheater." PHM Society European Conference 7, no. 1 (June 29, 2022): 219–30. http://dx.doi.org/10.36001/phme.2022.v7i1.3343.
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Air Preheater (APH) is a regenerative heat exchanger employed in thermal power plants to save fuel by improving their thermal efficiency. Monitoring the health of APH vis-a-vis its fouling is critical because fouling often results in forced outages of the power plant, incurring huge revenue losses. APH fouling is a complex thermo-chemical phenomenon governed by flue gas composition, operating temperatures, fuel type and ambient conditions. Absence of sensors within the APH make it difficult to estimate the level of fouling and its progression even for an experienced operator. Attempts to estimate APH fouling in real-time via modeling are scarce. Here we present a physics-informed neural network (PINN) that tracks the health of an APH by real-time estimation of fouling conditions within the APH as a function of real-time sensor measurements. To account for multi-fluid operation in a multi-sector design of APH, the domain is decomposed into several sub-domains. PINN is applied to each sub-domain and the overall solution is ensured by applying continuity conditions at the sub-domain interfaces. The model predicts the interior temperatures and fouling zones within the APH using external sensor measurements such as air temperature and gas composition. The model predictions are consistent with physics and yet computationally efficient in run-time. The model does not need sensor data but can be improved further by accommodating available sensor data. The real-time predictions by the model improve operator’s visibility in fouling. The predictions can be used further for estimating the remaining useful cycle life of the APH, thereby avoiding forced outages. The model can easily be integrated with the digital twin of an APH for its predictive maintenance.
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Lu, Yue, and Gang Mei. "A Deep Learning Approach for Predicting Two-Dimensional Soil Consolidation Using Physics-Informed Neural Networks (PINN)." Mathematics 10, no. 16 (August 16, 2022): 2949. http://dx.doi.org/10.3390/math10162949.
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The unidirectional consolidation theory of soils is widely used in certain conditions and approximate calculations. The multidirectional theory of soil consolidation is more reasonable than the unidirectional theory in practical applications but is much more complicated in terms of index determination and solution. To address the above problem, in this paper, we propose a deep learning method using physics-informed neural networks (PINN) to predict the excess pore water pressure of two-dimensional soil consolidation. In the proposed method, (1) a fully connected neural network is constructed; (2) the computational domain, partial differential equation (PDE), and constraints are defined to generate data for model training; and (3) the PDE of two-dimensional soil consolidation and the model of the neural network are connected to reduce the loss of the model. The effectiveness of the proposed method is verified by comparison with the numerical solution of PDE for two-dimensional consolidation. Moreover, the FEM and the proposed PINN-based method are applied to predict the consolidation of foundation soils in a real case of Sichuan Railway in China, and the results are quite consistent. The proposed deep learning approach can be used to investigate large and complex multidirectional soil consolidation.
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He, GaoYuan, YongXiang Zhao, and ChuLiang Yan. "MFLP-PINN: A physics-informed neural network for multiaxial fatigue life prediction." European Journal of Mechanics - A/Solids 98 (March 2023): 104889. http://dx.doi.org/10.1016/j.euromechsol.2022.104889.
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Borrel-Jensen, Nikolas, Allan P. Engsig-Karup, and Cheol-Ho Jeong. "Machine learning-based room acoustics using flow maps and physics-informed neural networks." Journal of the Acoustical Society of America 151, no. 4 (April 2022): A232—A233. http://dx.doi.org/10.1121/10.0011164.
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The development of efficient and accurate numerical methods for simulating realistic sound in virtual environments—such as computer games and VR/AR—has been an active research area for the last decades. However, handling dynamic scenes with many moving sources is still challenging due to intractable storage requirements and extensive computation time. A recently proposed physics-informed neural network (PINN) approach learns a compact and efficient surrogate model with parameterized moving sources and impedance boundaries on a grid-less 1-D domain. Contrary to traditional “black-box” deep learning, PINNs minimize the residuals of the governing equations through the loss function. We will extend this work using flow maps implemented as Residual Networks (ResNets). ResNets are interpreted from a dynamic systems perspective as ordinary differential equations that can be used as building blocks to approximate the governing equations in time. We will examine the pros and cons of ResNets in acoustics and compare them with state-of-the-art numerical methods and vanilla feed-forward neural networks in terms of accuracy and efficiency.
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Cheng, Chen, and Guang-Tao Zhang. "Deep Learning Method Based on Physics Informed Neural Network with Resnet Block for Solving Fluid Flow Problems." Water 13, no. 4 (February 5, 2021): 423. http://dx.doi.org/10.3390/w13040423.
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Solving fluid dynamics problems mainly rely on experimental methods and numerical simulation. However, in experimental methods it is difficult to simulate the physical problems in reality, and there is also a high-cost to the economy while numerical simulation methods are sensitive about meshing a complicated structure. It is also time-consuming due to the billion degrees of freedom in relevant spatial-temporal flow fields. Therefore, constructing a cost-effective model to settle fluid dynamics problems is of significant meaning. Deep learning (DL) has great abilities to handle strong nonlinearity and high dimensionality that attracts much attention for solving fluid problems. Unfortunately, the proposed surrogate models in DL are almost black-box models and lack interpretation. In this paper, the Physical Informed Neural Network (PINN) combined with Resnet blocks is proposed to solve fluid flows depending on the partial differential equations (i.e., Navier-Stokes equation) which are embedded into the loss function of the deep neural network to drive the model. In addition, the initial conditions and boundary conditions are also considered in the loss function. To validate the performance of the PINN with Resnet blocks, Burger’s equation with a discontinuous solution and Navier-Stokes (N-S) equation with continuous solution are selected. The results show that the PINN with Resnet blocks (Res-PINN) has stronger predictive ability than traditional deep learning methods. In addition, the Res-PINN can predict the whole velocity fields and pressure fields in spatial-temporal fluid flows, the magnitude of the mean square error of the fluid flow reaches to 10−5. The inverse problems of the fluid flows are also well conducted. The errors of the inverse parameters are 0.98% and 3.1% in clean data and 0.99% and 3.1% in noisy data.
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De Florio, Mario, Enrico Schiassi, and Roberto Furfaro. "Physics-informed neural networks and functional interpolation for stiff chemical kinetics." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 6 (June 2022): 063107. http://dx.doi.org/10.1063/5.0086649.
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This work presents a recently developed approach based on physics-informed neural networks (PINNs) for the solution of initial value problems (IVPs), focusing on stiff chemical kinetic problems with governing equations of stiff ordinary differential equations (ODEs). The framework developed by the authors combines PINNs with the theory of functional connections and extreme learning machines in the so-called extreme theory of functional connections (X-TFC). While regular PINN methodologies appear to fail in solving stiff systems of ODEs easily, we show how our method, with a single-layer neural network (NN) is efficient and robust to solve such challenging problems without using artifacts to reduce the stiffness of problems. The accuracy of X-TFC is tested against several state-of-the-art methods, showing its performance both in terms of computational time and accuracy. A rigorous upper bound on the generalization error of X-TFC frameworks in learning the solutions of IVPs for ODEs is provided here for the first time. A significant advantage of this framework is its flexibility to adapt to various problems with minimal changes in coding. Also, once the NN is trained, it gives us an analytical representation of the solution at any desired instant in time outside the initial discretization. Learning stiff ODEs opens up possibilities of using X-TFC in applications with large time ranges, such as chemical dynamics in energy conversion, nuclear dynamics systems, life sciences, and environmental engineering.
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Pioch, Fabian, Jan Hauke Harmening, Andreas Maximilian Müller, Franz-Josef Peitzmann, Dieter Schramm, and Ould el Moctar. "Turbulence Modeling for Physics-Informed Neural Networks: Comparison of Different RANS Models for the Backward-Facing Step Flow." Fluids 8, no. 2 (January 26, 2023): 43. http://dx.doi.org/10.3390/fluids8020043.
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Physics-informed neural networks (PINN) can be used to predict flow fields with a minimum of simulated or measured training data. As most technical flows are turbulent, PINNs based on the Reynolds-averaged Navier–Stokes (RANS) equations incorporating a turbulence model are needed. Several studies demonstrated the capability of PINNs to solve the Naver–Stokes equations for laminar flows. However, little work has been published concerning the application of PINNs to solve the RANS equations for turbulent flows. This study applied a RANS-based PINN approach to a backward-facing step flow at a Reynolds number of 5100. The standard k-ω model, the mixing length model, an equation-free νt and an equation-free pseudo-Reynolds stress model were applied. The results compared favorably to DNS data when provided with three vertical lines of labeled training data. For five lines of training data, all models predicted the separated shear layer and the associated vortex more accurately.
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Tang, Hesheng, Yangyang Liao, Hu Yang, and Liyu Xie. "A transfer learning-physics informed neural network (TL-PINN) for vortex-induced vibration." Ocean Engineering 266 (December 2022): 113101. http://dx.doi.org/10.1016/j.oceaneng.2022.113101.
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Praditia, Timothy, Thilo Walser, Sergey Oladyshkin, and Wolfgang Nowak. "Improving Thermochemical Energy Storage Dynamics Forecast with Physics-Inspired Neural Network Architecture." Energies 13, no. 15 (July 29, 2020): 3873. http://dx.doi.org/10.3390/en13153873.
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Thermochemical Energy Storage (TCES), specifically the calcium oxide (CaO)/calcium hydroxide (Ca(OH)2) system is a promising energy storage technology with relatively high energy density and low cost. However, the existing models available to predict the system’s internal states are computationally expensive. An accurate and real-time capable model is therefore still required to improve its operational control. In this work, we implement a Physics-Informed Neural Network (PINN) to predict the dynamics of the TCES internal state. Our proposed framework addresses three physical aspects to build the PINN: (1) we choose a Nonlinear Autoregressive Network with Exogeneous Inputs (NARX) with deeper recurrence to address the nonlinear latency; (2) we train the network in closed-loop to capture the long-term dynamics; and (3) we incorporate physical regularisation during its training, calculated based on discretized mole and energy balance equations. To train the network, we perform numerical simulations on an ensemble of system parameters to obtain synthetic data. Even though the suggested approach provides results with the error of 3.96×10−4 which is in the same range as the result without physical regularisation, it is superior compared to conventional Artificial Neural Network (ANN) strategies because it ensures physical plausibility of the predictions, even in a highly dynamic and nonlinear problem. Consequently, the suggested PINN can be further developed for more complicated analysis of the TCES system.
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Schiassi, Enrico, Mario De Florio, Andrea D’Ambrosio, Daniele Mortari, and Roberto Furfaro. "Physics-Informed Neural Networks and Functional Interpolation for Data-Driven Parameters Discovery of Epidemiological Compartmental Models." Mathematics 9, no. 17 (August 27, 2021): 2069. http://dx.doi.org/10.3390/math9172069.
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In this work, we apply a novel and accurate Physics-Informed Neural Network Theory of Functional Connections (PINN-TFC) based framework, called Extreme Theory of Functional Connections (X-TFC), for data-physics-driven parameters’ discovery of problems modeled via Ordinary Differential Equations (ODEs). The proposed method merges the standard PINNs with a functional interpolation technique named Theory of Functional Connections (TFC). In particular, this work focuses on the capability of X-TFC in solving inverse problems to estimate the parameters governing the epidemiological compartmental models via a deterministic approach. The epidemiological compartmental models treated in this work are Susceptible-Infectious-Recovered (SIR), Susceptible-Exposed-Infectious-Recovered (SEIR), and Susceptible-Exposed-Infectious-Recovered-Susceptible (SEIRS). The results show the low computational times, the high accuracy, and effectiveness of the X-TFC method in performing data-driven parameters’ discovery systems modeled via parametric ODEs using unperturbed and perturbed data.
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Carpenter, Chris. "Physics-Informed Neural Networks Help Predict Fluid Flow in Porous Media." Journal of Petroleum Technology 74, no. 07 (July 1, 2022): 52–54. http://dx.doi.org/10.2118/0722-0052-jpt.
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This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 203033, “Prediction of Fluid Flow in Porous Media Using Physics-Informed Neural Networks,” by Muhammad M. Almajid, SPE, and Moataz O. Abu-Alsaud, SPE, Saudi Aramco. The paper has not been peer reviewed. The authors of the complete paper write that the realm of reservoir engineering is considered to belong to the small-data regime because of the complex physical systems involved and the inherent uncertainty of the problems. The objective of the paper is to present a physics-informed neural network (PINN) technique that is able to use information from the fluid-flow physics and observed data to model the Buckley-Leverett problem. Fractional-Flow Theory Through their study of fluid displacement in sands, Buckley and Leverett introduced the fractional-flow theory. The theory estimates the rate at which one fluid displaces another and, consequently, the change in fluid saturations. The theory has been applied to many fluid-flow processes in porous media such as waterflooding, carbonated waterflooding, alcohol flooding, miscible flooding, steam flooding, foam flooding, low-salinity waterflooding, and carbon sequestration. The authors use the fractional-flow theory to simulate the displacement of water-filled porous media by gas, a process detailed in the complete paper. Once the Buckley-Leverett solution is obtained, the saturation profile of gas or water can be plotted at different times. It is noteworthy that a gas viscosity of 0.2 cp in this case is used so that the shock is visually apparent in the Buckley-Leverett solution. Additionally, having this large of a gas viscosity is justified. For instance, foamed gas can develop apparent viscosities orders of magnitude larger than unfoamed gas. Fig. 1 plots the gas-saturation profile along the dimensionless distance. Obtaining the corresponding water-saturation profiles is trivial. The authors compare the analytical solution and the PINN prediction with respect to water saturation.
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Guo, Yanan, Xiaoqun Cao, Bainian Liu, and Mei Gao. "Solving Partial Differential Equations Using Deep Learning and Physical Constraints." Applied Sciences 10, no. 17 (August 26, 2020): 5917. http://dx.doi.org/10.3390/app10175917.
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The various studies of partial differential equations (PDEs) are hot topics of mathematical research. Among them, solving PDEs is a very important and difficult task. Since many partial differential equations do not have analytical solutions, numerical methods are widely used to solve PDEs. Although numerical methods have been widely used with good performance, researchers are still searching for new methods for solving partial differential equations. In recent years, deep learning has achieved great success in many fields, such as image classification and natural language processing. Studies have shown that deep neural networks have powerful function-fitting capabilities and have great potential in the study of partial differential equations. In this paper, we introduce an improved Physics Informed Neural Network (PINN) for solving partial differential equations. PINN takes the physical information that is contained in partial differential equations as a regularization term, which improves the performance of neural networks. In this study, we use the method to study the wave equation, the KdV–Burgers equation, and the KdV equation. The experimental results show that PINN is effective in solving partial differential equations and deserves further research.
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Zhang, Yabin, Haiyi Liu, Lei Wang, and Wenrong Sun. "The line rogue wave solutions of the nonlocal Davey–Stewartson I equation with PT symmetry based on the improved physics-informed neural network." Chaos: An Interdisciplinary Journal of Nonlinear Science 33, no. 1 (January 2023): 013118. http://dx.doi.org/10.1063/5.0102741.
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In the paper, we employ an improved physics-informed neural network (PINN) algorithm to investigate the data-driven nonlinear wave solutions to the nonlocal Davey–Stewartson (DS) I equation with parity-time ( PT) symmetry, including the line breather, kink-shaped and W-shaped line rogue wave solutions. Both the PT symmetry and model are introduced into the loss function to strengthen the physical constraint. In addition, since the nonlocal DS I equation is a high-dimensional coupled system, this leads to an increase in the number of output results. The PT symmetry also needs to be learned that is not given in advance, which increases challenges in computing for multi-output neural networks. To address these problems, our objective is to assign various levels of weight to different items in the loss function. The experimental results show that the improved algorithm has better prediction accuracy to a certain extent compared with the original PINN algorithm. This approach is feasible to investigate complex nonlinear waves in a high-dimensional model with PT symmetry.
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Santana, Vinicius V., Marlon S. Gama, Jose M. Loureiro, Alírio E. Rodrigues, Ana M. Ribeiro, Frederico W. Tavares, Amaro G. Barreto, and Idelfonso B. R. Nogueira. "A First Approach towards Adsorption-Oriented Physics-Informed Neural Networks: Monoclonal Antibody Adsorption Performance on an Ion-Exchange Column as a Case Study." ChemEngineering 6, no. 2 (March 1, 2022): 21. http://dx.doi.org/10.3390/chemengineering6020021.
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Adsorption systems are characterized by challenging behavior to simulate any numerical method. A novel field of study emerged within the numerical method in the last two years: the physics-informed neural network (PINNs), the application of artificial intelligence to solve partial differential equations. This is a complete new standpoint for solving engineering first-principle models, which up to that date was not explored in the field of adsorption systems. Therefore, this work proposed the evaluation of PINN to address the numerical solutions of a fixed-bed column where a monoclonal antibody is purified. The PINNs solution is compared with a traditional numerical method. The results show the accuracy of the proposed PINNs when compared with the numerical method. This points towards the potential of this technique to address complex numerical problems found in chemical engineering.
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Chiu, Pao-Hsiung, Jian Cheng Wong, Chinchun Ooi, My Ha Dao, and Yew-Soon Ong. "CAN-PINN: A fast physics-informed neural network based on coupled-automatic–numerical differentiation method." Computer Methods in Applied Mechanics and Engineering 395 (May 2022): 114909. http://dx.doi.org/10.1016/j.cma.2022.114909.
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Lakshminarayana, Subhash, Saurav Sthapit, and Carsten Maple. "Application of Physics-Informed Machine Learning Techniques for Power Grid Parameter Estimation." Sustainability 14, no. 4 (February 11, 2022): 2051. http://dx.doi.org/10.3390/su14042051.
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Power grid parameter estimation involves the estimation of unknown parameters, such as the inertia and damping coefficients, from the observed dynamics. In this work, we present physics-informed machine learning algorithms for the power system parameter estimation problem. First, we propose a novel algorithm to solve the parameter estimation based on the Sparse Identification of Nonlinear Dynamics (SINDy) approach, which uses sparse regression to infer the parameters that best describe the observed data. We then compare its performance against another benchmark algorithm, namely, the physics-informed neural networks (PINN) approach applied to parameter estimation. We perform extensive simulations on IEEE bus systems to examine the performance of the aforementioned algorithms. Our results show that the SINDy algorithm outperforms the PINN algorithm in estimating the power grid parameters over a wide range of system parameters (including high and low inertia systems) and power grid architectures. Particularly, in case of the slow dynamics system, the proposed SINDy algorithms outperforms the PINN algorithm, which struggles to accurately determine the parameters. Moreover, it is extremely efficient computationally and so takes significantly less time than the PINN algorithm, thus making it suitable for real-time parameter estimation. Furthermore, we present an extension of the SINDy algorithm to a scenario where the operator does not have the exact knowledge of the underlying system model. We also present a decentralised implementation of the SINDy algorithm which only requires limited information exchange between the neighbouring nodes of a power grid.
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Zhai, Hanfeng, Quan Zhou, and Guohui Hu. "Predicting micro-bubble dynamics with semi-physics-informed deep learning." AIP Advances 12, no. 3 (March 1, 2022): 035153. http://dx.doi.org/10.1063/5.0079602.
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Utilizing physical information to improve the performance of the conventional neural networks is becoming a promising research direction in scientific computing recently. For multiphase flows, it would require significant computational resources for neural network training due to the large gradients near the interface between the two fluids. Based on the idea of the physics-informed neural networks (PINNs), a modified deep learning framework BubbleNet is proposed to overcome this difficulty in the present study. The deep neural network (DNN) with separate sub-nets is adopted to predict physics fields, with the semi-physics-informed part encoding the continuity equation and the pressure Poisson equation [Formula: see text] for supervision and the time discretized normalizer to normalize field data per time step before training. Two bubbly flows, i.e., single bubble flow and multiple bubble flow in a microchannel, are considered to test the algorithm. The conventional computational fluid dynamics software is applied to obtain the training dataset. The traditional DNN and the BubbleNet(s) are utilized to train the neural network and predict the flow fields for the two bubbly flows. Results indicate the BubbleNet frameworks are able to successfully predict the physics fields, and the inclusion of the continuity equation significantly improves the performance of deep NNs. The introduction of the Poisson equation also has slightly positive effects on the prediction results. The results suggest that constructing semi-PINNs by flexibly considering the physical information into neural networks will be helpful in the learning of complex flow problems.
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Bandai, Toshiyuki, and Teamrat A. Ghezzehei. "Forward and inverse modeling of water flow in unsaturated soils with discontinuous hydraulic conductivities using physics-informed neural networks with domain decomposition." Hydrology and Earth System Sciences 26, no. 16 (August 30, 2022): 4469–95. http://dx.doi.org/10.5194/hess-26-4469-2022.
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Abstract. Modeling water flow in unsaturated soils is vital for describing various hydrological and ecological phenomena. Soil water dynamics is described by well-established physical laws (Richardson–Richards equation – RRE). Solving the RRE is difficult due to the inherent nonlinearity of the processes, and various numerical methods have been proposed to solve the issue. However, applying the methods to practical situations is very challenging because they require well-defined initial and boundary conditions. Recent advances in machine learning and the growing availability of soil moisture data provide new opportunities for addressing the lingering challenges. Specifically, physics-informed machine learning allows both the known physics and data-driven modeling to be taken advantage of. Here, we present a physics-informed neural network (PINN) method that approximates the solution to the RRE using neural networks while concurrently matching available soil moisture data. Although the ability of PINNs to solve partial differential equations, including the RRE, has been demonstrated previously, its potential applications and limitations are not fully known. This study conducted a comprehensive analysis of PINNs and carefully tested the accuracy of the solutions by comparing them with analytical solutions and accepted traditional numerical solutions. We demonstrated that the solutions by PINNs with adaptive activation functions are comparable with those by traditional methods. Furthermore, while a single neural network (NN) is adequate to represent a homogeneous soil, we showed that soil moisture dynamics in layered soils with discontinuous hydraulic conductivities are correctly simulated by PINNs with domain decomposition (using separate NNs for each unique layer). A key advantage of PINNs is the absence of the strict requirement for precisely prescribed initial and boundary conditions. In addition, unlike traditional numerical methods, PINNs provide an inverse solution without repeatedly solving the forward problem. We demonstrated the application of these advantages by successfully simulating infiltration and redistribution constrained by sparse soil moisture measurements. As a free by-product, we gain knowledge of the water flux over the entire flow domain, including the unspecified upper and bottom boundary conditions. Nevertheless, there remain challenges that require further development. Chiefly, PINNs are sensitive to the initialization of NNs and are significantly slower than traditional numerical methods.
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Mehta, Pavan Pranjivan, Guofei Pang, Fangying Song, and George Em Karniadakis. "Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network." Fractional Calculus and Applied Analysis 22, no. 6 (December 18, 2019): 1675–88. http://dx.doi.org/10.1515/fca-2019-0086.
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Abstract The first fractional model for Reynolds stresses in wall-bounded turbulent flows was proposed by Wen Chen [2]. Here, we extend this formulation by allowing the fractional order α(y) of the model to vary with the distance from the wall (y) for turbulent Couette flow. Using available direct numerical simulation (DNS) data, we formulate an inverse problem for α(y) and design a physics-informed neural network (PINN) to obtain the fractional order. Surprisingly, we found a universal scaling law for α(y+), where y+ is the non-dimensional distance from the wall in wall units. Therefore, we obtain a variable-order fractional model that can be used at any Reynolds number to predict the mean velocity profile and Reynolds stresses with accuracy better than 1%.
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Zhai, Hanfeng, and Timothy Sands. "Controlling Chaos in Van Der Pol Dynamics Using Signal-Encoded Deep Learning." Mathematics 10, no. 3 (January 30, 2022): 453. http://dx.doi.org/10.3390/math10030453.
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Controlling nonlinear dynamics is a long-standing problem in engineering. Harnessing known physical information to accelerate or constrain stochastic learning pursues a new paradigm of scientific machine learning. By linearizing nonlinear systems, traditional control methods cannot learn nonlinear features from chaotic data for use in control. Here, we introduce Physics-Informed Deep Operator Control (PIDOC), and by encoding the control signal and initial position into the losses of a physics-informed neural network (PINN), the nonlinear system is forced to exhibit the desired trajectory given the control signal. PIDOC receives signals as physics commands and learns from the chaotic data output from the nonlinear van der Pol system, where the output of the PINN is the control. Applied to a benchmark problem, PIDOC successfully implements control with a higher stochasticity for higher-order terms. PIDOC has also been proven to be capable of converging to different desired trajectories based on case studies. Initial positions slightly affect the control accuracy at the beginning stage yet do not change the overall control quality. For highly nonlinear systems, PIDOC is not able to execute control with a high accuracy compared with the benchmark problem. The depth and width of the neural network structure do not greatly change the convergence of PIDOC based on case studies of van der Pol systems with low and high nonlinearities. Surprisingly, enlarging the control signal does not help to improve the control quality. The proposed framework can potentially be applied to many nonlinear systems for nonlinear controls.
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Oldenburg, Jan, Finja Borowski, Klaus-Peter Schmitz, and Michael Stiehm. "Computation of flow through TAVI device by means of physics informed neural networks." Current Directions in Biomedical Engineering 8, no. 2 (August 1, 2022): 741–44. http://dx.doi.org/10.1515/cdbme-2022-1189.
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Abstract Cardiovascular diseases are among the most common diseases with high mortality, including aortic valve stenosis and insufficiency. Minimally invasive implantation of transcatheter aortic valve prosthesis (TAVI) has become the standard procedure for patients with increased risk for open surgery. It is commonly accepted that the long-term outcome of aortic valve replacement depends on hemodynamic performance. This motivates the analysis of the velocity field in the vicinity of the TAVI. Computational fluid dynamics (CFD) methods have been established in the past, but show limitations in terms of computational effort when rapid design optimization or patient-specific decision making in real time is required. In this study we show the usage of PINNs for predicting fluid flow through a TAVI device. We also show a method of enforcing boundary conditions for this specific problem. Due to the physics involved in the training process, this principle does in theory not require additional training data. To validate the method, we performed CFD simulations that solved the Navier-Stokes equations be means of finite volume methods. Besides the good estimation of the main flow components, discrepancies between CFD and PINN results are present. Nevertheless, the flow structures have certain similarities in the coarse spatial localization of the vortex patterns occurring in flow around the TAVI device.
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Wandel, Nils, Michael Weinmann, Michael Neidlin, and Reinhard Klein. "Spline-PINN: Approaching PDEs without Data Using Fast, Physics-Informed Hermite-Spline CNNs." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 8 (June 28, 2022): 8529–38. http://dx.doi.org/10.1609/aaai.v36i8.20830.
Full textAbstract:
Partial Differential Equations (PDEs) are notoriously difficult to solve. In general, closed form solutions are not available and numerical approximation schemes are computationally expensive. In this paper, we propose to approach the solution of PDEs based on a novel technique that combines the advantages of two recently emerging machine learning based approaches. First, physics-informed neural networks (PINNs) learn continuous solutions of PDEs and can be trained with little to no ground truth data. However, PINNs do not generalize well to unseen domains. Second, convolutional neural networks provide fast inference and generalize but either require large amounts of training data or a physics-constrained loss based on finite differences that can lead to inaccuracies and discretization artifacts. We leverage the advantages of both of these approaches by using Hermite spline kernels in order to continuously interpolate a grid-based state representation that can be handled by a CNN. This allows for training without any precomputed training data using a physics-informed loss function only and provides fast, continuous solutions that generalize to unseen domains. We demonstrate the potential of our method at the examples of the incompressible Navier-Stokes equation and the damped wave equation. Our models are able to learn several intriguing phenomena such as Karman vortex streets, the Magnus effect, Doppler effect, interference patterns and wave reflections. Our quantitative assessment and an interactive real-time demo show that we are narrowing the gap in accuracy of unsupervised ML based methods to industrial solvers for computational fluid dynamics (CFD) while being orders of magnitude faster.
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Yang, Yuting, and Gang Mei. "A Deep Learning-Based Approach for a Numerical Investigation of Soil–Water Vertical Infiltration with Physics-Informed Neural Networks." Mathematics 10, no. 16 (August 15, 2022): 2945. http://dx.doi.org/10.3390/math10162945.
Full textAbstract:
The infiltration of water into the soil can lead to slope instability, which is one of the important causes of many geological hazards (such as landslides and debris flows). Therefore, the numerical investigation of the soil–water infiltration process provides the prerequisite for the determination of slope stability, which is of great significance for geological hazard prevention. In this study, we propose a deep learning-based approach for a numerical investigation of soil–water vertical infiltration with physics-informed neural networks and perform a comprehensive evaluation and analysis of the soil–water infiltration process in different soil types. In the proposed approach, the partial differential equation for soil–water infiltration is combined with the neural network based on physics-informed neural networks (PINNs) to obtain numerical analysis of the soil–water infiltration process. The results indicate that (1) compared with the traditional numerical method, the PINN-based method for the numerical investigation of soil–water vertical infiltration proposed in this study has a smaller error and can obtain more accurate numerical results. (2) During vertical infiltration of water in the different soil types, the light loam is the fastest, the heavy-loam the second and the medium loam the slowest. medium-loam soils are less susceptible to water infiltration of the three soil types and are more suitable for the filling of artificial slopes and dams. The proposed approach could be employed for the simulation of soil–water infiltration processes, not only for the discrimination of slope stability under rainfall conditions, but also for the selection of artificial slopes and dams to fill soil to prevent slope instability.