Academic literature on the topic 'Physics Informed Neural Network (PINN)'
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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
Dissertations / Theses on the topic "Physics Informed Neural Network (PINN)"
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Cedergren, Linnéa. "Physics-informed Neural Networks for Biopharma Applications." Thesis, Umeå universitet, Institutionen för fysik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-185423.
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Physics-Informed Neural Networks (PINNs) are hybrid models that incorporate differential equations into the training of neural networks, with the aim of bringing the best of both worlds. This project used a mathematical model describing a Continuous Stirred-Tank Reactor (CSTR), to test two possible applications of PINNs. The first type of PINN was trained to predict an unknown reaction rate law, based only on the differential equation and a time series of the reactor state. The resulting model was used inside a multi-step solver to simulate the system state over time. The results showed that the PINN could accurately model the behaviour of the missing physics also for new initial conditions. However, the model suffered from extrapolation error when tested on a larger reactor, with a much lower reaction rate. Comparisons between using a numerical derivative or automatic differentiation in the loss equation, indicated that the latter had a higher robustness to noise. Thus, it is likely the best choice for real applications. A second type of PINN was trained to forecast the system state one-step-ahead based on previous states and other known model parameters. An ordinary feed-forward neural network with an equal architecture was used as baseline. The second type of PINN did not outperform the baseline network. Further studies are needed to conclude if or when physics-informed loss should be used in autoregressive applications.
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Mirzai, Badi. "Physics-Informed Deep Learning for System Identification of Autonomous Underwater Vehicles : A Lagrangian Neural Network Approach." Thesis, KTH, Skolan för elektroteknik och datavetenskap (EECS), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-301626.
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In this thesis, we explore Lagrangian Neural Networks (LNNs) for system identification of Autonomous Underwater Vehicles (AUVs) with 6 degrees of freedom. One of the main challenges of AUVs is that they have limited wireless communication and navigation under water. AUVs operate under strict and uncertain conditions, where they need to be able to navigate and perform tasks in unknown ocean environments with limited and noisy sensor data. A crucial requirement for localization and adaptive control of AUVs is having an accurate and reliable model of the system’s nonlinear dynamics while taking into account the dynamic environment of the ocean. Most of these dynamics models do not incorporate data. The collection of data for AUVs is difficult, but necessary in order to have more flexibility in the model’s parameters due to the dynamic environment of the ocean. Yet, traditional system identification methods are still dominant today, despite the recent breakthroughs in Deep Learning. Therefore, in this thesis, we aim for a data-driven approach that embeds laws from physics in order to learn the state-space model of an AUV. More precisely, exploring the LNN framework for higher-dimensional systems. Furthermore, we also extend the LNN to account for non-conservative forces acting upon the system, such as damping and control inputs. The networks are trained to learn from simulated data of a second-order ordinary differential equation of an AUV. The trained model is evaluated by integrating paths from different initial states and comparing them to the true dynamics. The results yielded a model capable of predicting the output acceleration of the state space model but struggled in learning the direction of the forward movement with time.I den här uppsatsen utforskas Lagrangianska Neurala Nätverk (LNN) för systemidentifiering av Autonoma Undervattensfordon (AUV) med 6 frihetsgrader. En av de största utmaningarna med AUV är deras begränsningar när det kommer till trådlös kommunikation och navigering under vatten. Ett krav för att ha fungerande AUV är deras förmåga att navigera och utföra uppdrag under okända undervattensförhållanden med begränsad och brusig sensordata. Dessutom är ett kritiskt krav för lokalisering och adaptiv reglerteknik att ha noggranna modeller av systemets olinjära dynamik, samtidigt som den dynamiska miljön i havet tas i beaktande. De flesta sådana modeller tar inte i beaktande sensordata för att reglera dess parameterar. Insamling av sådan data för AUVer är besvärligt, men nödvändigt för att skapa större flexibilitet hos modellens parametrar. Trots de senaste genombrotten inom djupinlärning är traditionella metoder av systemidentifiering dominanta än idag för AUV. Det är av dessa anledningar som vi i denna uppsats strävar efter en datadriven metod, där vi förankrar lagar från fysik under inlärningen av systemets state-space modell. Mer specifikt utforskar vi LNN för ett system med högre dimension. Vidare expanderar vi även LNN till att även ta ickekonservativa krafter som verkar på systemet i beaktande, såsom dämpning och styrsignaler. Nätverket tränas att lära sig från simulerad data från en andra ordningens differentialekvation som beskriver en AUV. Den tränade modellen utvärderas genom att iterativt integrera fram dess rörelse från olika initialstillstånd, vilket jämförs med den korrekta modellen. Resultaten visade en modell som till viss del var kapabel till att förutspå korrekt acceleration, med begränsad framgång i att lära sig korrekt rörelseriktning framåt i tiden.
Book chapters on the topic "Physics Informed Neural Network (PINN)"
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Dhamirah Mohamad, Najwa Zawani, Akram Yousif, Nasiha Athira Binti Shaari, Hasreq Iskandar Mustafa, Samsul Ariffin Abdul Karim, Afza Shafie, and Muhammad Izzatullah. "Heat Transfer Modelling with Physics-Informed Neural Network (PINN)." In Studies in Systems, Decision and Control, 25–35. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-04028-3_3.
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Madenci, Erdogan, Pranesh Roy, and Deepak Behera. "Peridynamics for Physics Informed Neural Network." In Advances in Peridynamics, 399–418. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-97858-7_16.
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Mahesh, Ragini Bal, Jorge Leandro, and Qing Lin. "Physics Informed Neural Network for Spatial-Temporal Flood Forecasting." In Lecture Notes in Civil Engineering, 77–91. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-5501-2_7.
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Mathias, Marlon S., Wesley P. de Almeida, Jefferson F. Coelho, Lucas P. de Freitas, Felipe M. Moreno, Caio F. D. Netto, Fabio G. Cozman, et al. "Augmenting a Physics-Informed Neural Network for the 2D Burgers Equation by Addition of Solution Data Points." In Intelligent Systems, 388–401. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-21689-3_28.
Full textConference papers on the topic "Physics Informed Neural Network (PINN)"
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My Ha, Dao, Chiu Pao-Hsiung, Wong Jian Cheng, and Ooi Chin Chun. "Physics-Informed Neural Network With Numerical Differentiation for Modelling Complex Fluid Dynamic Problems." In ASME 2022 41st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/omae2022-81237.
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Abstract In this study, novel physics-informed neural network (PINN) methods are proposed to allow efficient training with improved accuracy. The computation of differential operators required for loss evaluation at collocation points are conventionally obtained via automatic differentiation (AD). Such PINNs require large optimization iterations and are very sample intensive because they are prone to optimizing towards unphysical solutions without sufficient collocation points. To make PINN training sample efficient, the idea of using numerical differentiation, coupled with automatic differentiation, is employed to define the loss function. The proposed coupled-automatic-numerical differentiation scheme — labeled as can-PINN — strongly links the collocation points, thus enabling efficient training in sparse sample regimes. The superior performance of can-PINNs is demonstrated on several challenging PINN problems, including the rotational flow problem and the channel flow over a backward facing step problem. The results reveal that for the challenging problems, can-PINNs can always achieve very good accuracy while the conventional PINNs based on AD fail.
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MORADI, SARVIN, SAEED (YASHAR) EFTEKHAR AZAM, and MASSOOD MOFID. "PHYSICS-INFORMED NEURAL NETWORK APPROACH FOR IDENTIFICATION OF DYNAMIC SYSTEMS." In Structural Health Monitoring 2021. Destech Publications, Inc., 2022. http://dx.doi.org/10.12783/shm2021/36352.
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In this study, a novel method for online and real-time identification of dynamic systems is presented. This method is based on the newly introduced algorithm Physics Informed Neural Network (PINN). In order to find the dynamic characteristics of the system, sparse displacement measurements are fed to the Artificial Neural Network (ANN); By introducing the classic vibration equation of the system to the ANN as a physics constraint, the PINN estimates both dynamic characteristic and state of the system. The proposed framework is evaluated by several numerical studies with different system properties, noise levels, architecture, and training data. On that account, four structural systems are presented: (1) single-degree-of-freedom (SDOF) systems with different properties and noise levels, as basis model with an accurate analytical solution (2) a three-degree-of-freedom (3-DOF) system with both complete and sparse measurements, representing the structural model of the n-story shear frames (3) a simple supported beam subjected to an initial displacement with several NNs architecture and sensor numbers, and (4) a Pure Cubic Oscillator (PCO) as a nonlinear dynamic system. The results of the proposed platform for the PINN are compared to a mutual ANN in all cases to emphasize the superiority of the PINN in both determining the dynamic characteristics and state estimation of dynamic systems. In addition, the performance of both NNs is examined with different training data to ensure the resilience of the algorithm and affirm the role of the added criteria, physics constraint, in reducing the dependency on the training data. The proposed algorithm can accurately estimate the dynamic characteristics of different dynamic systems with sparse, noisy measurements; by means of the classic dynamic equations and smartly selection of the hidden layer numbers, the PINN will be a powerful predictive tool for the dynamic analysis in the absence of any prior knowledge of the dynamic systems.
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Maniglio, Marco, Giorgio Fighera, Laura Dovera, and Carlo Cristiano Stabile. "Physics Informed Neural Networks Based on a Capacitance Resistance Model for Reservoirs Under Water Flooding Conditions." In Abu Dhabi International Petroleum Exhibition & Conference. SPE, 2021. http://dx.doi.org/10.2118/207800-ms.
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Abstract In recent years great interest has risen towards surrogate reservoir models based on data-driven methodologies with the purpose of speeding up reservoir management decisions. In this work, a Physics Informed Neural Network (PINN) based on a Capacitance Resistance Model (CRM) has been developed and tested on a synthetic and on a real dataset to predict the production of oil reservoirs under waterflooding conditions. CRMs are simple models based on material balance that estimate the liquid production as a function of injected water and bottom hole pressure. PINNs are Artificial Neural Networks (ANNs) that incorporate prior physical knowledge of the system under study to regularize the network. A PINN based on a CRM is obtained by including the residual of the CRM differential equations in the loss function designed to train the neural network on the historical data. During training, weights and biases of the network and parameters of the physical equations, such as connectivity factors between wells, are updated with the backpropagation algorithm. To investigate the effectiveness of the novel methodology on waterflooded scenarios, two test cases are presented: a small synthetic one and a real mature reservoir. Results obtained with PINN are compared with respect to CRM and ANN alone. In the synthetic case CRM and PINN give slightly better quality history matches and predictions than ANN. The connectivity factors estimated by CRM and PINN are very similar and correctly represent the underlying geology. In the real case PINN gives better quality history matches and predictions than ANN, and both significantly outperform CRM. Even though the CRM formulation is too simple to predict the complex behavior of a real reservoir, the CRM based regularization contributes to improving the PINN predictions quality compared to the purely data-driven ANN model. The connectivity factors estimated by CRM and PINN are not in agreement. However, the latter method provided results closer to our understanding of the flooding process after many years of operations and data analysis. All considered, PINN outperformed both CRM and ANN in terms of predictivity and interpretability, effectively combining strengths from both methodologies. The presented approach does not require the construction of a 3D model since it learns directly from production data, while preserving physical consistency. Moreover, it represents a computationally inexpensive alternative to traditional full-physics reservoir simulations which could have vast applications for problems requiring many forward evaluations, like the optimization of water allocation for mature reservoirs.
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Tay, Wee-Beng, Murali Damodaran, Zhi-Da Teh, and Rahul Halder. "Investigation of Applying Physics Informed Neural Networks (PINN) and Variants on 2D Aerodynamics Problems." In ASME 2020 Fluids Engineering Division Summer Meeting collocated with the ASME 2020 Heat Transfer Summer Conference and the ASME 2020 18th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/fedsm2020-20184.
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Abstract Investigation of applying physics informed neural networks on the test case involving flow past Converging-Diverging (CD) Nozzle has been investigated. Both Artificial Neural Network (ANN) and Physics Informed Neural Network (PINN) are used to do the training and prediction. Results show that Artificial Neural Network (ANN) by itself is already able to give relatively good prediction. With the addition of PINN, the error reduces even more, although by only a relatively small amount. This is perhaps due to the already good prediction. The effects of batch size, training iteration and number of epochs on the prediction accuracy have already been tested. It is found that increasing batch size improves the prediction. On the other hand, increasing the training iteration may give poorer prediction due to overfitting. Lastly, in general, increasing epochs reduces the error. More investigations should be done in the future to further reduce the error while at the same time using less training data. More complicated cases with time varying results should also be included. Extrapolation of the results using PINN can also be tested.
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Alhubail, Ali, Xupeng He, Marwa AlSinan, Hyung Kwak, and Hussein Hoteit. "Extended Physics-Informed Neural Networks for Solving Fluid Flow Problems in Highly Heterogeneous Media." In International Petroleum Technology Conference. IPTC, 2022. http://dx.doi.org/10.2523/iptc-22163-ms.
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Abstract Utilization of neural networks to solve physical problems has been receiving wide attention recently. These neural networks are commonly named physics-informed neural network (PINN), in which the physics are employed through the governing partial differential equations (PDEs). Traditional PINNs suffer from unstable performance when dealing with flow problems in highly heterogeneous domains. This work presents the applicability of the extended PINN (XPINN) method in solving heterogeneous problems. XPINN can create a full solution model to the solution of the governing PDEs by training the neural network on the PDEs and its constraints such as boundary and initial conditions, and known solution points. The heterogeneous problem is solved by performing domain decomposition, which divides the original heterogeneous domain into various homogeneous sub-domains. Each sub-domain incorporates its own PINN structure. The different PINNs are connected through interface conditions, allowing for information to communicate across the interfaces. These conditions include pressure and flux continuities. Various heterogeneous scenarios are implemented in this study to investigate the robustness of the proposed method. We demonstrate the accuracy of the XPINN model by comparing it with the ground truth solved from high-fidelity simulations. Results show a good match in terms of pressure and velocity with errors of less than 1%. Different interface conditions were tested, and it was observed that without the inclusion of pressure and flux continuities, the solver does not converge to the solution of interest. Sensitivity analysis was performed to explore the effects of the neural network architecture, the weights given to each loss term, and the number of training iterations. Results show that wide and shallow networks performed well due to avoiding the gradient vanishing issue that comes with deeper networks. In addition, balanced weights produced better accuracy in general. Moreover, more training iterations improved the accuracy of the results but at lower rates in later training stages. This paper presents XPINN to solve fluid flow in heterogeneous media. We demonstrate the robustness and accuracy of the proposed XPINN model by comparing it with the ground truth solutions in multiple heterogeneous cases. The model shows good potential and can be readily implemented in reservoir characterization workflow.
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MORADI, SARVIN, SAEED (YASHAR) EFTEKHAR AZAM, and MASSOOD MOFID. "A PHYSICS INFORMED NEURAL NETWORK INTEGRATED DIGITAL TWIN FOR MONITORING OF THE BRIDGES." In Structural Health Monitoring 2021. Destech Publications, Inc., 2022. http://dx.doi.org/10.12783/shm2021/36326.
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In recent years the Digital Twin (DT) paradigm has been studied as a futuristic tool for the next generation of infrastructures. Due to the interdisciplinary nature of the design, construction, monitoring, and maintenance of the infrastructures and the cooperation of several stakeholders throughout their lifetime, it is indispensable to introduce a comprehensive platform for the digital representation of infrastructures. Although the DT emphasizes the role of digital modeling and data analysis, there is a gap between physical modeling and data-driven tools. The newly introduced Physics Informed Neural Networks (PINNs) are capable of not only filling this gap but also representing a unified real-time platform for different users from various fields. These algorithms suggest an agile environment for users to introduce different criteria from the design stage to the health monitoring period. The PINN integrates both physical modeling and data analysis in a unique algorithm, helping them interact simultaneously and providing real-time, reliable responses. By means of the PINN, the DT can learn and update the model from various data sources with a unique platform, which plays an essential role in the rapid flow of information and transparency of data-based calculations. The dynamic ambiance of the PINN enables the users to interact with the modeling procedure and track the analysis. In this study, the details of the proposed platform for the integration of the PINNs in the DT are addressed for monitoring the bridges. Extensive numerical studies are provided for various scenarios of sensor equipment, including sensor type, data accuracy, and installation pattern. The performance of the proposed platform is evaluated for predicting subsequent responses to ensure the reliability of the responses in future decision makings.
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Laubscher, Ryno, Pieter Rousseau, and Chris Meyer. "Modeling of Inviscid Flow Shock Formation in a Wedge-Shaped Domain Using a Physics-Informed Neural Network-Based Partial Differential Equation Solver." In ASME Turbo Expo 2022: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/gt2022-81768.
Full textAbstract:
Abstract Physics-informed neural networks (PINN) can potentially be applied to develop computationally efficient surrogate models, perform anomaly detection, and develop time-series forecasting models. However, predicting small-scale features such as the exact location of shocks and the associated rapid changes in fluid properties across it, have proven to be challenging when using standard PINN architectures, due to spatial biasing during network training. This paper investigates the ability of PINNs to capture these features of an oblique shock by applying Fourier feature network architectures. Four PINN architectures are applied namely a standard PINN architecture with the direct and indirect implementation of the ideal gas equation of state, as well as the direct implementation combined with a standard and modified Fourier feature transformation function. The case study is 2D steady-state compressible Euler flow over a 15° wedge at a Mach number of 5. The PINN predictions are compared to results generated using proven numerical CFD techniques. The results show that the indirect implementation of the equation of state is unable to enforce the prescribed boundary conditions. The application of the Fourier feature up-sampling to the low-dimensional spatial coordinates improves the ability of the PINN model to capture the small-scale features, with the standard implementation performing better than the modified version.
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Almeldein, Ahmed, and Noah Van Dam. "Accelerating Chemical Kinetics Calculations With Physics Informed Neural Networks." In ASME 2022 ICE Forward Conference. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/icef2022-90371.
Full textAbstract:
Abstract Detailed chemical kinetics calculations can be very computationally expensive, and so various approaches have been used to speed up combustion calculations. Deep neural networks (DNNs) are one promising approach that has seen significant development recently. Standard DNNs, however, do not necessarily follow physical constraints such as conservation of mass. Physics Informed Neural Networks (PINNs) are a class of neural networks that have physical laws embedded within the training process to create networks that follow those physical laws. A new PINN-based DNN approach to chemical kinetics modeling has been developed to make sure mass fraction predictions adhere to the conservation of atomic species. The approach also utilizes a mixture-of-experts (MOE) architecture where the data is distributed on multiple sub-networks followed by a softmax selective layer. The MOE architecture allows the different sub-networks to specialize in different thermochemical regimes, such as early stage ignition reactions or post-flame equilibrium chemistry, then the softmax layer smoothly transitions between the sub-network predictions. This modeling approach was applied to the prediction of methane-air combustion using the GRI-Mech 3.0 as the reference mechanism. The training database was composed of data from 0D ignition delay simulations under initial conditions of 0.2–50 bar pressure, 500–2000 K temperature, an equivalence ratio between 0 and 2, and an N2-dilution percentage of up to 50%. A wide variety of network sizes and architectures of between 3 and 20 sub-networks and 6,600 to 77,000 neurons were tested. The resulting networks were able to predict 0D combustion simulations with similar accuracy and atomic mass conservation as standard kinetics solvers while having a 10–50× speedup in online evaluation time using CPUs, and on average over 200× when using a GPU.
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Brandolin, Francesco, Matteo Ravasi, and Tariq Alkhalifah. "Pwd-pinn: Slope-assisted seismic interpolation with physics-informed neural networks." In Second International Meeting for Applied Geoscience & Energy. Society of Exploration Geophysicists and American Association of Petroleum Geologists, 2022. http://dx.doi.org/10.1190/image2022-3742422.1.
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Izzatullah, M., I. E. Yildirim, U. B. Waheed, and T. Alkhalifah. "Predictive Uncertainty Quantification for Bayesian Physics-Informed Neural Network (Pinn) in Hypocentre Estimation Problem." In 83rd EAGE Annual Conference & Exhibition. European Association of Geoscientists & Engineers, 2022. http://dx.doi.org/10.3997/2214-4609.202210063.
Full textReports on the topic "Physics Informed Neural Network (PINN)"
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Pettit, Chris, and D. Wilson. A physics-informed neural network for sound propagation in the atmospheric boundary layer. Engineer Research and Development Center (U.S.), June 2021. http://dx.doi.org/10.21079/11681/41034.
Full textAbstract:
We describe what we believe is the first effort to develop a physics-informed neural network (PINN) to predict sound propagation through the atmospheric boundary layer. PINN is a recent innovation in the application of deep learning to simulate physics. The motivation is to combine the strengths of data-driven models and physics models, thereby producing a regularized surrogate model using less data than a purely data-driven model. In a PINN, the data-driven loss function is augmented with penalty terms for deviations from the underlying physics, e.g., a governing equation or a boundary condition. Training data are obtained from Crank-Nicholson solutions of the parabolic equation with homogeneous ground impedance and Monin-Obukhov similarity theory for the effective sound speed in the moving atmosphere. Training data are random samples from an ensemble of solutions for combinations of parameters governing the impedance and the effective sound speed. PINN output is processed to produce realizations of transmission loss that look much like the Crank-Nicholson solutions. We describe the framework for implementing PINN for outdoor sound, and we outline practical matters related to network architecture, the size of the training set, the physics-informed loss function, and challenge of managing the spatial complexity of the complex pressure.