Artículos de revistas: "Physics-Informed neural network"

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Hofmann, Tobias, Jacob Hamar, Marcel Rogge, Christoph Zoerr, Simon Erhard y Jan Philipp Schmidt. "Physics-Informed Neural Networks for State of Health Estimation in Lithium-Ion Batteries". Journal of The Electrochemical Society 170, n.º 9 (1 de septiembre de 2023): 090524. http://dx.doi.org/10.1149/1945-7111/acf0ef.

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One of the most challenging tasks of modern battery management systems is the accurate state of health estimation. While physico-chemical models are accurate, they have high computational cost. Neural networks lack physical interpretability but are efficient. Physics-informed neural networks tackle the aforementioned shortcomings by combining the efficiency of neural networks with the accuracy of physico-chemical models. A physics-informed neural network is developed and evaluated against three different datasets: A pseudo-two-dimensional Newman model generates data at various state of health points. This dataset is fused with experimental data from laboratory measurements and vehicle field data to train a neural network in which it exploits correlation from internal modeled states to the measurable state of health. The resulting physics-informed neural network performs best with the synthetic dataset and achieves a root mean squared error below 2% at estimating the state of health. The root mean squared error stays within 3% for laboratory test data, with the lowest error observed for constant current discharge samples. The physics-informed neural network outperforms several other purely data-driven methods and proves its advantage. The inclusion of physico-chemical information from simulation increases accuracy and further enables broader application ranges.

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Karakonstantis, Xenofon, Diego Caviedes-Nozal, Antoine Richard y Efren Fernandez-Grande. "Room impulse response reconstruction with physics-informed deep learning". Journal of the Acoustical Society of America 155, n.º 2 (1 de febrero de 2024): 1048–59. http://dx.doi.org/10.1121/10.0024750.

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A method is presented for estimating and reconstructing the sound field within a room using physics-informed neural networks. By incorporating a limited set of experimental room impulse responses as training data, this approach combines neural network processing capabilities with the underlying physics of sound propagation, as articulated by the wave equation. The network's ability to estimate particle velocity and intensity, in addition to sound pressure, demonstrates its capacity to represent the flow of acoustic energy and completely characterise the sound field with only a few measurements. Additionally, an investigation into the potential of this network as a tool for improving acoustic simulations is conducted. This is due to its proficiency in offering grid-free sound field mappings with minimal inference time. Furthermore, a study is carried out which encompasses comparative analyses against current approaches for sound field reconstruction. Specifically, the proposed approach is evaluated against both data-driven techniques and elementary wave-based regression methods. The results demonstrate that the physics-informed neural network stands out when reconstructing the early part of the room impulse response, while simultaneously allowing for complete sound field characterisation in the time domain.

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Kenzhebek, Y., T. S. Imankulov y D. Zh Akhmed-Zaki. "PREDICTION OF OIL PRODUCTION USING PHYSICS-INFORMED NEURAL NETWORKS". BULLETIN Series of Physics & Mathematical Sciences 76, n.º 4 (15 de diciembre de 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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Pu, Ruilong y Xinlong Feng. "Physics-Informed Neural Networks for Solving Coupled Stokes–Darcy Equation". Entropy 24, n.º 8 (11 de agosto de 2022): 1106. http://dx.doi.org/10.3390/e24081106.

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In this paper, a grid-free deep learning method based on a physics-informed neural network is proposed for solving coupled Stokes–Darcy equations with Bever–Joseph–Saffman interface conditions. This method has the advantage of avoiding grid generation and can greatly reduce the amount of computation when solving complex problems. Although original physical neural network algorithms have been used to solve many differential equations, we find that the direct use of physical neural networks to solve coupled Stokes–Darcy equations does not provide accurate solutions in some cases, such as rigid terms due to small parameters and interface discontinuity problems. In order to improve the approximation ability of a physics-informed neural network, we propose a loss-function-weighted function strategy, a parallel network structure strategy, and a local adaptive activation function strategy. In addition, the physical information neural network with an added strategy provides inspiration for solving other more complicated problems of multi-physical field coupling. Finally, the effectiveness of the proposed strategy is verified by numerical experiments.

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Yoon, Seunghyun, Yongsung Park y Woojae Seong. "Improving mode extraction with physics-informed neural network". Journal of the Acoustical Society of America 154, n.º 4_supplement (1 de octubre de 2023): A339—A340. http://dx.doi.org/10.1121/10.0023729.

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This study aims to enhance conventional mode extraction methods in ocean waveguides using a physics-informed neural network (PINN). Mode extraction involves estimating mode wavenumbers and corresponding mode depth functions. The approach considers a scenario with a single frequency source towed at a constant depth and measured from a vertical line array (VLA). Conventional mode extraction methods applied to experimental data face two problems. First, mode shape estimation is limited because the receivers only cover a partial waveguide. Second, the wavenumber spectrum is affected by issues such as Doppler shift and range errors. To address these challenges, we train the PINN with measured data, generating a densely sampled complex pressure field, including the unmeasured region above the VLA. We then apply the same mode extraction methods to both the raw data and the PINN-generated data for comparison. The proposed method is validated using data from the SWellEx-96, demonstrating improved mode extraction performance compared to using raw experimental data directly.

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Stenkin, Dmitry y Vladimir Gorbachenko. "Mathematical Modeling on a Physics-Informed Radial Basis Function Network". Mathematics 12, n.º 2 (11 de enero de 2024): 241. http://dx.doi.org/10.3390/math12020241.

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The article is devoted to approximate methods for solving differential equations. An approach based on neural networks with radial basis functions is presented. Neural network training algorithms adapted to radial basis function networks are proposed, in particular adaptations of the Nesterov and Levenberg-Marquardt algorithms. The effectiveness of the proposed algorithms is demonstrated for solving model problems of function approximation, differential equations, direct and inverse boundary value problems, and modeling processes in piecewise homogeneous media.

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Schmid, Johannes D., Philipp Bauerschmidt, Caglar Gurbuz y Steffen Marburg. "Physics-informed neural networks for characterization of structural dynamic boundary conditions". Journal of the Acoustical Society of America 154, n.º 4_supplement (1 de octubre de 2023): A99. http://dx.doi.org/10.1121/10.0022923.

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Structural dynamics simulations are often faced with challenges arising from unknown boundary conditions, leading to considerable prediction uncertainties. Direct measurement of these boundary conditions can be impractical for certain mounting scenarios, such as joints or screw connections. In addition, conventional inverse methods face limitations in integrating measured data and solving inverse problems when the forward model is computationally expensive. In this study, we explore the potential of physics-informed neural networks that incorporate the residual of a partial differential equation into the loss function of a neural network to ensure physically consistent predictions. We train the neural network using noisy boundary displacement data of a structure from a finite element reference solution. The network learns to predict the displacement field within the structure while satisfying the Navier–Lamé equations in the frequency domain. Our results show that physics-informed neural networks accurately predict the displacement field within a three-dimensional structure using only boundary training data. Additionally, differentiating the trained network allows precise characterization of previously unknown boundary conditions and facilitates the assessment of non-measurable quantities, such as the stress tensor.

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Zhai, Hanfeng, Quan Zhou y Guohui Hu. "Predicting micro-bubble dynamics with semi-physics-informed deep learning". AIP Advances 12, n.º 3 (1 de marzo de 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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Karakonstantis, Xenofon y Efren Fernandez-Grande. "Advancing sound field analysis with physics-informed neural networks". Journal of the Acoustical Society of America 154, n.º 4_supplement (1 de octubre de 2023): A98. http://dx.doi.org/10.1121/10.0022920.

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This work introduces a method that employs physics-informed neural networks to reconstruct sound fields in diverse rooms, including both typical acoustically damped meeting rooms and more spaces of cultural significance, such as concert halls or theatres. The neural network is trained using a limited set of room impulse responses, integrating the expressive capacity of neural networks with the fundamental physics of sound propagation governed by the wave equation. Consequently, the network accurately represents sound fields within an aperture without requiring extensive measurements, regardless of the complexity of the sound field. Notably, our approach extends beyond sound pressure estimation and includes valuable vectorial quantities, such as particle velocity and intensity, resembling classical holography methods. Experimental results confirm the efficacy of the proposed approach, underscoring its reconstruction accuracy and computational efficiency. Moreover, by enabling the acquisition of sound field quantities in the time domain, which were previously challenging to obtain from measurements, our method opens up new frontiers for the analysis and comprehension of sound propagation phenomena in rooms.

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Pannekoucke, Olivier y Ronan Fablet. "PDE-NetGen 1.0: from symbolic partial differential equation (PDE) representations of physical processes to trainable neural network representations". Geoscientific Model Development 13, n.º 7 (30 de julio de 2020): 3373–82. http://dx.doi.org/10.5194/gmd-13-3373-2020.

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Abstract. Bridging physics and deep learning is a topical challenge. While deep learning frameworks open avenues in physical science, the design of physically consistent deep neural network architectures is an open issue. In the spirit of physics-informed neural networks (NNs), the PDE-NetGen package provides new means to automatically translate physical equations, given as partial differential equations (PDEs), into neural network architectures. PDE-NetGen combines symbolic calculus and a neural network generator. The latter exploits NN-based implementations of PDE solvers using Keras. With some knowledge of a problem, PDE-NetGen is a plug-and-play tool to generate physics-informed NN architectures. They provide computationally efficient yet compact representations to address a variety of issues, including, among others, adjoint derivation, model calibration, forecasting and data assimilation as well as uncertainty quantification. As an illustration, the workflow is first presented for the 2D diffusion equation, then applied to the data-driven and physics-informed identification of uncertainty dynamics for the Burgers equation.

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Schmid, Johannes. "Physics-informed neural networks for solving the Helmholtz equation". INTER-NOISE and NOISE-CON Congress and Conference Proceedings 267, n.º 1 (5 de noviembre de 2023): 265–68. http://dx.doi.org/10.3397/no_2023_0049.

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Discretization-based methods like the finite element method have proven to be effective for solving the Helmholtz equation in computational acoustics. However, it is very challenging to incorporate measured data into the model or infer model input parameters based on observed response data. Machine learning approaches have shown promising potential in data-driven modeling. In practical applications, purely supervised approaches suffer from poor generalization and physical interpretability. Physics-informed neural networks (PINNs) incorporate prior knowledge of the underlying partial differential equation by including the residual into the loss function of an artificial neural network. Training the neural network minimizes the residual of both the differential equation and the boundary conditions and learns a solution that satisfies the corresponding boundary value problem. In this contribution, PINNs are applied to solve the Helmholtz equation within a two-dimensional acoustic duct and mixed boundary conditions are considered. The results show that PINNs are able to solve the Helmholtz equation very accurately and provide a promising data-driven method for physics-based surrogate modeling.

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Yoon, Seunghyun, Yongsung Park, Peter Gerstoft y Woojae Seong. "Predicting ocean pressure field with a physics-informed neural network". Journal of the Acoustical Society of America 155, n.º 3 (1 de marzo de 2024): 2037–49. http://dx.doi.org/10.1121/10.0025235.

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Ocean sound pressure field prediction, based on partially measured pressure magnitudes at different range-depths, is presented. Our proposed machine learning strategy employs a trained neural network with range-depth as input and outputs complex acoustic pressure at the location. We utilize a physics-informed neural network (PINN), fitting sampled data while considering the additional information provided by the partial differential equation (PDE) governing the ocean sound pressure field. In vast ocean environments with kilometer-scale ranges, pressure fields exhibit rapidly fluctuating phases, even at frequencies below 100 Hz, posing a challenge for neural networks to converge to accurate solutions. To address this, we utilize the envelope function from the parabolic-equation technique, fundamental in ocean sound propagation modeling. The envelope function shows slower variations across ranges, enabling PINNs to predict sound pressure in an ocean waveguide more effectively. Additional PDE information allows PINNs to capture PDE solutions even with a limited amount of training data, distinguishing them from purely data-driven machine learning approaches that require extensive datasets. Our approach is validated through simulations and using data from the SWellEx-96 experiment.

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Yoon, Seunghyun, Yongsung Park, Peter Gerstoft y Woojae Seong. "Physics-informed neural network for predicting unmeasured ocean acoustic pressure field". Journal of the Acoustical Society of America 154, n.º 4_supplement (1 de octubre de 2023): A97. http://dx.doi.org/10.1121/10.0022916.

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This study employs a physics-informed neural network in an ocean waveguide to predict the unmeasured acoustic pressure field, leveraging partially measured data. The method addresses a scenario where an acoustic source transmits signals across different ranges and is measured by multiple receivers. The acoustic pressure field in ocean waveguides exhibits rapid spatial variations over kilometer-range scales. The fully connected neural networks encounter challenges when approximating high-frequency functions, known as spectral bias. To mitigate this problem, the measured pressure field is transformed into a low-frequency function for training the neural network. We propose two methods sharing the same neural network architecture but utilizing different information. The first method uses a complex value of the pressure field (i.e., both magnitude and phase), while the second method uses only magnitude. We validate the proposed methods using simulations and experimental data from the SWellEx-96 environment. Results demonstrate that the first method exhibits superior performance with sparse data, while the second method works better in real-world scenarios.

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Hassanaly, Malik, Peter J. Weddle, Kandler Smith, Subhayan De, Alireza Doostan y Ryan King. "Physics-Informed Neural Network Modeling of Li-Ion Batteries". ECS Meeting Abstracts MA2022-02, n.º 3 (9 de octubre de 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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Guler Bayazit, Nilgun. "Physics informed neural network consisting of two decoupled stages". Engineering Science and Technology, an International Journal 46 (octubre de 2023): 101489. http://dx.doi.org/10.1016/j.jestch.2023.101489.

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Sha, Yanliang, Jun Lan, Yida Li y Quan Chen. "A Physics-Informed Recurrent Neural Network for RRAM Modeling". Electronics 12, n.º 13 (2 de julio de 2023): 2906. http://dx.doi.org/10.3390/electronics12132906.

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Extracting behavioral models of RRAM devices is challenging due to their unique “memory” behaviors and rapid developments, for which well-established modeling frameworks and systematic parameter extraction processes are not available. In this work, we propose a physics-informed recurrent neural network (PiRNN) methodology to generate behavioral models of RRAM devices from practical measurement/simulation data. The proposed framework can faithfully capture the evolution of internal state and its impacts on the output. A series of modifications informed by the RRAM device physics are proposed to enhance the modeling capabilities. The integration strategy of Verilog-A equivalent circuits, is also developed for compatibility with existing general-purpose circuit simulators. The Verilog-A model can be easily adopted into the SPICE-type simulator for the circuit design with a variable step that differs from the training process. Numerical experiments with real RRAM devices data demonstrate the feasibility and advantages of the proposed methodology.

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Liu, Chen-Xu, Xinghao Wang, Weiming Liu, Yi-Fan Yang, Gui-Lan Yu y Zhanli Liu. "A physics-informed neural network for Kresling origami structures". International Journal of Mechanical Sciences 269 (mayo de 2024): 109080. http://dx.doi.org/10.1016/j.ijmecsci.2024.109080.

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Olivieri, Marco, Mirco Pezzoli, Fabio Antonacci y Augusto Sarti. "A Physics-Informed Neural Network Approach for Nearfield Acoustic Holography". Sensors 21, n.º 23 (25 de noviembre de 2021): 7834. http://dx.doi.org/10.3390/s21237834.

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In this manuscript, we describe a novel methodology for nearfield acoustic holography (NAH). The proposed technique is based on convolutional neural networks, with autoencoder architecture, to reconstruct the pressure and velocity fields on the surface of the vibrating structure using the sampled pressure soundfield on the holographic plane as input. The loss function used for training the network is based on a combination of two components. The first component is the error in the reconstructed velocity. The second component is the error between the sound pressure on the holographic plane and its estimate obtained from forward propagating the pressure and velocity fields on the structure through the Kirchhoff–Helmholtz integral; thus, bringing some knowledge about the physics of the process under study into the estimation algorithm. Due to the explicit presence of the Kirchhoff–Helmholtz integral in the loss function, we name the proposed technique the Kirchhoff–Helmholtz-based convolutional neural network, KHCNN. KHCNN has been tested on two large datasets of rectangular plates and violin shells. Results show that it attains very good accuracy, with a gain in the NMSE of the estimated velocity field that can top 10 dB, with respect to state-of-the-art techniques. The same trend is observed if the normalized cross correlation is used as a metric.

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Hooshyar, Saman y Arash Elahi. "Sequencing Initial Conditions in Physics-Informed Neural Networks". Journal of Chemistry and Environment 3, n.º 1 (26 de marzo de 2024): 98–108. http://dx.doi.org/10.56946/jce.v3i1.345.

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The scientific machine learning (SciML) field has introduced a new class of models called physics-informed neural networks (PINNs). These models incorporate domain-specific knowledge as soft constraints on a loss function and use machine learning techniques to train the model. Although PINN models have shown promising results for simple problems, they are prone to failure when moderate level of complexities are added to the problems. We demonstrate that the existing baseline models, in particular PINN and evolutionary sampling (Evo), are unable to capture the solution to differential equations with convection, reaction, and diffusion operators when the imposed initial condition is non-trivial. We then propose a promising solution to address these types of failure modes. This approach involves coupling Curriculum learning with the baseline models, where the network first trains on PDEs with simple initial conditions and is progressively exposed to more complex initial conditions. Our results show that we can reduce the error by 1 – 2 orders of magnitude with our proposed method compared to regular PINN and Evo.

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Oluwasakin, Ebenezer O. y Abdul Q. M. Khaliq. "Optimizing Physics-Informed Neural Network in Dynamic System Simulation and Learning of Parameters". Algorithms 16, n.º 12 (28 de noviembre de 2023): 547. http://dx.doi.org/10.3390/a16120547.

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Artificial neural networks have changed many fields by giving scientists a strong way to model complex phenomena. They are also becoming increasingly useful for solving various difficult scientific problems. Still, people keep trying to find faster and more accurate ways to simulate dynamic systems. This research explores the transformative capabilities of physics-informed neural networks, a specialized subset of artificial neural networks, in modeling complex dynamical systems with enhanced speed and accuracy. These networks incorporate known physical laws into the learning process, ensuring predictions remain consistent with fundamental principles, which is crucial when dealing with scientific phenomena. This study focuses on optimizing the application of this specialized network for simultaneous system dynamics simulations and learning time-varying parameters, particularly when the number of unknowns in the system matches the number of undetermined parameters. Additionally, we explore scenarios with a mismatch between parameters and equations, optimizing network architecture to enhance convergence speed, computational efficiency, and accuracy in learning the time-varying parameter. Our approach enhances the algorithm’s performance and accuracy, ensuring optimal use of computational resources and yielding more precise results. Extensive experiments are conducted on four different dynamical systems: first-order irreversible chain reactions, biomass transfer, the Brusselsator model, and the Lotka-Volterra model, using synthetically generated data to validate our approach. Additionally, we apply our method to the susceptible-infected-recovered model, utilizing real-world COVID-19 data to learn the time-varying parameters of the pandemic’s spread. A comprehensive comparison between the performance of our approach and fully connected deep neural networks is presented, evaluating both accuracy and computational efficiency in parameter identification and system dynamics capture. The results demonstrate that the physics-informed neural networks outperform fully connected deep neural networks in performance, especially with increased network depth, making them ideal for real-time complex system modeling. This underscores the physics-informed neural network’s effectiveness in scientific modeling in scenarios with balanced unknowns and parameters. Furthermore, it provides a fast, accurate, and efficient alternative for analyzing dynamic systems.

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Liu, Zhixiang, Yuanji Chen, Ge Song, Wei Song y Jingxiang Xu. "Combination of Physics-Informed Neural Networks and Single-Relaxation-Time Lattice Boltzmann Method for Solving Inverse Problems in Fluid Mechanics". Mathematics 11, n.º 19 (1 de octubre de 2023): 4147. http://dx.doi.org/10.3390/math11194147.

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Physics-Informed Neural Networks (PINNs) improve the efficiency of data utilization by combining physical principles with neural network algorithms and thus ensure that their predictions are consistent and stable with the physical laws. PINNs open up a new approach to address inverse problems in fluid mechanics. Based on the single-relaxation-time lattice Boltzmann method (SRT-LBM) with the Bhatnagar–Gross–Krook (BGK) collision operator, the PINN-SRT-LBM model is proposed in this paper for solving the inverse problem in fluid mechanics. The PINN-SRT-LBM model consists of three components. The first component involves a deep neural network that predicts equilibrium control equations in different discrete velocity directions within the SRT-LBM. The second component employs another deep neural network to predict non-equilibrium control equations, enabling the inference of the fluid’s non-equilibrium characteristics. The third component, a physics-informed function, translates the outputs of the first two networks into physical information. By minimizing the residuals of the physical partial differential equations (PDEs), the physics-informed function infers relevant macroscopic quantities of the flow. The model evolves two sub-models that are applicable to different dimensions, named the PINN-SRT-LBM-I and PINN-SRT-LBM-II models according to the construction of the physics-informed function. The innovation of this work is the introduction of SRT-LBM and discrete velocity models as physical drivers into a neural network through the interpretation function. Therefore, the PINN-SRT-LBM allows a given neural network to handle inverse problems of various dimensions and focus on problem-specific solving. Our experimental results confirm the accurate prediction by this model of flow information at different Reynolds numbers within the computational domain. Relying on the PINN-SRT-LBM models, inverse problems in fluid mechanics can be solved efficiently.

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Silva, Roberto Mamud Guedes da, Helio dos Santos Migon y Antônio José da Silva Neto. "Parameter estimation in the pollutant dispersion problem with Physics-Informed Neural Networks". Ciência e Natura 45, esp. 3 (1 de diciembre de 2023): e74615. http://dx.doi.org/10.5902/2179460x74615.

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In this work, the inverse problem of parameter estimation in the advection-dispersion-reaction equation, modelling the pollutant dispersion in a river, is studied with a Neural Network approach. In the direct problem, the dispersion, velocity and reaction parameters are known and then the initial and boundary value problem is solved by classical numerical methods, where it is used as input dataset for the inverse problem and formulation. In the inverse problem, we know the dispersion and the velocity parameters and also the information about the pollutant concentration from the synthetic experimental data, and then the aim is to estimate the reaction parameter in the advection-dispersion-reaction equation. This inverse problem is solved by an usual Artificial Neural Network (ANN) and by a Physics-Informed Neural Network (PINN), which is a special type of neural networks that includes in its formulation the physical laws that describe the phenomena involved. Numerical experiments with both the ANN and PINN are presented, demonstrating the feasibility of the approach considered.

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Li, Jianfeng, Liangying Zhou, Jingwei Sun y Guangzhong Sun. "Physically plausible and conservative solutions to Navier-Stokes equations using Physics-Informed CNNs". JUSTC 53 (2023): 1. http://dx.doi.org/10.52396/justc-2022-0174.

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Physics-informed Neural Network (PINN) is an emerging approach for efficiently solving partial differential equations (PDEs) using neural networks. Physics-informed Convolutional Neural Network (PICNN), a variant of PINN enhanced by convolutional neural networks (CNNs), has achieved better results on a series of PDEs since the parameter-sharing property of CNNs is effective to learn spatial dependencies. However, applying existing PICNN-based methods to solve Navier-Stokes equations can generate oscillating predictions, which are inconsistent with the laws of physics and the conservation properties. To address this issue, we propose a novel method that combines PICNN with the finite volume method to obtain physically plausible and conservative solutions to Navier-Stokes equations. We derive the second-order upwind difference scheme of Navier-Stokes equations using the finite volume method. Then we use the derived scheme to calculate the partial derivatives and construct the physics-informed loss function. The proposed method is assessed by experiments on steady-state Navier-Stokes equations under different scenarios, including convective heat transfer, lid-driven cavity flow, etc. The experimental results demonstrate that our method can effectively improve the plausibility and the accuracy of the predicted solutions from PICNN.

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Tarkhov, Dmitriy, Tatiana Lazovskaya y 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, n.º 2 (6 de enero de 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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25

Leung, Wing Tat, Guang Lin y Zecheng Zhang. "NH-PINN: Neural homogenization-based physics-informed neural network for multiscale problems". Journal of Computational Physics 470 (diciembre de 2022): 111539. http://dx.doi.org/10.1016/j.jcp.2022.111539.

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Antonion, Klapa, Xiao Wang, Maziar Raissi y Laurn Joshie. "Machine Learning Through Physics–Informed Neural Networks: Progress and Challenges". Academic Journal of Science and Technology 9, n.º 1 (20 de enero de 2024): 46–49. http://dx.doi.org/10.54097/b1d21816.

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Physics-Informed Neural Networks (PINNs) represent a groundbreaking approach wherein neural networks (NNs) integrate model equations, such as Partial Differential Equations (PDEs), within their architecture. This innovation has become instrumental in solving diverse problem sets including PDEs, fractional equations, integral-differential equations, and stochastic PDEs. It's a versatile multi-task learning framework that tasks NNs with fitting observed data while simultaneously minimizing PDE residuals. This paper delves into the landscape of PINNs, aiming to delineate their inherent strengths and weaknesses. Beyond exploring the fundamental characteristics of these networks, this review endeavors to encompass a wider spectrum of collocation-based physics-informed neural networks, extending beyond the core PINN model. Variants like physics-constrained neural networks (PCNN), variational hp-VPINN, and conservative PINN (CPINN) constitute pivotal aspects of this exploration. The study accentuates a predominant focus in research on tailoring PINNs through diverse strategies: adapting activation functions, refining gradient optimization techniques, innovating neural network structures, and enhancing loss function architectures. Despite the extensive applicability demonstrated by PINNs, surpassing classical numerical methods like Finite Element Method (FEM) in certain contexts, the review highlights ongoing opportunities for advancement. Notably, there are persisting theoretical challenges that demand resolution, ensuring the continued evolution and refinement of this revolutionary approach.

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Cao, Fujun, Xiaobin Guo, Fei Gao y Dongfang Yuan. "Deep Learning Nonhomogeneous Elliptic Interface Problems by Soft Constraint Physics-Informed Neural Networks". Mathematics 11, n.º 8 (13 de abril de 2023): 1843. http://dx.doi.org/10.3390/math11081843.

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It is a great challenge to solve nonhomogeneous elliptic interface problems, because the interface divides the computational domain into two disjoint parts, and the solution may change dramatically across the interface. A soft constraint physics-informed neural network with dual neural networks is proposed, which is composed of two separate neural networks for each subdomain, which are coupled by the connecting conditions on the interface. It is beneficial to capture the singularity of the solution across the interface. We formulate the PDEs, boundary conditions, and jump conditions on the interface into the loss function by means of the physics-informed neural network (PINN), and the different terms in the loss function are balanced by optimized penalty weights. To enhance computing efficiency for increasingly difficult issues, adaptive activation functions and the adaptive sampled method are used, which may be improved to produce the optimal network performance, as the topology of the loss function involved in the optimization process changes dynamically. Lastly, we present many numerical experiments, in both 2D and 3D, to demonstrate the proposed method’s flexibility, efficacy, and accuracy in tackling nonhomogeneous interface issues.

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Grubas, Serafim I., Sergey V. Yaskevich y Anton A. Duchkov. "LOCALIZATION OF MICROSEISMIC EVENTS USING PHYSICS-INFORMED NEURAL NETWORK SOLUTION TO THE EIKONAL EQUATION". Interexpo GEO-Siberia 2, n.º 2 (21 de mayo de 2021): 32–38. http://dx.doi.org/10.33764/2618-981x-2021-2-2-32-38.

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The paper demonstrates an algorithm for using physics-informed neural networks in workflow of processing microseismic data regarding the problem of localization of microseismic events. The proposed algorithm involves the use of a physics-informed neural network solution to the eikonal equation to calculate the traveltimes of the first arrivals. As a result, the network solution is compared with the observed arrival times to solve the inverse kinematic problem to determine the coordinates of the event locations. Using a synthetic 3D example, it was shown that the average absolute error of the arrival time misfit was less than 0.25 ms, and the average localization error did not exceed 4.5 meters.

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Zhi, Peng, Yuching Wu, Cheng Qi, Tao Zhu, Xiao Wu y Hongyu Wu. "Surrogate-Based Physics-Informed Neural Networks for Elliptic Partial Differential Equations". Mathematics 11, n.º 12 (15 de junio de 2023): 2723. http://dx.doi.org/10.3390/math11122723.

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The purpose of this study is to investigate the role that a deep learning approach could play in computational mechanics. In this paper, a convolutional neural network technique based on modified loss function is proposed as a surrogate of the finite element method (FEM). Several surrogate-based physics-informed neural networks (PINNs) are developed to solve representative boundary value problems based on elliptic partial differential equations (PDEs). According to the authors’ knowledge, the proposed method has been applied for the first time to solve boundary value problems with elliptic partial differential equations as the governing equations. The results of the proposed surrogate-based approach are in good agreement with those of the conventional FEM. It is found that modification of the loss function could improve the prediction accuracy of the neural network. It is demonstrated that to some extent, the deep learning approach could replace the conventional numerical method as a significant surrogate model.

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Rafiq, Muhammad, Ghazala Rafiq y 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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31

Razakh, Taufeq Mohammed, Beibei Wang, Shane Jackson, Rajiv K. Kalia, Aiichiro Nakano, Ken-ichi Nomura y Priya Vashishta. "PND: Physics-informed neural-network software for molecular dynamics applications". SoftwareX 15 (julio de 2021): 100789. http://dx.doi.org/10.1016/j.softx.2021.100789.

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32

Ji, Weiqi, Weilun Qiu, Zhiyu Shi, Shaowu Pan y Sili Deng. "Stiff-PINN: Physics-Informed Neural Network for Stiff Chemical Kinetics". Journal of Physical Chemistry A 125, n.º 36 (31 de agosto de 2021): 8098–106. http://dx.doi.org/10.1021/acs.jpca.1c05102.

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33

Chakraborty, Souvik. "Transfer learning based multi-fidelity physics informed deep neural network". Journal of Computational Physics 426 (febrero de 2021): 109942. http://dx.doi.org/10.1016/j.jcp.2020.109942.

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34

Meng, Xuhui, Zhen Li, Dongkun Zhang y George Em Karniadakis. "PPINN: Parareal physics-informed neural network for time-dependent PDEs". Computer Methods in Applied Mechanics and Engineering 370 (octubre de 2020): 113250. http://dx.doi.org/10.1016/j.cma.2020.113250.

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35

Dalton, David, Dirk Husmeier y Hao Gao. "Physics-informed graph neural network emulation of soft-tissue mechanics". Computer Methods in Applied Mechanics and Engineering 417 (diciembre de 2023): 116351. http://dx.doi.org/10.1016/j.cma.2023.116351.

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36

Liu, Yu y Wentao Ma. "Gradient auxiliary physics-informed neural network for nonlinear biharmonic equation". Engineering Analysis with Boundary Elements 157 (diciembre de 2023): 272–82. http://dx.doi.org/10.1016/j.enganabound.2023.09.013.

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37

Du, Meiyuan, Chi Zhang, Sheng Xie, Fang Pu, Da Zhang y Deyu Li. "Investigation on aortic hemodynamics based on physics-informed neural network". Mathematical Biosciences and Engineering 20, n.º 7 (2023): 11545–67. http://dx.doi.org/10.3934/mbe.2023512.

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<abstract> <p>Pressure in arteries is difficult to measure non-invasively. Although computational fluid dynamics (CFD) provides high-precision numerical solutions according to the basic physical equations of fluid mechanics, it relies on precise boundary conditions and complex preprocessing, which limits its real-time application. Machine learning algorithms have wide applications in hemodynamic research due to their powerful learning ability and fast calculation speed. Therefore, we proposed a novel method for pressure estimation based on physics-informed neural network (PINN). An ideal aortic arch model was established according to the geometric parameters from human aorta, and we performed CFD simulation with two-way fluid-solid coupling. The simulation results, including the space-time coordinates, the velocity and pressure field, were obtained as the dataset for the training and validation of PINN. Nondimensional Navier-Stokes equations and continuity equation were employed for the loss function of PINN, to calculate the velocity and relative pressure field. Post-processing was proposed to fit the absolute pressure of the aorta according to the linear relationship between relative pressure, elastic modulus and displacement of the vessel wall. Additionally, we explored the sensitivity of the PINN to the vascular elasticity, blood viscosity and blood velocity. The velocity and pressure field predicted by PINN yielded good consistency with the simulated values. In the interested region of the aorta, the relative errors of maximum and average absolute pressure were 7.33% and 5.71%, respectively. The relative pressure field was found most sensitive to blood velocity, followed by blood viscosity and vascular elasticity. This study has proposed a method for intra-vascular pressure estimation, which has potential significance in the diagnosis of cardiovascular diseases.</p> </abstract>

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38

Ngo, Quang-Ha, Bang L. H. Nguyen, Tuyen V. Vu, Jianhua Zhang y Tuan Ngo. "Physics-informed graphical neural network for power system state estimation". Applied Energy 358 (marzo de 2024): 122602. http://dx.doi.org/10.1016/j.apenergy.2023.122602.

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39

ma, fei, Sipei Zhao y Thushara Abhayapala. "Physics-informed neural network assisted spherical microphone array signal processing". Journal of the Acoustical Society of America 154, n.º 4_supplement (1 de octubre de 2023): A182. http://dx.doi.org/10.1121/10.0023200.

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Thanks to their rotational symmetry that facilitates three-dimensional signal processing, spherical microphone arrays are the common array apertures used for spatial audio and acoustic applications. However, practical implementations of spherical microphone arrays suffer from two issues. First, at high frequency range, a large number of sensors are needed to accurately capture a sound field. Second, the accompanying signal processing algorithm, i.e., the spherical harmonic decomposition method, requires a variable radius array or a rigid surface array to circumvent the spherical Bessel function nulls. Such arrays are hard to design and introduce a scattering field. To address these issues, this paper proposes to assist a spherical microphone array with a physics-informed neural network (PINN) for three-dimensional signal processing. The PINN models the sound field around the array based on the sensor measurements and the acoustic wave equation, augmenting the sound field information captured by the array through prediction. This makes it possible to analyze a high frequency sound field with a reduced number of sensors and avoid the spherical Bessel function nulls with a simple single radius open-sphere microphone array.

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40

Yin, Jichao, Ziming Wen, Shuhao Li, Yaya Zhang y Hu Wang. "Dynamically configured physics-informed neural network in topology optimization applications". Computer Methods in Applied Mechanics and Engineering 426 (junio de 2024): 117004. http://dx.doi.org/10.1016/j.cma.2024.117004.

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41

Xypakis, Emmanouil, Valeria deTurris, Fabrizio Gala, Giancarlo Ruocco y Marco Leonetti. "Physics-informed machine learning for microscopy". EPJ Web of Conferences 266 (2022): 04007. http://dx.doi.org/10.1051/epjconf/202226604007.

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We developed a physics-informed deep neural network architecture able to achieve signal to noise ratio improvements starting from low exposure noisy data. Our model is based on the nature of the photon detection process characterized by a Poisson probability distribution which we included in the training loss function. Our approach surpasses previous algorithms performance for microscopy data, moreover, the generality of the physical concepts employed here, makes it readily exportable to any imaging context.

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42

Lee, Brandon M. y David R. Dowling. "Training physics-informed neural networks to directly predict acoustic field values in simple environments". Journal of the Acoustical Society of America 152, n.º 4 (octubre de 2022): A49. http://dx.doi.org/10.1121/10.0015499.

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As acousticians turn to machine learning for solutions to old and new problems, neural networks have become a go-to tool due to their capacity for model representation and quick forward computations. However, these benefits come at the cost of obscurity; it is difficult to determine whether the proficiency of a trained neural network is limited by training effort, training dataset size or scope, or compatibility of the network’s design with the data’s underlying pattern of interest. For neural networks trained to provide solutions to the point-source Helmholtz-equation in axisymmetric single-path, two-path, and multi-path (ideal waveguide) environments with constant sound speed, the key limitations are the dataset composition and network design. This study examines the effects on performance and explainablity which result from providing physical information (governing equation and boundary conditions) to these neural networks, instead of only acoustic-field solutions generated from well-known analytic solutions. The outcome of using physics-informed neural networks (PINNs) for these simple environments informs their possible extension to more complex, realistic environments. This study emphasizes source frequencies in the 100’s of Hz, depths up to 500 m, and ranges up to 10 km for sound speeds near 1500 m/s. [Work supported by the NDSEG fellowship program.]

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43

Zhang, Guangtao, Huiyu Yang, Guanyu Pan, Yiting Duan, Fang Zhu y Yang Chen. "Constrained Self-Adaptive Physics-Informed Neural Networks with ResNet Block-Enhanced Network Architecture". Mathematics 11, n.º 5 (22 de febrero de 2023): 1109. http://dx.doi.org/10.3390/math11051109.

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Physics-informed neural networks (PINNs) have been widely adopted to solve partial differential equations (PDEs), which could be used to simulate physical systems. However, the accuracy of PINNs does not meet the needs of the industry, and severely degrades, especially when the PDE solution has sharp transitions. In this paper, we propose a ResNet block-enhanced network architecture to better capture the transition. Meanwhile, a constrained self-adaptive PINN (cSPINN) scheme is developed to move PINN’s objective to the areas of the physical domain, which are difficult to learn. To demonstrate the performance of our method, we present the results of numerical experiments on the Allen–Cahn equation, the Burgers equation, and the Helmholtz equation. We also show the results of solving the Poisson equation using cSPINNs on different geometries to show the strong geometric adaptivity of cSPINNs. Finally, we provide the performance of cSPINNs on a high-dimensional Poisson equation to further demonstrate the ability of our method.

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44

Usama, Muhammad, Rui Ma, Jason Hart y Mikaela Wojcik. "Physics-Informed Neural Networks (PINNs)-Based Traffic State Estimation: An Application to Traffic Network". Algorithms 15, n.º 12 (27 de noviembre de 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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Silva Garzon, Camilo Fernando, Philip Bonnaire, Nguyen Anh Khoa Doan, Korbinian Niebler y Camilo Fernando Silva. "Towards reconstruction of acoustic fields via physics-informed neural networks". INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, n.º 3 (1 de febrero de 2023): 4773–82. http://dx.doi.org/10.3397/in_2022_0690.

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Acoustic measurements, obtained by microphones positioned at strategic places, are of great utility for the monitoring of a given acoustic system and for its protection in case large pressure fluctuations are measured. Such strategies are reliable as long as the microphones are properly positioned, which is not evident: in some cases the excited acoustic modes are not known beforehand. In this work, we proposed a method based on physics informed neural networks (PINN) in order to reconstruct the entire acoustic field of a given acoustic element, provided some acoustic measurements at some few locations. Such a method makes use of a feed forward neural network, where the cost function is taken as the residual of the acoustic wave equation. Such a residual is computed exploiting the automatic differentiation property of neural networks, in order to obtain the corresponding spatial and time derivatives. Additionally, the measurements of the aforementioned microphones are gathered and used also for the calculation of additional terms in the PINN cost function. By doing so, the most adequate acoustic state is obtained, which satisfy both measurements and the acoustic wave equation. In other words, the acoustic field within the system is reconstructed.

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46

Manikkan, Sreehari y Balaji Srinivasan. "Transfer physics informed neural network: a new framework for distributed physics informed neural networks via parameter sharing". Engineering with Computers, 19 de julio de 2022. http://dx.doi.org/10.1007/s00366-022-01703-9.

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47

Dourado, Arinan y Felipe A. C. Viana. "Physics-Informed Neural Networks for Corrosion-Fatigue Prognosis". Annual Conference of the PHM Society 11, n.º 1 (22 de septiembre de 2019). http://dx.doi.org/10.36001/phmconf.2019.v11i1.814.

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In this paper, we present a novel physics-informed neural network modeling approach for corrosion-fatigue. The hybrid approach is designed to merge physics- informed and data-driven layers within deep neural networks. The result is a cumulative damage model where the physics-informed layers are used to model the relatively well understood physics (crack growth through Paris law) and the data-driven layers account for the hard to model effects (bias in damage accumulation due to corrosion). A numerical experiment is used to present the main features of the proposed physics-informed recurrent neural network for damage accumulation. The test problem consists of predicting corrosion-fatigue of an Al 2024-T3 alloy used on panels of aircraft wing. Besides cyclic loading, the panels are also subjected to saline corrosion. The physics-informed neural network is trained using full observation of inputs (far-field loads, stress ratio and a corrosivity index – defined per airport) and very limited observation of outputs (crack length at inspection for only a small portion of the fleet). Results show that the physics-informed neural network is able to learn the correction in the original fatigue model due to corrosion and predictions are accurate enough for ranking damage in different airplanes in the fleet (which can be used to prioritizing inspection).

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48

Liu Jin-Pin, Wang Bing-Zhong, Chen Chuan-Sheng y Wang Ren. "Inverse design of microwave waveguide devices based on deep physics-informed neural networks". Acta Physica Sinica, 2023, 0. http://dx.doi.org/10.7498/aps.72.20230031.

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Using physics-informed neural networks to solve physical inverse problems is becoming a trend.However,it is difficult to solve the scheme that only introduces physical knowledge through the loss function.Constructing a reasonable loss function to make the results converge becomes a challenge.To address the challenge of physics-informed neural network models for inverse design of electromagnetic devices,a deep physics-informed neural network is introduced by using pattern matching method.The physical equations have been integrated into the network structure when the network is constructed.This feature makes the deep physics-informed neural network have a more concise loss function and higher computational efficiency when solving physical inverse problems.In addition,the training parameters of deep physics-informed neural networks are physically meaningful compared to traditional physicsinformed neural networks.Users can control the network by parameters more easily.Taking the scattering parameter design of a two-port waveguide as an example,we present a new metal topology inverse design scheme and give a detailed explanation.In numerical experiments,we target a set of physically realizable scattering parameters and inversely design the metallic septum using a deep physics-informed neural network.The results show that the method can not only achieve the design target but also obtain solutions with different topologies.The establishment of multiple solutions is extremely valuable in the implementation of the inverse design.It can allow the designer to decide the size and location of the design area more freely while achieving the performance requirements.This scheme is expected to promote the application and development of the inverse design of electromagnetic devices.

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Zapf, Bastian, Johannes Haubner, Miroslav Kuchta, Geir Ringstad, Per Kristian Eide y Kent-Andre Mardal. "Investigating molecular transport in the human brain from MRI with physics-informed neural networks". Scientific Reports 12, n.º 1 (14 de septiembre de 2022). http://dx.doi.org/10.1038/s41598-022-19157-w.

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AbstractIn recent years, a plethora of methods combining neural networks and partial differential equations have been developed. A widely known example are physics-informed neural networks, which solve problems involving partial differential equations by training a neural network. We apply physics-informed neural networks and the finite element method to estimate the diffusion coefficient governing the long term spread of molecules in the human brain from magnetic resonance images. Synthetic testcases are created to demonstrate that the standard formulation of the physics-informed neural network faces challenges with noisy measurements in our application. Our numerical results demonstrate that the residual of the partial differential equation after training needs to be small for accurate parameter recovery. To achieve this, we tune the weights and the norms used in the loss function and use residual based adaptive refinement of training points. We find that the diffusion coefficient estimated from magnetic resonance images with physics-informed neural networks becomes consistent with results from a finite element based approach when the residuum after training becomes small. The observations presented here are an important first step towards solving inverse problems on cohorts of patients in a semi-automated fashion with physics-informed neural networks.

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50

Fang Bo-Lang, Wang Jian-Guo y Feng GuoBin. "Centroid prediction using physics informed neural networks". Acta Physica Sinica, 2022, 0. http://dx.doi.org/10.7498/aps.71.20220670.

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To determine the centroid of far field laser beam spots with highly precision and accuracy under intense noise contamination, a positioning algorithm named Centroid-PINN is proposed, which is based on physics information neural network. A U-Net neural network is utilized to optimize the centroid estimation error. In order to demonstrate this new method, Gaussian spots, polluted with two kinds of noise, including ramp noise and white noise, were generated by simulation to train the neural network. The neural network was tested by two kinds of spots that were Gaussian spots and Sinc-like spots. Both were predicted with high accuracy. Compared with traditional centroid method, the Centroid-PINN needs no parameter tuning, especially can cope with ramp noise interference, being capable of obtaining a high accuracy. This work could be helpful in the development of far field laser beam spot measurement device, also be a reference for the development of Shack-Hartmann wavefront sensor.

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