Solving High-Dimensional PDEs with Latent Spectral Models [PDF]
International Conference on Machine Learning, 2023 Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs.
Haixu Wu +4 more
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A graph convolutional autoencoder approach to model order reduction for parametrized PDEs [PDF]
Journal of Computational Physics, 2023 The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real-time and many-query evaluations of parametric
F. Pichi, B. Moya, J. Hesthaven
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NAS-PINN: Neural architecture search-guided physics-informed neural network for solving PDEs [PDF]
Journal of Computational Physics, 2023 Physics-informed neural network (PINN) has been a prevalent framework for solving PDEs since proposed. By incorporating the physical information into the neural network through loss functions, it can predict solutions to PDEs in an unsupervised manner ...
Yifan Wang, L. Zhong
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PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs [PDF]
Neural Information Processing Systems, 2023 While significant progress has been made on Physics-Informed Neural Networks (PINNs), a comprehensive comparison of these methods across a wide range of Partial Differential Equations (PDEs) is still lacking.
Zhongkai Hao +10 more
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PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs [PDF]
Computer Methods in Applied Mechanics and Engineering, 2021 Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks (PINNs) to solve ...
Pu Ren +4 more
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PhyGeoNet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain [PDF]
Journal of Computational Physics, 2020 Recently, the advent of deep learning has spurred interest in the development of physics-informed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a parametric setting.
Han Gao, Luning Sun, Jian-Xun Wang
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POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition [PDF]
Computer Methods in Applied Mechanics and Engineering, 2021 Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional reduced order models (ROMs) - built, e.g., through proper orthogonal decomposition (POD) - when applied to nonlinear time-
S. Fresca, A. Manzoni
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Bridging Traditional and Machine Learning-based Algorithms for Solving PDEs: The Random Feature Method [PDF]
Journal of Machine Learning, 2022 One of the oldest and most studied subject in scientific computing is algorithms for solving partial differential equations (PDEs). A long list of numerical methods have been proposed and successfully used for various applications.
Jingrun Chen +3 more
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Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEs [PDF]
at - Automatisierungstechnik, 2023 Unlike ODEs, whose models involve system matrices and whose controllers involve vector or matrix gains, PDE models involve functions in those roles functional coefficients, dependent on the spatial variables, and gain functions dependent on space as well.
M. Krstić, L. Bhan, Yuanyuan Shi
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Optimal control of PDEs using physics-informed neural networks [PDF]
Journal of Computational Physics, 2021 Physics-informed neural networks (PINNs) have recently become a popular method for solving forward and inverse problems governed by partial differential equations (PDEs). By incorporating the residual of the PDE into the loss function of a neural network-
Saviz Mowlavi, S. Nabi
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