PhyCRNet: Physics-informed convolutional-recurrent network for solving spatiotemporal PDEs

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 PDEs as a basis for data-driven modeling and inve...

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Vydané v:Computer methods in applied mechanics and engineering Ročník 389; s. 114399
Hlavní autori: Ren, Pu, Rao, Chengping, Liu, Yang, Wang, Jian-Xun, Sun, Hao
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Amsterdam Elsevier B.V 01.02.2022
Elsevier BV
Predmet:
Boundary conditions
Burgers equation
Coders
Convolutional-recurrent learning
Deep learning
Encoder–decoder
Feature extraction
Hard-encoding of I/BCs
Machine learning
Mathematical models
Modelling
Neural networks
Partial differential equations
Physics
Physics-informed deep learning
Residual connection
Time marching
Encoder–decoder
Residual connection
Convolutional-recurrent learning
Partial differential equations
Physics-informed deep learning
Hard-encoding of I/BCs
ISSN:0045-7825, 1879-2138
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Shrnutí: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 PDEs as a basis for data-driven modeling and inverse analysis. However, the majority of existing PINN methods, based on fully-connected NNs, pose intrinsic limitations to low-dimensional spatiotemporal parameterizations. Moreover, since the initial/boundary conditions (I/BCs) are softly imposed via penalty, the solution quality heavily relies on hyperparameter tuning. To this end, we propose the novel physics-informed convolutional-recurrent learning architectures (PhyCRNet and PhyCRNet-s) for solving PDEs without any labeled data. Specifically, an encoder–decoder convolutional long short-term memory network is proposed for low-dimensional spatial feature extraction and temporal evolution learning. The loss function is defined as the aggregated discretized PDE residuals, while the I/BCs are hard-encoded in the network to ensure forcible satisfaction (e.g., periodic boundary padding). The networks are further enhanced by autoregressive and residual connections that explicitly simulate time marching. The performance of our proposed methods has been assessed by solving three nonlinear PDEs (e.g., 2D Burgers’ equations, the λ-ω and FitzHugh Nagumo reaction–diffusion equations), and compared against the start-of-the-art baseline algorithms. The numerical results demonstrate the superiority of our proposed methodology in the context of solution accuracy, extrapolability and generalizability. •Presented a novel physics-informed discrete learning strategy for solving PDEs without any labeled data.•Proposed an encoder–decoder convolutional-recurrent scheme for low-dimensional feature learning.•Employed hard-encoding of initial and boundary conditions.•Incorporated autoregressive and residual connections to explicitly simulate time marching.•Demonstrated excellent solution accuracy, extrapolability and generalizability of the proposed methodology.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2021.114399