Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

By Sifan Wang, Hanwen Wang, Paris Perdikaris. Science Advances, 2021

1,131 citations recorded by the source corpus.

Enabling the rapid emulation of parametric differential equations with physics-informed deep operator networks.

Subfields: Computational Mechanics, Mechanical Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/664e48f5a674b38c7765e1011b16a96feab359d2

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Citations in the corpus

Neural Operator: Learning Maps Between Function Spaces (2021, background): “Similarly, one can combine operator learning with physics constraints (Wang et al., 2021; Li et al., 2021).”
Transformer for Partial Differential Equations' Operator Learning (2022, methodology): “The random Fourier projection γ ( · ) alleviate the spectral bias of coordinate-based neural networks (Tancik et al., 2020; Mildenhall et al., 2020), which has also been introduced into physics-informed machine learning in Wang et al. (2021c).”
Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations (2021, background): “[26] proposed DeepONets, which also condition neural networks on their initial conditions such that they learn families of solutions, and DeepONets can be extended to include PINN loss functions [27].”
MIONet: Learning multiple-input operators via tensor product (2022, methodology): “We can also embed physics into the loss function [42, 9] of MIONet to develop physics-informed MIONet.”
GNOT: A General Neural Operator Transformer for Operator Learning (2023, methodology): “Wang et al. (2021; 2022) introduces improved architecture and training methods of DeepONets.”
Multiwavelet-based Operator Learning for Differential Equations (2021, background): “In parallel, another stream of work focuses on constructing the PDE solution function as a NN architecture [31, 42, 57, 65].”
Neural operators for accelerating scientific simulations and design (2023, positive): “This issue can be alleviated by extending PINN to a physics-informed neural operator (PINO) [18, 69, 70], which incorporates training data in addition to PDE information, making the optimization landscape more tractable and enables us to learn the solution operator of complex time-varying PDEs.”
Choose a Transformer: Fourier or Galerkin (2021, methodology): “[90, 91] proposed a DeepONet roughly equivalent to an additive attention, similar to the one in the Neural Turing Machine (NMT) in [7].”
A physics-informed variational DeepONet for predicting the crack path in brittle materials (2021, background): “It is interesting to note that we have tried to solve the problem by minimizing the residual [52].”
A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data (2021, methodology): “However, as demonstrated in [45], a hybrid physics-data training is more effective for realistic problems of the type considered herein, and simply using the governing equations in the loss as suggested in [46] without using data may lead to erroneous results, e.”