Resolution invariant deep operator network for PDEs with complex geometries
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Abstract (arXiv)
Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO have demonstrated the superiority of solving partial differential equations (PDEs) over other deep learning methods. However, the spatial domain of its input function needs to be identical to its output, which limits its applicability. For instance, the widely used Fourier neural operator (FNO) fails to approximate the operator that maps the boundary condition to the PDE solution. To address this issue, we propose a novel framework called resolution-invariant deep operator (RDO) that decouples the spatial domain of the input and output. RDO is motivated by the Deep operator network (DeepONet) and it does not require retraining the network when the input/output is changed compared with DeepONet. RDO takes functional input and its output is also functional so that it keeps the resolution invariant property of NO. It can also resolve PDEs with complex geometries whereas NO fail. Various numerical experiments demonstrate the advantage of our method over DeepONet and FNO.
Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 34 of its 61 references that are in the map. First posted on arXiv 1 Feb 2024.
Builds on
34 of 61 references.
References · 34
- 2017Attention Is All You Needcited by 59,932
- 2015Deep Residual Learning for Image Recognitioncited by 51,809
- 2014Adam: A Method for Stochastic Optimizationcited by 36,960
- 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
- 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
- 2014Neural Machine Translation by Jointly Learning to Align and Translatecited by 4,530
- 2018Neural Ordinary Differential Equationscited by 3,733
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
- 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
- 2021Generalizing to Unseen Domains: A Survey on Domain Generalizationcited by 762
- 2017Solving high-dimensional partial differential equations using deep learningcited by 549
22 more
- 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 516
- 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 416
- 2021Choose a Transformer: Fourier or Galerkincited by 333
- 2022Transformer for Partial Differential Equations' Operator Learningcited by 270
- 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 261
- 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 220
- 2020Transformers for Modeling Physical Systemscited by 105
- 2021A physics-informed variational DeepONet for predicting the crack path in brittle materialscited by 98
- 2022Learning Operators with Coupled Attentioncited by 88
- 2018Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantificationcited by 81
- 2022Failure-informed adaptive sampling for PINNscited by 64
- 2023Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustnesscited by 60
- 2022Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodologycited by 43
- 2019Almost Unsupervised Text to Speech and Automatic Speech Recognitioncited by 41
- 2021Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow modelscited by 34
- 2021A Metalearning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEscited by 31
- 2022Semi-supervised Invertible Neural Operators for Bayesian Inverse Problemscited by 25
- 2022Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equationscited by 20
- 2023GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEscited by 20
- 2022Learning the Solution Operator of Boundary Value Problems using Graph Neural Networkscited by 17
- 2023Koopman operator learning using invertible neural networkscited by 12
- 2022PhyGNNet: Solving spatiotemporal PDEs with Physics-informed Graph Neural Networkcited by 5
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