mlsanityData to 14 Oct 2026

Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problems

arXiv 2202.02710 ↗First posted 6 Feb 2022cs.LG cs.NA math.APcited by 9

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Abstract (arXiv)

Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. Accurately solving unbounded domain PDEs requires efficient numerical methods that can resolve the dependence of the PDE on the unbounded variable over at least several orders of magnitude. We propose a solution to such problems by combining two classes of numerical methods: (i) adaptive spectral methods and (ii) physics-informed neural networks (PINNs). The numerical approach that we develop takes advantage of the ability of physics-informed neural networks to easily implement high-order numerical schemes to efficiently solve PDEs and extrapolate numerical solutions at any point in space and time. We then show how recently introduced adaptive techniques for spectral methods can be integrated into PINN-based PDE solvers to obtain numerical solutions of unbounded domain problems that cannot be efficiently approximated by standard PINNs. Through a number of examples, we demonstrate the advantages of the proposed spectrally adapted PINNs in solving PDEs and estimating model parameters from noisy observations in unbounded domains.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 23 of its 70 references that are in the map. First posted on arXiv 6 Feb 2022.

Builds on

23 of 70 references.

References · 23

  1. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 7,005
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
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  6. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 527
  7. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 335
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11 more
  1. 2019Variational Physics-Informed Neural Networks For Solving Partial Differential Equationscited by 148
  2. 2020Minimum Width for Universal Approximationcited by 94
  3. 2017Regularization for Deep Learning: A Taxonomycited by 91
  4. 2019How Much Over-parameterization Is Sufficient to Learn Deep ReLU Networks?cited by 84
  5. 2019Physics-Informed Neural Networks for Power Systemscited by 80
  6. 2020Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanicscited by 32
  7. 2021A Metalearning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEscited by 32
  8. 2021Implicit energy regularization of neural ordinary-differential-equation controlcited by 29
  9. 2020Neural Ordinary Differential Equation Control of Dynamics on Graphscited by 24
  10. 2021Recipes for when Physics Fails: Recovering Robust Learning of Physics Informed Neural Networkscited by 18
  11. 2021Adversarial Multi-task Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equationscited by 13

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 3; 2024: 2; 2025: 2; 2026: 1.

9 papers.

  1. 2022Failure-informed adaptive sampling for PINNscited by 64
  2. 2023Neural Spectral Methods: Self-supervised learning in the spectral domaincited by 14
  3. 2024Spectral Informed Neural Network: An Efficient and Low-Memory PINNcited by 6
  4. 2025EddyFormer: Accelerated Neural Simulations of Three-Dimensional Turbulence at Scalecited by 6
  5. 2023Numerical Methods For PDEs Over Manifolds Using Spectral Physics Informed Neural Networkscited by 1
  6. 2025A comprehensive analysis of PINNs: Variants, Applications, and Challengescited by 1
  7. 2023A Spectral Approach for Learning Spatiotemporal Neural Differential Equationscited by 0
  8. 2024Statistical Mechanics and Artificial Neural Networks: Principles, Models, and Applicationscited by 0
  9. 2026Solving nonlinear subsonic compressible flow in infinite domain via multi-stage neural networkscited by 0