mlsanityData to 7 Oct 2026

On the Generalization of PINNs outside the training domain and the Hyperparameters influencing it

arXiv 2302.07557 ↗First posted 15 Feb 2023cs.LGcited by 10

Not on the map. Why?

Abstract (arXiv)

Physics-Informed Neural Networks (PINNs) are Neural Network architectures trained to emulate solutions of differential equations without the necessity of solution data. They are currently ubiquitous in the scientific literature due to their flexible and promising settings. However, very little of the available research provides practical studies that aim for a better quantitative understanding of such architecture and its functioning. In this paper, we perform an empirical analysis of the behavior of PINN predictions outside their training domain. The primary goal is to investigate the scenarios in which a PINN can provide consistent predictions outside the training area. Thereinafter, we assess whether the algorithmic setup of PINNs can influence their potential for generalization and showcase the respective effect on the prediction. The results obtained in this study returns insightful and at times counterintuitive perspectives which can be highly relevant for architectures which combines PINNs with domain decomposition and/or adaptive training strategies.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 30 of its 55 references that are in the map. First posted on arXiv 15 Feb 2023.

Builds on

30 of 55 references.

References · 30

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2021Characterizing possible failure modes in physics-informed neural networkscited by 632
  3. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  4. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  5. 2019The generalization error of random features regression: Precise asymptotics and double descent curvecited by 410
  6. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 362
  7. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 329
  8. 2017High-dimensional dynamics of generalization error in neural networkscited by 238
  9. 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
  10. 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 233
  11. 2018Deep learning generalizes because the parameter-function map is biased towards simple functionscited by 180
  12. 2017Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equationscited by 158
18 more
  1. 2022Respecting causality is all you need for training physics-informed neural networkscited by 154
  2. 2021Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equationscited by 142
  3. 2020Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEscited by 101
  4. 2019Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networkscited by 76
  5. 2022Error estimates for physics informed neural networks approximating the Navier-Stokes equationscited by 63
  6. 2021Scientific Machine Learning Benchmarkscited by 60
  7. 2021Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEscited by 56
  8. 2022Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodologycited by 43
  9. 2022Machine Learning in Aerodynamic Shape Optimizationcited by 39
  10. 2021Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domainscited by 37
  11. 2018Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Datacited by 36
  12. 2022Accelerated Training of Physics-Informed Neural Networks (PINNs) using Meshless Discretizationscited by 26
  13. 2022Investigating molecular transport in the human brain from MRI with physics-informed neural networkscited by 24
  14. 2022On the Role of Fixed Points of Dynamical Systems in Training Physics-Informed Neural Networkscited by 23
  15. 2022Experience report of physics-informed neural networks in fluid simulations: pitfalls and frustrationcited by 21
  16. 2020Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequencescited by 20
  17. 2022Improved Training of Physics-Informed Neural Networks with Model Ensemblescited by 19
  18. 2022Auto-PINN: Understanding and Optimizing Physics-Informed Neural Architecturecited by 13

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 0; 2025: 6; 2026: 3.

10 papers.

  1. 2023Solutions to Elliptic and Parabolic Problems via Finite Difference Based Unsupervised Small Linear Convolutional Neural Networkscited by 2
  2. 2025A Generalizable Physics-Enhanced State Space Model for Long-Term Dynamics Forecasting in Complex Environmentscited by 2
  3. 2025Limitations of Physics-Informed Neural Networks: a Study on Smart Grid Surrogationcited by 0
  4. 2025Benchmarking Physics-Informed Neural Networks and Boundary Elements Methods for Wave Scatteringcited by 0
  5. 2025A Neural Network for the Identical Kuramoto Equation: Architectural Considerations and Performance Evaluationcited by 0
  6. 2025Physics-Informed Spiking Neural Networks via Conservative Flux Quantizationcited by 0
  7. 2025Physics-Informed Neural Networks for Modeling the Martian Induced Magnetospherecited by 0
  8. 2026On the Role of Consistency Between Physics and Data in Physics-Informed Neural Networkscited by 0
  9. 2026UniPINN: A Unified PINN Framework for Multi-task Learning of Diverse Navier-Stokes Equationscited by 0
  10. 2026Hybrid Quantum-Classical PINNs for Scientific Computing: A Multi-GPU Open-Source Frameworkcited by 0