mlsanityData to 14 Oct 2026

RoPINN: Region Optimized Physics-Informed Neural Networks

arXiv 2405.14369 ↗First posted 23 May 2024cs.LGcited by 26

Not on the map. Why?

Abstract (arXiv)

Physics-informed neural networks (PINNs) have been widely applied to solve partial differential equations (PDEs) by enforcing outputs and gradients of deep models to satisfy target equations. Due to the limitation of numerical computation, PINNs are conventionally optimized on finite selected points. However, since PDEs are usually defined on continuous domains, solely optimizing models on scattered points may be insufficient to obtain an accurate solution for the whole domain. To mitigate this inherent deficiency of the default scatter-point optimization, this paper proposes and theoretically studies a new training paradigm as region optimization. Concretely, we propose to extend the optimization process of PINNs from isolated points to their continuous neighborhood regions, which can theoretically decrease the generalization error, especially for hidden high-order constraints of PDEs. A practical training algorithm, Region Optimized PINN (RoPINN), is seamlessly derived from this new paradigm, which is implemented by a straightforward but effective Monte Carlo sampling method. By calibrating the sampling process into trust regions, RoPINN finely balances optimization and generalization error. Experimentally, RoPINN consistently boosts the performance of diverse PINNs on a wide range of PDEs without extra backpropagation or gradient calculation. Code is available at this repository: https://github.com/thuml/RoPINN.

Key facts. Cited by 26 papers in the map (data through 14 Oct 2026). Builds on 34 of its 59 references that are in the map. First posted on arXiv 23 May 2024.

Builds on

34 of 59 references.

References · 34

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,399
  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  4. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  5. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,621
  6. 2017Visualizing the Loss Landscape of Neural Netscited by 1,130
  7. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 678
  8. 2024KAN: Kolmogorov-Arnold Networkscited by 649
  9. 2021Characterizing possible failure modes in physics-informed neural networkscited by 643
  10. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 634
  11. 2019DeepXDE: A deep learning library for solving differential equationscited by 619
  12. 2015Train faster, generalize better: Stability of stochastic gradient descentcited by 552
22 more
  1. 2019PyHessian: Neural Networks Through the Lens of the Hessiancited by 292
  2. 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
  3. 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 236
  4. 2018Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equationscited by 235
  5. 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 222
  6. 2018AdaGrad stepsizes: Sharp convergence over nonconvex landscapescited by 182
  7. 2020PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domaincited by 174
  8. 2019Variational Physics-Informed Neural Networks For Solving Partial Differential Equationscited by 148
  9. 2023An Expert's Guide to Training Physics-informed Neural Networkscited by 126
  10. 2020Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEscited by 116
  11. 2024Challenges in Training PINNs: A Loss Landscape Perspectivecited by 113
  12. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 92
  13. 2023PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEscited by 87
  14. 2022Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Samplingcited by 73
  15. 2023PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networkscited by 64
  16. 2021Learning in Sinusoidal Spaces with Physics-Informed Neural Networkscited by 62
  17. 2021Quadratic Residual Networks: A New Class of Neural Networks for Solving Forward and Inverse Problems in Physics Involving PDEscited by 43
  18. 2021Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networkscited by 43
  19. 2019VarNet: Variational Neural Networks for the Solution of Partial Differential Equationscited by 35
  20. 2022Stability Analysis and Generalization Bounds of Adversarial Trainingcited by 30
  21. 2022Lagrangian PINNs: A causality-conforming solution to failure modes of physics-informed neural networkscited by 26
  22. 2023MultiAdam: Parameter-wise Scale-invariant Optimizer for Multiscale Training of Physics-informed Neural Networkscited by 17

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 3; 2025: 14; 2026: 9.

26 papers.

Sort:

  1. 2024Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networkscited by 38
  2. 2026Transolver-3: Scaling Up Transformer Solvers to Industrial-Scale Geometriescited by 20
  3. 2024Higher-order-ReLU-KANs (HRKANs) for solving physics-informed neural networks (PINNs) more accurately, robustly and fastercited by 13
  4. 2025FP64 is All You Need: Rethinking Failure Modes in Physics-Informed Neural Networkscited by 12
  5. 2025Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunitiescited by 11
  6. 2025PhySense: Sensor Placement Optimization for Accurate Physics Sensingcited by 11
  7. 2025ProPINN: Demystifying Propagation Failures in Physics-Informed Neural Networkscited by 6
  8. 2025Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspectivecited by 6
  9. 2026Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operatorscited by 6
  10. 2025Integration Matters for Learning PDEs with Backward SDEscited by 3
  11. 2025Neuro-Spectral Architectures for Causal Physics-Informed Networkscited by 3
  12. 2024SetPINNs: Set-based Physics-informed Neural Networkscited by 2
14 more
  1. 2025Revisiting Heat Flux Analysis of Tungsten Monoblock Divertor on EAST using Physics-Informed Neural Networkcited by 2
  2. 2025KAA: Kolmogorov-Arnold Attention for Enhancing Attentive Graph Neural Networkscited by 1
  3. 2025Neural Modular Physics for Elastic Simulationcited by 1
  4. 2026naPINN: Noise-Adaptive Physics-Informed Neural Networks for Recovering Physics from Corrupted Measurementcited by 1
  5. 2026Unveiling Multi-regime Patterns in SciML: Distinct Failure Modes and Regime-specific Optimizationcited by 1
  6. 2025Conformal mapping based Physics-informed neural networks for designing neutral inclusionscited by 0
  7. 2025Quasi-Random Physics-informed Neural Networkscited by 0
  8. 2025PHASE: Physics-Integrated, Heterogeneity-Aware Surrogates for Scientific Simulationscited by 0
  9. 2025AutoBalance: An Automatic Balancing Framework for Training Physics-Informed Neural Networkscited by 0
  10. 2026MetaColloc: Optimization-Free PDE Solving via Meta-Learned Basis Functionscited by 0
  11. 2026One-Step Evolution for Long-Time Extrapolation: An Error-Bound-Informed and Prior-Guided Neural Residual Framework for Autonomous PDEscited by 0
  12. 2026PINNForge: Execution-Grounded Evolutionary Design of Physics-Informed Neural Networkscited by 0
  13. 2026NEXT: Physics-Informed Neuro-Spectral Exponential Time Differencing Architecturescited by 0
  14. 2026PE-EK-PINN: Physics Embedding with Evolving Kernel for Scalable Physics-Informed Neural Networkscited by 0