mlsanityData to 14 Oct 2026

Physics-Informed Neural Networks and Extensions

arXiv 2408.16806 ↗First posted 29 Aug 2024cs.LG cs.AIcited by 8

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Abstract (arXiv)

In this paper, we review the new method Physics-Informed Neural Networks (PINNs) that has become the main pillar in scientific machine learning, we present recent practical extensions, and provide a specific example in data-driven discovery of governing differential equations.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 10 of its 18 references that are in the map. First posted on arXiv 29 Aug 2024.

Builds on

10 of 18 references.

References · 10

  1. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 634
  2. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 373
  3. 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
  4. 2020Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanismcited by 233
  5. 2017Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equationscited by 161
  6. 2018Physics-Informed Generative Adversarial Networks for Stochastic Differential Equationscited by 135
  7. 2020Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEscited by 116
  8. 2018Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systemscited by 89
  9. 2023A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositionscited by 48
  10. 2023AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identificationcited by 29

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 5; 2026: 2.

8 papers.

  1. 2025Representation Meets Optimization: Training PINNs and PIKANs for Gray-Box Discovery in Systems Pharmacologycited by 10
  2. 2024CMINNs: Compartment Model Informed Neural Networks -- Unlocking Drug Dynamicscited by 7
  3. 2025Physics-Informed Machine Learning in Biomedical Science and Engineeringcited by 4
  4. 2026A Physics-Informed Fourier-Wavelet Transformer for Multiscale Computational Fluid Dynamics Surrogate Modelingcited by 2
  5. 2025A Unified Framework for Simultaneous Parameter and Function Discovery in Differential Equationscited by 1
  6. 2025Random Gradient-Free Optimization in Infinite Dimensional Spacescited by 1
  7. 2026Can AI Follow In Einstein's Footsteps?cited by 1
  8. 2025Physics-Informed Neural Networks for Modeling the Martian Induced Magnetospherecited by 0