Physics-Informed Machine Learning & Scientific ML Reading List
Curated by Mouhssine Rifaki | Stanford Electrical Engineering | Last updated August 2026
Physics-informed learning ties neural networks to differential equations, letting data and physics regularize each other. The papers below follow that thread from the original PINN papers and DeepXDE through operator learning, Bayesian formulations, and recent error analyses for the Navier–Stokes setting.
Physics-Informed Machine Learning & Scientific ML: 10 key papers
- Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Raissi et al. Journal of Computational Physics 2019.
- Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
Raissi and Karniadakis. arXiv 2017.
- DeepXDE: A deep learning library for solving differential equations
Lu et al. arXiv 2019.
- Understanding and mitigating gradient pathologies in physics-informed neural networks
Wang et al. arXiv 2020.
- When and why PINNs fail to train: A neural tangent kernel perspective
Wang et al. arXiv 2020.
- Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
Jagtap and Karniadakis. arXiv 2019.
- Error estimates for physics informed neural networks approximating the Navier-Stokes equations
De Ryck et al. arXiv 2022.
- Characterizing possible failure modes in physics-informed neural networks
Krishnapriyan et al. arXiv 2021.
- Learning data driven discretizations for partial differential equations
Bar-Sinai et al. arXiv 2018.
- Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next
Cuomo et al. arXiv 2022.
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