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Physics-informed neural networks (PINNs) as a means of solving partial differential equations (PDE) have garnered much attention in the Computational Science and Engineering (CS&E) world.
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X. Meng, Z. Li, D. Zhang, G. E. Karniadakis, PPINN: Parareal physics-informed neural network for time-dependent PDEs, Computer Methods in Applied Mechanics and Engineering 370 (2020) 113250
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A. Krishnapriyan, A. Gholami, S. Zhe, R. Kirby, M. W. Mahoney, Characterizing possible failure modes in physics-informed neural networks, Advances in Neural Information Processing Systems 34 (2021) 26548–26560
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K. Shukla, A. D. Jagtap, J. L. Blackshire, D. Sparkman, G. Em Karniadakis, A Physics-Informed Neural Network for Quantifying the Microstructural Properties of Polycrystalline Nickel Using Ultrasound Data: A promising approach for solving inverse problems, IEEE Signal Processing Magazine 39 (1) (2022) 68–77 · 2021
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L. Lu, X. Meng, Z. Mao, G. E. Karniadakis, DeepXDE: A deep learning library for solving differential equations, SIAM Review 63 (1) (2021) 208–228
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S. Wang, Y. Teng, P. Perdikaris, Understanding and mitigating gradient flow pathologies in physics-informed neural networks, SIAM Journal on Scientific Computing 43 (5) (2021) A3055–A3081
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A. D. Jagtap, D. Mitsotakis, G. E. Karniadakis, Deep learning of inverse water waves problems using multi-fidelity data: Application to Serre–Green–Naghdi equations, Ocean Engineering 248 (2022) 110775
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S. Mishra, R. Molinaro, Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs, IMA Journal of Numerical Analysis 42 (2) (2022) 981–1022
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S. Wang, X. Yu, P. Perdikaris, When and why PINNs fail to train: A neural tangent kernel perspective, Journal of Computational Physics 449 (2022) 110768
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A. Bihlo, R. O. Popovych, Physics-informed neural networks for the shallow-water equations on the sphere, Journal of Computational Physics 456 (2022) 111024
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