Theoretical Background of PINNs

[DKreuter]

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• T. Chen and H. Chen. Universal approximation to nonlinear operators by neural networks with arbitrary
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• G.E. Karniadakis, I.G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, and L. Yang. Physics-informed machine
  learning. Nature Reviews Physics, 3(6):422–440, 2021.

• Lu Lu, Xuhui Meng, Zhiping Mao, and George Em Karniadakis. DeepXDE: A deep learning library for
  solving differential equations. SIAM Review, 63(1):208–228, 2021.

• S.Mishra and 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, 2021.

• M. Raissi, P. Perdikaris, and G.E. Karniadakis. Physics informed deep learning (part i): Data-driven solutions
  of nonlinear partial differential equations. arXiv preprint arXiv:1711.10561, 2017.

• K. Teeratorn, T.M. Jørgensen, and N.M. Hamidreza. Physics-informed neural networks for solving inverse
  problems of nonlinear biot’s equations: Batch training. arXiv preprint arXiv:2005.09638, 2020.

• N. Thuerey, P. Holl, M.Mueller, P. Schnell, F. Trost, and K. Um. Physics-based Deep Learning. WWW, 2021.

• L. Yang, X.Meng, and G.E. Karniadakis. B-pinns: Bayesian physics-informed neural networks for forward
  and inverse pde problems with noisy data. Journal of Computational Physics, 425:109913, 2021.