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Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs).
IEEE Transactions on Neural Networks 9
Lagaris, I.E., Likas, A., Fotiadis, D.I.: Artificial neural networks for solving ordinary and partial differential equations · 1998
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Tech. rep., USDOE Office of Science (SC) (United States) (2019)
Baker, N., Alexander, F., Bremer, T., Hagberg, A., Kevrekidis, Y., Najm, H., Parashar, M., Patra, A., Sethian, J., Wild, S., Willcox, K., Lee, S.: Workshop Report on Basic Research Needs for Scientific Machine Learning: Core Technologies for Artificial Intelligence · 2019
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SIAM Journal on Scientific Computing 41
Heinlein, A., Klawonn, A., Lanser, M., Weber, J.: Machine learning in adaptive domain decomposition methods - predicting the geometric location of constraints · 2019
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IEEE Access 8
Li, K., Tang, K., Wu, T., Liao, Q.: D3m: A deep domain decomposition method for partial differential equations · 2019
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In: K. Chaudhuri, R. Salakhutdinov (eds.) Proceedings of the 36th International Conference on Machine Learning, Proceedings of Machine Learning Research , vol. 97, pp. 5301–5310. PMLR (2019)
Rahaman, N., Baratin, A., Arpit, D., Draxler, F., Lin, M., Hamprecht, F., Bengio, Y., Courville, A.: On the spectral bias of neural networks · 2019
Cited alongside, same era.
Journal of Computational physics 378
Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations · 2019
Cited alongside, same era.
In: Mathematical and Scientific Machine Learning, pp. 269–286. PMLR (2020)
Li, W., Xiang, X., Xu, Y.: Deep domain decomposition method: Elliptic problems · 2020
Cited alongside, same era.
GAMM-Mitteilungen 44
Heinlein, A., Klawonn, A., Lanser, M., Weber, J.: Combining machine learning and domain decomposition methods for the solution of partial differential equations – a review · 2021
Cited alongside, same era.
arXiv preprint arXiv:2107.07871 (2021)
Moseley, B., Markham, A., Nissen-Meyer, T.: Finite basis physics-informed neural networks (fbpinns): a scalable domain decomposition approach for solving differential equations · 2021
Later among the works it cites.
Computer Methods in Applied Mechanics and Engineering 384
Wang, S., Wang, H., Perdikaris, P.: On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks · 2021
Later among the works it cites.
Ph.D. thesis, University of Oxford (2022)
Moseley, B.: Physics-informed machine learning: from concepts to real-world applications · 2022
Closest in time.
Journal of Computational Physics 449
Wang, S., Yu, X., Perdikaris, P.: When and why pinns fail to train: A neural tangent kernel perspective · 2022
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