Transferable Neural Networks for Partial Differential Equations

Author:

Zhang Zezhong,Bao Feng,Ju LiliORCID,Zhang Guannan

Funder

U.S. Department of Energy

Publisher

Springer Science and Business Media LLC

Reference45 articles.

1. 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. J. Comput. Phys. 378, 686–707 (2019)

2. Weinan, E., Bing, Y.: The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems. Commun. Math. Stat. 6(1), 1–12 (2018)

3. Long, Z., Lu, Y., Ma, X., Dong, B.: PDE-Net: Learning PDEs from data. In: International Conference on Machine Learning, pp. 3214–3222, (2018)

4. Zang, Y., Bao, G., Ye, X., Zhou, H.: Weak adversarial networks for high dimensional partial differential equations. J. Comput. Phys. 411, 109409 (2020)

5. Li, Z., Kovachki, N.B., Azizzadenesheli, K., Bhattacharya, K., Stuart, A., Anandkumar, A. et al.: Fourier neural operator for parametric partial differential equations. In: International Conference on Learning Representations, (2021)

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