Machine Learning and PDEs

[13] Z. Song, M. Cameron, H. Yang*. A Finite Expression Method for Solving High-Dimensional Committor Problems. Submitted. [pdf]

[12] W. Hao^, C. Wang^*, X. Xu^, H. Yang^. Deep Learning via Neural Energy Descent. Submitted. [pdf]

[11] S. Liang, S. W. Jiang, J. Harlim, H. Yang^*, Solving PDEs on Unknown Manifolds with Machine Learning. Applied and Computational Harmonic Analysis, 2024.  [pdf] [doi]

[10] Y. Jiao^, Y. Lai^, Y. Wang^, H. Yang}^*, Y. Yang^. Convergence Analysis of the Deep Galerkin Method for Weak Solutions. In Patricia Alonso Ruiz, Michael Hinz, Kasso A. Okoudjou, Luke G. Rogers, Alexander Teplyaev, From Classical Analysis to Analysis on Fractals, A Tribute to Robert Strichartz, Volume 1. [pdf] [doi]

[9] K. Chen^, C. Wang^, H. Yang^*. Deep Operator Learning Lessens the Curse of Dimensionality for PDEs. Submitted. [pdf] [doi]

[8] Y. Ong^, Z. Shen^, H. Yang^*. IAE-Net: Integral Autoencoders for Discretization-Invariant Learning. Journal of Machine Learning Research, 2022.  [pdf] [doi]

[7] S. Liang^, L. Lyu^, C. Wang ^, H. Yang^*. Reproducing Activation Function for Deep Learning. Communication in Mathematical Sciences. [pdf] [doi]

[6] F. Chen^, J. Huang^, C. Wang ^, H. Yang^*. Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning. SIAM Journal of Scientific Computing, 2023. [pdf] [doi]

[5] T. Luo^, H. Yang^*. Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory. Submitted. [pdf] 

[4] Y. Gu^, J. Harlim^, S. Liang^*, H. Yang^, Stationary Density Estimation of Itô Diffusions Using Deep Learning. SIAM Journal on Numerical Analysis, 2022. [pdf] [doi]

[3] Y. Gu, H. Yang*, C. Zhou. SelectNet: Self-Paced Learning for High-dimensional Partial Differential Equations. Submitted.  Journal of Computational Physics, 2021. [pdf] [doi]

[2] Y. Gu^, C. Wang ^, H. Yang^*. Structure Probing Neural Network Deflation. Journal of Computational Physics, 2021.  [pdf]  [doi]

[1] J. Huang^, H. Wang^, H. Yang^*. Int-Deep: A Deep Learning Initialized Iterative Method for Nonlinear Problems. Journal of Computational Physics, 2020. [pdf] [doi]

^: Equal contribution; *: Corresponding author.