Machine Learning and Computational Mathematics

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Weinan E, Chao Ma, Stephan Wojtowytsch and Lei Wu, “Towards a mathematical understanding of machine learning: What is known and what is not”, https://arxiv.org/pdf/2009.10713.pdf

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2009

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Assyr Abdulle, Weinan E, Bjorn Engquist and Eric Vanden-Eijnden, The heterogenous multiscale methods, Acta Numerica, vol. 21, pp. 1-87, 2012

2012

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Jiequn Han and Weinan E, “Deep learning approximation for stochastic control problems”, Deep Reinforcement Learning Workshop, NIPS (2016), https://arxiv.org/pdf/1611.07422.pdf

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2016

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2016

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Francis Bach, “Breaking the curse of dimensionality with convex neural networks”, Journal of Machine Learning Research, 18(19):1-53, 2017

2017

Cited alongside, same era.

Weinan E, Jiequn Han and Arnulf Jentzen, “Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations”, Communications in Mathematics and Statistics 5, 4 (2017), 349-380

2017

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Lenaic Chizat and Francis Bach, “On the global convergence of gradient descent for over-parameterized models using optimal transport”, In Advances in neural information processing systems, pages 3036-3046, 2018

2018

Cited alongside, same era.

Weinan E, Chao Ma and Lei Wu, “A priori estimates of the population risk for two-layer neural networks”, Communications in Mathematical Sciences, 17(5):1407-1425, 2019; arXiv:1810.06397, 2018

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2018

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Linfeng Zhang, Han Wang and Weinan E, “Reinforced dynamics for the enhanced sampling in large atomic and molecular systems. I. Basic Methodology”, J. Chem. Phys., vol. 148, pp.124113, 2018

2018

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Weinan E, Chao Ma and Lei Wu, “Barron spaces and the flow-induced function spaces for neural network models”, arXiv:1906.08039, 2019

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2019

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Weinan E, Chao Ma, and Lei Wu, “Machine learning from a continuous viewpoint”, arXiv:1912.12777, 2019

Original

2019

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Jiequn Han, Chao Ma, Zheng Ma, Weinan E, “Uniformly Accurate Machine Learning Based Hydrodynamic Models for Kinetic Equations”, Proceedings of the National Academy of Sciences, 116 (44) 21983-21991; DOI: 10.1073/pnas.1909854116, 2019

2019

Later among the works it cites.