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Numerical study of metastability due to tunneling: The quantum string method, , , , and . Physica A: Statistical Mechanics and its Applications, 379 (2): 491--502 (Jun 15, 2007)Towards a Theory of Transition Paths, and . Journal of Statistical Physics, 123 (3): 503--523 (2006)The local microscale problem in the multiscale modeling of strongly heterogeneous media: Effects of boundary conditions and cell size., and . J. Comput. Phys., 222 (2): 556-572 (2007)Analysis of the Gradient Descent Algorithm for a Deep Neural Network Model with Skip-connections., , , and . CoRR, (2019)A Priori Estimates of the Population Risk for Residual Networks., , and . CoRR, (2019)A Machine Learning Enhanced Algorithm for the Optimal Landing Problem., , , , , and . MSML, volume 190 of Proceedings of Machine Learning Research, page 319-334. PMLR, (2022)Efficient sampling of high-dimensional free energy landscapes using adaptive reinforced dynamics., , , , , and . Nat. Comput. Sci., 2 (1): 20-29 (2022)Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations., , and . CoRR, (2017)Stochastic Modified Equations and Adaptive Stochastic Gradient Algorithms., , and . ICML, volume 70 of Proceedings of Machine Learning Research, page 2101-2110. PMLR, (2017)86 PFLOPS Deep Potential Molecular Dynamics simulation of 100 million atoms with ab initio accuracy., , , , , , , , and . CoRR, (2020)