Solving high-dimensional partial differential equations using deep learning J Han, A Jentzen, W E Proceedings of the National Academy of Sciences 115 (34), 8505-8510, 2018 | 1247 | 2018 |

String method for the study of rare events E Weinan, W Ren, E Vanden-Eijnden Physical Review B 66 (5), 052301, 2002 | 1149* | 2002 |

Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics L Zhang, J Han, H Wang, R Car, E Weinan Physical review letters 120 (14), 143001, 2018 | 1012 | 2018 |

DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics H Wang, L Zhang, J Han, E Weinan Computer Physics Communications 228, 178-184, 2018 | 578 | 2018 |

Onsager's conjecture on the energy conservation for solutions of Euler's equation P Constantin, W E, ES Titi | 564 | 1994 |

The heterognous multiscale methods E Weinan, B Engquist Communications in Mathematical Sciences 1 (1), 87-132, 2003 | 481 | 2003 |

Heterogeneous multiscale methods: a review E Weinan, B Engquist, X Li, W Ren, E Vanden-Eijnden Communications in computational physics 2 (3), 367-450, 2007 | 477 | 2007 |

A proposal on machine learning via dynamical systems E Weinan Communications in Mathematics and Statistics 1 (5), 1-11, 2017 | 472 | 2017 |

Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations J Han, A Jentzen Communications in mathematics and statistics 5 (4), 349-380, 2017 | 469 | 2017 |

Principles of multiscale modeling E Weinan Cambridge University Press, 2011 | 432 | 2011 |

The heterogeneous multiscale method A Abdulle, E Weinan, B Engquist, E Vanden-Eijnden Acta Numerica 21, 1-87, 2012 | 425 | 2012 |

Transition-path theory and path-finding algorithms for the study of rare events. E Vanden-Eijnden Annual review of physical chemistry 61, 391-420, 2010 | 368 | 2010 |

Finite temperature string method for the study of rare events E Weinan, W Ren, E Vanden-Eijnden J. Phys. Chem. B 109 (14), 6688-6693, 2005 | 333 | 2005 |

Active learning of uniformly accurate interatomic potentials for materials simulation L Zhang, DY Lin, H Wang, R Car, E Weinan Physical Review Materials 3 (2), 023804, 2019 | 326 | 2019 |

Heterogeneous multiscale method: a general methodology for multiscale modeling E Weinan, B Engquist, Z Huang Physical Review B 67 (9), 092101, 2003 | 294 | 2003 |

Towards a theory of transition paths E Vanden-Eijnden Journal of statistical physics 123 (3), 503-523, 2006 | 276 | 2006 |

Boundary conditions for the moving contact line problem W Ren Physics of fluids 19 (2), 2007 | 264 | 2007 |

Invariant measures for Burgers equation with stochastic forcing E Weinan, K Khanin, A Mazel, Y Sinai Annals of Mathematics, 877-960, 2000 | 260 | 2000 |

Stochastic modified equations and adaptive stochastic gradient algorithms Q Li, C Tai, E Weinan International Conference on Machine Learning, 2101-2110, 2017 | 250 | 2017 |

Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics W Ren, E Weinan Journal of Computational Physics 204 (1), 1-26, 2005 | 231 | 2005 |