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Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundations
Qianxiao Li, Cheng Tai, Weinan E
We develop the mathematical foundations of the stochastic modified equations (SME) framework for analyzing the dynamics of stochastic gradient algorithms, where the latter is appro…
Active Learning of Uniformly Accurate Inter-atomic Potentials for Materials Simulation
Linfeng Zhang, De-Ye Lin, Han Wang +2
An active learning procedure called Deep Potential Generator (DP-GEN) is proposed for the construction of accurate and transferable machine learning-based models of the potential e…
Monge-Ampère Flow for Generative Modeling
Linfeng Zhang, Weinan E, Lei Wang
We present a deep generative model, named Monge-Ampère flow, which builds on continuous-time gradient flow arising from the Monge-Ampère equation in optimal transport theory. The g…
Model Reduction with Memory and the Machine Learning of Dynamical Systems
Chao Ma, Jianchun Wang, Weinan E
The well-known Mori-Zwanzig theory tells us that model reduction leads to memory effect. For a long time, modeling the memory effect accurately and efficiently has been an importan…
Solving Many-Electron Schrödinger Equation Using Deep Neural Networks
Jiequn Han, Linfeng Zhang, Weinan E
We introduce a new family of trial wave-functions based on deep neural networks to solve the many-electron Schrödinger equation. The Pauli exclusion principle is dealt with explici…
End-to-end Symmetry Preserving Inter-atomic Potential Energy Model for Finite and Extended Systems
Linfeng Zhang, Jiequn Han, Han Wang +3
Machine learning models are changing the paradigm of molecular modeling, which is a fundamental tool for material science, chemistry, and computational biology. Of particular inter…