10 citations · 20 across the 9 of their papers we have counts for
13 papers · 1 filter
Stationary Density Estimation of Itô Diffusions Using Deep Learning
Yiqi Gu, John Harlim, Senwei Liang +1
In this paper, we consider the density estimation problem associated with the stationary measure of ergodic Itô diffusions from a discrete-time series that approximate the solution…
Multiscale and Nonlocal Learning for PDEs using Densely Connected RNNs
Ricardo A. Delgadillo, Jingwei Hu, Haizhao Yang
Learning time-dependent partial differential equations (PDEs) that govern evolutionary observations is one of the core challenges for data-driven inference in many fields. In this…
A fast Petrov-Galerkin spectral method for the multi-dimensional Boltzmann equation using mapped Chebyshev functions
Jingwei Hu, Xiaodong Huang, Jie Shen +1
Numerical approximation of the Boltzmann equation presents a challenging problem due to its high-dimensional, nonlinear, and nonlocal collision operator. Among the deterministic me…
Structure Probing Neural Network Deflation
Yiqi Gu, Chunmei Wang, Haizhao Yang
Deep learning is a powerful tool for solving nonlinear differential equations, but usually, only the solution corresponding to the flattest local minimizer can be found due to the…
Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory
Tao Luo, Haizhao Yang
The problem of solving partial differential equations (PDEs) can be formulated into a least-squares minimization problem, where neural networks are used to parametrize PDE solution…
Machine Learning for Prediction with Missing Dynamics
John Harlim, Shixiao W. Jiang, Senwei Liang +1
This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the pre…