64 citations · 115 across the 18 of their papers we have counts for
6 papers · 1 filter
Learning Closure of Dynamical Systems with Kernel Ridge Regression
Evan Habbershaw, John Harlim, Senwei Liang
We develop a closure modeling framework for identifying missing components of dynamical systems using Kernel Ridge Regression (KRR). The framework addresses two classes of closure…
Solving High-Dimensional Partial Integral Differential Equations: The Finite Expression Method
Gareth Hardwick, Senwei Liang, Haizhao Yang
In this paper, we introduce a new finite expression method (FEX) to solve high-dimensional partial integro-differential equations (PIDEs). This approach builds upon the original FE…
Finite Expression Method for Solving High-Dimensional Partial Differential Equations
Senwei Liang, Haizhao Yang
Designing efficient and accurate numerical solvers for high-dimensional partial differential equations (PDEs) remains a challenging and important topic in computational science and…
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…
Solving PDEs on Unknown Manifolds with Machine Learning
Senwei Liang, Shixiao W. Jiang, John Harlim +1
This paper proposes a mesh-free computational framework and machine learning theory for solving elliptic PDEs on unknown manifolds, identified with point clouds, based on diffusion…
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…