109 citations · 443 across the 45 of their papers we have counts for
48 papers
A Geometric Local Parameterization Method for Generalized Hele-Shaw Free Boundary Problems with Source Terms
Zengyan Zhang, Wenrui Hao, John Harlim
We develop a meshfree numerical framework for Hele--Shaw free boundary problems with surface tension and source terms based on geometric local parameterization and boundary integra…
A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Series
Xuyang Li, John Harlim, Dibyajyoti Chakraborty +1
The accurate forecasting of complex, high-dimensional dynamical systems from observational data is a fundamental task across numerous scientific and engineering disciplines. A sign…
Geometric local parameterization for solving Hele-Shaw problems with surface tension
Zengyan Zhang, Wenrui Hao, John Harlim
In this work, we introduce a novel computational framework for solving the two-dimensional Hele-Shaw free boundary problem with surface tension. The moving boundary is represented…
A Higher Order Local Mesh Method for Approximating 1-Laplacians on Unknown Manifolds
John Wilson Peoples, John Harlim
We introduce a numerical method for approximating arbitrary differential operators on vector fields in the weak form given point cloud data sampled randomly from a dimensional…
Learning Coarse-Grained Dynamics on Graph
Yin Yu, John Harlim, Daning Huang +1
We consider a Graph Neural Network (GNN) non-Markovian modeling framework to identify coarse-grained dynamical systems on graphs. Our main idea is to systematically determine the G…
Generalized Finite Difference Method on unknown manifolds
Shixiao W. Jiang, Rongji Li, Qile Yan +1
In this paper, we extend the Generalized Finite Difference Method (GFDM) on unknown compact submanifolds of the Euclidean domain, identified by randomly sampled data that (almost s…