From the 1 of 6 linked papers with an AI index.
6 papers
A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Series
Xuyang Li, John Harlim, Dibyajyoti Chakraborty +1
The paper introduces a weak-form loss function for training Neural ODEs that improves learning of chaotic dynamics from noisy time‑series data, yielding more stable and accurate sh…
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…
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…
Spectral Convergence of Symmetrized Graph Laplacian on manifolds with boundary
J. Wilson Peoples, John Harlim
We study the spectral convergence of a symmetrized Graph Laplacian matrix induced by a Gaussian kernel evaluated on pairs of embedded data, sampled from a manifold with boundary, a…
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…