3 papers
cs.LG2026
Structure-Preserving Learning Improves Geometry Generalization in Neural PDEs
Benjamin D. Shaffer, Shawn Koohy, Brooks Kinch +2
We aim to develop physics foundation models for science and engineering that provide real-time solutions to Partial Differential Equations (PDEs) which preserve structure and accur…
cs.LG2026
A meshfree exterior calculus for generalizable and data-efficient learning of physics from point clouds
Benjamin D. Shaffer, Brooks Kinch, M. Ani Hsieh +1
We introduce a meshfree exterior calculus (MEEC) for learning structure-preserving descriptions of physics on point clouds, and use it to build MEEC-Net, a data-efficient surrogate…
cs.LG2026
Learned Lagrangian Models of PDEs via Euler-Lagrange Residual Minimization
Lyra Zhornyak, Eric Forgoston, M. Ani Hsieh
We present the first method to directly use a learned continuous Lagrangian to forecast the dynamics of systems governed by partial differential equations, exploiting the inherent…