Mesh Field Theory: Port-Hamiltonian Formulation of Mesh-Based Physics
We present Mesh Field Theory (MeshFT) and its neural realization, MeshFT-Net: a structure-preserving framework for mesh-based continuum physics that cleanly separates the physics' topological structure from its metric structure. Imposing minimal physical principles (locality, permutation equivariance, orientation covariance, and energy balance/dissipation inequality), we prove a reduction theorem for mesh-based physics. Under these conditions, the physical dynamics admit a local factorization into a port-Hamiltonian form: the conservative interconnection is fixed uniquely by mesh topology, whereas metric effects enter only through constitutive relations and dissipation. This reduction cla...
| Authors | Satoshi Noguchi, Yoshinobu Kawahara |
|---|---|
| Primary category | cs.LG |
| Published | 1 May 2026 |
| Last updated at source | 31 May 2026 |
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