AI RESEARCH
Mesh Field Theory: Port-Hamiltonian Formulation of Mesh-Based Physics
arXiv CS.LG
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ArXi:2605.00394v1 Announce Type: new 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.