arXiv AI October 5, 2026 By Luis Medrano-Navarro, Giacomo Baldan, Qiang Liu, Benjamin Holzschuh, Jan Hagnberger, Mathias Niepert, Nils Thuerey

Geometry Meets Physics: Data-Efficient Pre-Training for Unstructured Neural PDE Solvers

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The paper presents a data‑efficient pre‑training framework for neural surrogate models solving PDEs on unstructured 3D geometries. It introduces a geometry‑driven strategy for steady‑state problems that uses intrinsic shape descriptors, and a physics‑driven approach for transient problems that generates synthetic PDE data online. Experiments show faster convergence, higher data efficiency, and improved accuracy during fine‑tuning, especially in low‑data settings.

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