Neural surrogate models for PDEs on unstructured 3D geometries often suffer from poor generalization and expensive training data. Pre‑training on large collections of related PDE dynamics has become a key way to improve robustness and scalability, yet it relies on massive pre‑computed datasets, making it neither compute‑ nor data‑efficient. We therefore introduce a disk‑free pre‑training framework that supports both steady‑state and transient regimes. For steady‑state problems we use a geometry‑driven strategy, learning domain representations from intrinsic shape descriptors such as curvature and topological features. For transient problems we adopt a physics‑driven approach that generates synthetic PDE samples on‑the‑fly, eliminating the need for costly data collection. Experiments on several benchmarks show faster convergence, higher data efficiency and better accuracy during fine‑tuning, especially under realistic low‑data conditions. This methodology offers a practical, data‑efficient path toward neural emulators for large‑scale simulations.
Review: By coupling intrinsic geometric encoding with online physics‑based data generation, the paper dramatically cuts pre‑training overhead and delivers a viable neural PDE solver for engineering scenarios where data are scarce.