DeAL: Density-Agnostic Learning for Sampling-Stable Geometry-to-Field Surrogates

Geometry-to-field surrogates predict physical fields from geometry and operating conditions, reducing the need for repeated numerical simulation. Because practical models receive finite meshes or point clouds rather than the underlying continuous domain, remeshing can redistribute local sampling density and connectivity without changing the physical case yet still alter predictions, a phenomenon we call sampling-distribution sensitivity. We introduce DeAL (Density-Agnostic Learning), a backbone-agnostic training principle that draws two fixed-budget views from a continuous inverse-density family for each case, supervises both predictions at common physical queries, and penalizes their disagreement. Dual supervision anchors both views to the physical target, while prediction consistency suppresses representation-dependent variation without changing the backbone or single-view inference. Across nine surrogate architectures and four physical systems, we find that DeAL reduces error and inconsistency among predictions by roughly half on average over a large number of matched comparisons when the same physical cases are evaluated under held-out spatial redistributions and independently generated remeshes, demonstrating transfer across distinct encoder designs and physical settings. Together, these results show that DeAL substantially improves predictions when the same physical case is presented through different numerical representations, without changing the underlying architecture or deployment path. In this way, our method increases robustness and reliability of neural surrogates as a key component for industrial applications.