ScaleAware-JEPA: Latent Representation for Discovery in Multiscale Physical Fields

Aerodynamic surrogate models are increasingly used to replace repeated high-fidelity CFD evaluations in many-query design settings, but current approaches still face two important limitations: they often scale poorly to the very large fields arising in realistic 3D aerodynamics, and they rarely produce latent representations that are directly useful for analysis and design. We introduce AeroJEPA, a Joint-Embedding Predictive Architecture for aerodynamic field modeling that addresses both issues. Rather than predicting the full flow field directly from geometry, AeroJEPA predicts a target latent representation of the flow from a context latent representation of the geometry and operating conditions, and optionally reconstructs the field through a continuous implicit decoder. This formulation decouples latent prediction from field resolution while encouraging the latent space to organize semantically. We evaluate AeroJEPA on two complementary datasets: HiLiftAeroML, which stresses the method in a high-fidelity regime with extremely large boundary-layer fields, and SuperWing, which tests large-scale generalization and latent-space optimization over a broad family of transonic wings. Across these benchmarks, AeroJEPA is competitive as a continuous surrogate for aerodynamic fields, scales naturally to high-resolution outputs, and learns context and predicted latents that encode geometry and aerodynamic quantities not used directly as supervision. We further show that the resulting latent space supports controlled interpolation, linear probing, concept-vector arithmetic, and a constrained design latent-optimization experiment. These results suggest that predictive latent learning is a promising direction for scalable and design-meaningful aerodynamic surrogate modeling.

Scientific measurements are often bottlenecked by suboptimal conditions, whether that be noise, incomplete spatial coverage, or limited resolution, rendering accurate field reconstruction a difficult task. We introduce LatentPDE, a latent diffusion framework designed to simultaneously resolve sparse-observation reconstruction and super-resolution. While existing physics-guided diffusion models typically rely on soft loss penalties or uninterpretable representations, our approach enforces physical compliance by constructing an inherently interpretable latent space. Specifically, we parameterize the latent variables directly as the coefficients and source terms of an assumed governing PDE. In doing so, LatentPDE is able to reliably reconstruct dynamics across highly disparate and structured data gaps. Empirical results on diverse configurations demonstrate that our model achieves high-fidelity recovery at any desired resolution while also tracking the underlying predictive uncertainty.

Joint-embedding predictive architectures learn by predicting latent representations of missing observations, yet many masked JEPAs are evaluated primarily through the encoders they produce. We ask what a trained predictive pathway itself infers when an entire entity is absent from a native 3D scene. We introduce SR-JEPA, a point-native JEPA for scene-scale point clouds whose original frozen predictive pathway can be queried at a supplied location. At evaluation, every point of one object is removed before encoding and replaced by the same shape-free 32-point query at its centroid. Training uses only self-contained 3D EMA targets: no reconstruction, semantic labels, language, or lifted 2D features. On 5,953 held-out ARKitScenes objects, the imputed latent reaches 43.13% semantic-identity macro accuracy, 22.18 points above the strongest floor. Randomizing the prediction path removes 9.78 points, while substituting matched donor context removes 21.98 points. On 8,570 Sr3D support pairs, the full latent reaches 41.15 AP; identity decoded from the missing-object latent, combined with anchor identity and geometry, reaches 39.37 AP, leaving an unresolved 1.78-point residual. These results reveal a queryable, compositional 3D predictive state: the model completes context-dependent entity content, which downstream computation combines with metric geometry.