Cross-Domain Pretraining for Steady-State Neural CFD Surrogates

Pretraining a neural PDE surrogate can reduce the amount of new CFD data needed when geometry or modeled physics changes. However, it remains unclear how different components of distribution shift affect this benefit. We pretrain a surrogate on 254,909 RANS solutions from one airfoil family and fine-tune it on a new family under two target settings with matched freestream ranges: the same Spalart-Allmaras (SA) modeling and SA with added $e^N$ transition modeling. At $N=1000$, the pretrained model matches the accuracy of a model trained from scratch on $3.25\times$ as many samples for the same-SA target, but $2.58\times$ as many for the transition-modeled target. By $N=5000$, this ordering reverses ($1.56\times$ versus $1.86\times$). At $N=1000$, sampling more distinct airfoils lowers error on both targets, but only for the same-SA target is the gain increase larger than the observed draw-to-draw variation ($3.3\times$ to $4.0\times$). These results show that pretraining value depends jointly on target-data budget, target-data coverage, and whether source and target differ in modeled physics.

Neural surrogate models for computational fluid dynamics (CFD) are typically trained as forward operators that map explicit problem specifications, such as geometry and boundary conditions, to solution fields. This ties the model to the conditioning variables seen during training and limits reuse under boundary-condition shifts or local geometry changes. We propose to reformulate steady CFD inference as an inpainting problem: instead of training on explicit boundary conditions, we learn a self-supervised prior over velocity fields and impose boundary constraints only during inference by fixing known regions such as inlet, outlet or unchanged regions from previous simulations. To scale this idea to large 3D meshes, we introduce a local neighbourhood tokeniser that represents high-resolution velocity fields as compact spatial latent tokens and train latent flow-matching and masked-autoencoder models on these tokens. On intracranial aneurysm hemodynamics, our method reconstructs full velocity fields from sparse boundary context, outperforms supervised neural surrogates under boundary-condition and dataset shift and enables local geometry editing by reusing unchanged simulation context. These results suggest that viewing CFD inference as context-conditioned inpainting can turn neural surrogates from task-specific predictors into reusable flow priors.

Neural surrogates can accelerate computational fluid dynamics (CFD) simulations by orders of magnitude, but practical deployment in engineering and healthcare applications requires architectures that scale to high-resolution meshes and learn effectively from limited data. Explicit equivariance offers a principled inductive bias, yet its accuracy benefits may depend on the prediction task and the distribution of anatomical orientations. We investigate this dependence across three hemodynamic benchmarks with different degrees of natural canonical alignment. To support this study, we introduce the Anchored-Branched Geometric Algebra Transformer (AB-GATr), an $E(3)$-equivariant surrogate that efficiently predicts coupled surface and volume quantities. Across these benchmarks, AB-GATr consistently outperforms the evaluated non-equivariant models, including variants trained with rotational augmentation, while achieving accuracy competitive with $E(3)$-equivariant LaB-GATr at substantially lower training cost. In comparison, rotational augmentation provides inconsistent benefits across architectures and can reduce accuracy. A controlled experiment on ShapeNet-Car shows that strong canonical alignment can favor non-equivariant models, but their accuracy generally deteriorates as training orientations broaden and can decline sharply under broader test rotations. We further investigate these patterns using extended symmetry-breaking diagnostics and probes of the predictive information associated with canonical alignment across all benchmarks. Together, these results support explicit equivariance for the evaluated hemodynamic tasks with natural orientation variation, while showing that its accuracy benefits depend on the task and orientation distribution.