Potential-flow labels replace costly CFD pretraining: SimpFlow beats scratch training in all 24 flow settings and cuts CFD cases by 35–68%
Synopsis
Neural surrogates for three-dimensional fluid simulation need large sets of costly high-fidelity CFD labels. SimpFlow instead generates supervision from simplified physics: a source-panel potential-flow solver that needs only a surface mesh labels about 9,000 unlabeled ShapeNet geometries with velocity and pressure fields, reusing precomputed velocity fields across inflow directions for an amortized 0.111 s per example. A Transolver pretrained on these labels and fine-tuned on independent CFD datasets improves over training from scratch in all 24 task–budget settings across five flow tasks; with fine-tuning fixed at 200 epochs, interpolation indicates 35–68% fewer CFD training cases are needed to match scratch error at each task's largest budget.
Interpretation
Neural surrogates for flow over three-dimensional geometries can start from supervision generated by simplified physics rather than from high-fidelity CFD labels, then transfer to independent CFD tasks. Earlier pretraining either reused existing PDE solution corpora or CFD datasets, or relied on geometry-only auxiliary targets; GeoPT's analysis showed that static geometry-only supervision can cause negative transfer. Across 24 task–budget settings on five flow tasks, the shared SimpFlow initialization beats training from scratch at epoch 200 in every setting and beats GeoPT retrained at the same data scale in 21 of them.
The labels come from potential flow: a source-panel solver discretizes only the body surface and returns velocity and pressure coefficients that keep geometry-induced acceleration, stagnation and suction but omit viscosity, separated wakes, turbulence, compressibility and free-surface effects. One matrix factorization yields velocity bases for three Cartesian unit inflow directions, so a new query cloud needs only basis evaluation and a new inflow direction reuses the stored velocities and recomputes only pressure, avoiding a fresh solve per condition. On four CPU threads of an AMD EPYC 9684X, the 4k-panel configuration takes 0.111 s per example amortized, 64.2% less than the GeoPT reproduction under the same protocol at 0.309 s; timing covers labeling from existing meshes and queries and excludes mesh preparation, query sampling and I/O.
The content of the supervision matters: potential-flow labels transfer better than a local-geometry-field control that uses the same inputs, targets and training schedule. The local-geometry rule only attenuates the inflow and cannot accelerate it above unit magnitude, so it produces no suction; it causes negative transfer at every surface DrivAerML budget. SimpFlow lowers error relative to the local-geometry-field control by 20.7% on average and beats scratch in every flow setting; on this car the potential-flow surface relative error is 1.61 versus 1.56 for the local field, showing that useful flow structure can accompany large pointwise errors.
Perspective
The demonstrated scope is potential-flow labels generated on ShapeNet car, airplane and watercraft geometries, plus fine-tuning on five independent CFD benchmarks: AirCraft, NASA-CRM, DrivAerML surface and volume, and DTCHull; all main comparisons are single-seed with fine-tuning fixed at 200 epochs, and label timing covers only labeling from existing meshes and queries, excluding mesh preparation, query sampling and I/O.
Potential flow omits viscosity, separated wakes, turbulence, compressibility and free-surface effects, so pointwise label errors can be large; raising panel resolution from 2k to 8k gives no consistent monotonic improvement while labeling cost rises from 0.055 to 0.322 s per example; on the Car-Crash solid-mechanics test, error is 13.2% below scratch at 20 training cases, 21.7% and 7.7% above scratch at 40 and 60 cases, and 0.7% below at 80 cases.