Composable Spatial Sequence Learning for Steady Flow Prediction

There is current interest in neural surrogates for steady flow-field solutions to partial differential equations (PDEs). These surrogates are typically trained as global mappings from geometry and operating conditions to complete solution fields, but extrapolation to domains with substantially greater spatial extent remains challenging. This study investigates whether reformulating the learning problem as repeated local transitions can improve domain-length extrapolation, without increasing the number of model parameters or changing the model architecture. Chip-to-chip (C2C) learning represents a steady velocity-magnitude field as an ordered sequence of narrow slices taken perpendicular to the streamwise direction, termed chips, and learns the geometry-conditioned transitions from upstream chip states to downstream chip states. Repeated composition of such transitions allows the domain length to change through rollout depth rather than model architecture. The proposed C2C-MLP is compared with five non-C2C baselines: a Multilayer Perceptron (MLP), a Physics-Informed Neural Network (PINN), a Graph Neural Operator (GNO), a General Neural Operator Transformer (GNOT), and Transolver, on domains of one, two, and three times the training length and on four out-of-distribution (OOD) geometries. All baseline models are provided with the same initial velocity-magnitude profile and geometric information available to C2C. Across five independent training runs, the C2C-MLP achieves the lowest mean absolute error (MAE) across all three domain lengths; on the 3× domain, its MAE was 0.0679 m/s, a 39.5% reduction relative to the most accurate baseline. OOD performance is geometry-dependent: C2C-MLP achieved the lowest MAEs on the Ahmed body and airfoil cases, while its MAE remained within 5.4% of the best baseline on the periodic-hill and backward-facing step cases. These four geometries are widely used CFD benchmark configurations representing bluff-body, aerodynamic, and separated-flow problems. Overall, the results of this study highlight spatial composition as a promising strategy for surrogate models that must operate on domains extending beyond those represented during training, without retraining or changing the model architecture.