ScaleComposer: Scale-Conditioned Compositional Learning for Source-Count Extrapolation in Physical Fields

Air movement enhances convective heat exchange with occupants and exposed surfaces, motivating accurate prediction of spatial air speed distributions in buildings. As the number of interacting sources grows, characterizing airflow across all possible configurations becomes costly. Predicting collective airflow responses from limited measurements is therefore critical. Neural operators can capture complex interactions and multiscale features by learning mappings between function spaces. However, representative architectures do not explicitly represent interactions among momentum sources or their dependence on spatial scale. We propose a compositional learning framework that builds reusable representations of individual sources and source pairs from single-source priors and inter-source relations. Location- and scale-conditioned aggregation combines these representations, allowing the same learned composition rules to operate across source counts. Residual reconstruction then refines a pretrained reference field by constraining scale-specific corrections to corresponding spatial frequency bands. This connects the scale at which source information is aggregated to the spatial structure of the predicted corrections. We evaluate extrapolation from single- and two-source configurations to configurations with up to six sources, using measured multi-ceiling-fan airflow and six controlled numerical regimes spanning source overlap and advective dynamics. On measured data, the framework reduces overall extrapolation error by up to 17.1% relative to the baselines. Replacing adaptive aggregation with fixed pooling improves low-source validation performance but worsens extrapolation, highlighting the importance of learning how source information is combined. In controlled experiments, the framework demonstrates competitive overall error and better reconstructs spatial patterns than baselines.