FlowGEM: a multi-scale neural surrogate model based on geometry and physics enrichment

Neural networks learn the low-frequency components of a target signal before the high-frequency ones, a phenomenon known as spectral bias. This failure mode also affects neural surrogate models used to simulate systems governed by PDEs. The bias is particularly consequential in automotive and aerospace aerodynamics, where the flow is shaped both by millimeter-scale geometric details and by meter-scale structures such as the windshield angle. To address this challenge, CFD surrogates commonly employ hierarchical modelling, mixing reads that target local geometry features with reads that target large-scale information, and combining them into a learned latent representation with little control over how these scales interact. In this study, we present FlowGEM, a neural surrogate model trained on surface and volume point clouds. FlowGEM reads the geometry at multiple spatial scales in sequence, with shared weights across scales, recursively conditioning through a scale-dependent gate. In addition, it learns global conditioning through a physics enrichment module, injecting learned physics information into the model's latent geometry representation. With this setup, we compare FlowGEM against state-of-the-art surrogate models on realistic aerodynamics benchmarks (DrivAerML and NASA CRM), where it outperforms them on 4 of the 6 metrics tested. To understand the impact of spectral bias on the model, we analyze the prediction error in spectral bands and show how the multi-scale attention reduces frequency-dependent errors. Finally, because the output is predicted independently at each input point, FlowGEM's inference cost grows linearly with the number of points evaluated, and a full mesh can be decoded in chunks that fit the available memory.