KolmoGraph: A Multi-Scale Energy Conservative Graph Neural Network for Variable Closure Fluid Modelling
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Machine learning (ML) based surrogate models for fluid mechanics enable a range of multi-query simulation, inverse design, and control in real-world engineering applications. In recent years, the ability to generate and train large datasets and models has become increasingly accessible. However, flexibility, scale, and generalizability remain significant challenges. Some works have used mesh free, surface-only, patching and point-cloud or graph coarsening methods in developing fluid foundation models. These choices improve scale but weaken alignment with physics and, in turn, compromise trust in their outputs. Graph neural networks (GNNs) show promise as a highly interpretable architecture for spatiotemporal surrogate models. Message passing in a GNN mimics quantity transport in partial differential equations such as the Navier-Stokes equations. Furthermore, GNNs are easily adaptable to unstructured meshes. Recent research has increased surrogate interpretability by enforcing conservation laws into the message passing layers of a GNN. Despite increased interpretability, GNNs remain difficult to scale. In this talk, we present KolmoGraph: an energy conserving GNN-based surrogate model that factorizes the learning into separate multi-scale energy transfer and direction resolution tasks. The architecture employs a novel training strategy inspired by turbulence theory. This framework also allows for adaptive message passing at the pareto front of spatial resolution, accuracy and computational cost. The result is a tool that may give engineers the ability to simulate transient modes and to query at multiple resolutions to resolve fine scale vortical structures with compliance with physics. We then benchmark this architecture against results expected from turbulence theory. Finally, we demonstrate scalability of the model on large meshes by employing graph partitioning. Applications of this technique extend from automotive and aerospace design optimization to flow control in plasmas.
