Title: From Numerical Solvers to Graph Surrogates: Physics-Informed Losses for Data-Efficient CFD Modeling
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Physics Informed Neural Networks; Graph Neural Networks; Fluid Dynamics Surrogate

Abstract: Graph neural networks (GNN) represent a promising method for creating robust and physically interpretable surrogate models for fluid dynamics. These surrogates offer a significant advantage over traditional computational fluid dynamics (CFD) solvers based on numerical methods because they require much less computational cost. In a GNN designed as a surrogate model for spatio-temporal partial differential equations, message passing can be interpreted as the propagation of physical quantities such as velocity, pressure, and temperature. The complexity of the Navier-Stokes equations, however, can limit the generalizability of existing models and lead to long training times.
We show that including a physics-informed loss function based on the numerical methods used to generate the training data, specifically the finite volume method, can reduce the amount of data needed to train an accurate physics-informed surrogate compared with a purely data-driven baseline. By reducing the dataset size by 20\% and applying this approach, we achieved a 33\% reduction in convergence time. For larger datasets, model accuracy improved by up to 7.4\% within the same timeframe. Our method also avoids interpolation between cell centers and vertices, which can introduce errors from numerical discretization. Applying this soft constraint during training can support the development of future CFD surrogate GNN models that perform well even with smaller datasets.