Geometry-Guided Conditional Adaptation for Surrogate Models of Large-Scale 3D PDEs on Arbitrary Geometries

Deep learning surrogate models aim to accelerate the solving of partial differential equations (PDEs) and have achieved certain promising results. Although several main-stream models through neural operator learning have been applied to delve into PDEs on varying geometries, they were designed to map the complex geometry to a latent uniform grid, which is still challenging to learn by the networks with general architectures. In this work, we rethink the critical factors of PDE solutions and propose a novel model-agnostic framework, called 3D Geometry-Guided Conditional adaptation (3D-GeoCA), for solving PDEs on arbitrary 3D geometries. Starting with a 3D point cloud geometry encoder, 3D-GeoCA can extract the essential and robust representations of any kind of geometric shapes, which conditionally guides the adaptation of hidden features in the surrogate model. We conduct experiments on two public computational fluid dynamics datasets, the Shape-Net Car and Ahmed-Body dataset, using several surrogate models as the backbones with various point cloud geometry encoders to simulate corresponding large-scale Reynolds Average Navier-Stokes equations. Equipped with 3D-GeoCA, these backbone models can reduce the L-2 error by a large margin. Moreover, this 3D-GeoCA is model-agnostic so that it can be applied to any surrogate model.