Geometry-Guided Conditional Adaption for Surrogate Models of Large-Scale 3D PDEs on Arbitrary Geometries
Keywords: partial differential equations, surrogate model, geometry-guided conditional adaption, 3D understanding
Abstract: 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 Adaption (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 is regarded as a conditioning key to guiding the adaption of hidden features in the surrogate model. We conduct experiments on the public Shape-Net Car computational fluid dynamics 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 their L-2 errors by a large margin. Moreover, this 3D-GeoCA is model-agnostic so that it can be applied to any surrogate model. Our experimental results further show that its overall performance is positively correlated to the power of the applied backbone model.
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Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
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Submission Number: 7355
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