Equivariant geometric convolutions for emulation of dynamical systems
This addresses the need for efficient, physics-compliant surrogate models in natural sciences, though it is incremental as it adapts existing CNN methods.
The paper tackled the problem of creating coordinate-free surrogate models for dynamical systems by using geometric convolutions in three CNN architectures, achieving better accuracy and improved stability in emulating 2D compressible Navier-Stokes compared to baselines.
Machine learning methods are increasingly being employed as surrogate models in place of computationally expensive and slow numerical integrators for a bevy of applications in the natural sciences. However, while the laws of physics are relationships between scalars, vectors, and tensors that hold regardless of the frame of reference or chosen coordinate system, surrogate machine learning models are not coordinate-free by default. We enforce coordinate freedom by using geometric convolutions in three model architectures: a ResNet, a Dilated ResNet, and a UNet. In numerical experiments emulating 2D compressible Navier-Stokes, we see better accuracy and improved stability compared to baseline surrogate models in almost all cases. The ease of enforcing coordinate freedom without making major changes to the model architecture provides an exciting recipe for any CNN-based method applied to an appropriate class of problems