Learning Efficient Surrogate Dynamic Models with Graph Spline Networks

Chuanbo Hua, Federico Berto, Michael Poli, Stefano Massaroli, Jinkyoo Park

Keywords: Graph, Spline Collocation Method, Graph Neural Networks, Simulation, Partial Differential Equations, PDEs, Physics, Scientific Computing, Surrogate Models, Weather Forecasting

TL;DR: We propose a novel model to exploit the synergy between graph neural networks and orthogonal spline collocation to accelerate learned simulations of physical systems by interpolating solutions of graph neural networks.

Abstract: While complex simulations of physical systems have been widely used in engineering and scientific computing, lowering their often prohibitive computational requirements has only recently been tackled by deep learning approaches. In this paper, we present GraphSplineNets, a novel deep-learning method to speed up the forecasting of physical systems by reducing the grid size and number of iteration steps of deep surrogate models. Our method uses two differentiable orthogonal spline collocation methods to efficiently predict response at any location in time and space. Additionally, we introduce an adaptive collocation strategy in space to prioritize sampling from the most important regions. GraphSplineNets improve the accuracy-speedup tradeoff in forecasting various dynamical systems with increasing complexity, including the heat equation, damped wave propagation, Navier-Stokes equations, and real-world ocean currents in both regular and irregular domains.

Submission Number: 7758