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.

提出 GraphSplineNets 深度学习方法，在物理系统的预测中通过减少深度替代模型的网格大小和迭代步骤数来提高计算效率和准确性，包括研究热方程、阻尼波传播、纳维 - 斯托克斯方程和现实世界中规则和不规则域的海流。