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.

翻译：尽管物理系统的复杂模拟已被广泛应用于工程和科学计算领域，但降低其通常高昂的计算需求直到近期才通过深度学习方法得到解决。本文提出GraphSplineNets，一种新颖的深度学习方法，通过减少深度替代模型的网格尺寸和迭代步数来加速物理系统的预测。我们的方法采用两种可微正交样条配置方法，高效预测任意时空位置的响应。此外，我们引入空间自适应配置策略，优先对关键区域进行采样。GraphSplineNets在预测各类复杂度递增的动力系统（包括热传导方程、阻尼波传播、纳维-斯托克斯方程以及规则与不规则域中的真实洋流）时，有效提升了精度-速度权衡性能。