Learning Efficient Surrogate Dynamic Models with Graph Spline Networks
This work addresses computational bottlenecks for engineers and scientists using simulations, offering an incremental improvement in surrogate modeling efficiency.
The paper tackles the problem of high computational costs in simulating physical systems by introducing GraphSplineNets, a deep-learning method that reduces grid size and iteration steps to speed up forecasting, achieving improved accuracy-speedup tradeoffs across systems like the heat equation and Navier-Stokes equations.
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.