用于高速流动建模的自适应时间步长的两阶段深度学习框架

我们考虑了使用机器学习方法建模 high-speed flows 的问题。虽然大多数 prior 研究 focus on low-speed fluid flows in which uniform time-stepping is practical，但接近和超过声速的 flows exhibit sudden changes such as shock waves。 In such cases, it is essential to use adaptive time-stepping methods to allow a temporal resolution sufficient to resolve these phenomena while simultaneously balancing computational costs。 Here, we propose a two-phase machine learning method, known as ShockCast, to model high-speed flows with adaptive time-stepping。 In the first phase, we propose to employ a machine learning model to predict the timestep size。 In the second phase, the predicted timestep is used as an input along with the current fluid fields to advance the system state by the predicted timestep。 We explore several physically-motivated components for timestep prediction and introduce timestep conditioning strategies inspired by neural ODE and Mixture of Experts。 We evaluate our methods by generating three supersonic flow datasets, available at https://huggingface.co/divelab。 Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS)。