A Two-Phase Deep Learning Framework for Adaptive Time-Stepping in High-Speed Flow Modeling
This addresses the challenge of computational efficiency and accuracy in high-speed flow modeling for fluid dynamics applications, but it appears incremental as it builds on existing adaptive time-stepping concepts with machine learning integration.
The authors tackled the problem of modeling high-speed flows with adaptive time-stepping to resolve sudden changes like shock waves, proposing a two-phase machine learning framework called ShockCast that predicts timestep sizes and advances system states, and they generated two supersonic flow datasets for evaluation.
We consider the problem of modeling high-speed flows using machine learning methods. While most prior studies focus on low-speed fluid flows in which uniform time-stepping is practical, flows approaching and exceeding the speed of sound 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. As ShockCast is the first framework for learning high-speed flows, we evaluate our methods by generating two supersonic flow datasets, available at https://huggingface.co/datasets/divelab. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).