A Two-Phase Deep Learning Framework for Adaptive Time-Stepping in High-Speed Flow Modeling

TL;DR

This paper introduces ShockCast, a two-phase machine learning framework that predicts adaptive timesteps for high-speed flow simulations, enabling efficient and accurate modeling of shock phenomena.

Contribution

It presents a novel two-phase approach combining timestep prediction and flow advancement, with strategies inspired by neural ODEs and Mixture of Experts.

Findings

Successfully generated supersonic flow datasets for evaluation.

Demonstrated effective adaptive time-stepping in high-speed flow modeling.

Code is publicly available in the AIRS library.

Abstract

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. 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).