ShockCast: A Novel Two-Phase Machine Learning Approach for Adaptive High-Speed Flow Simulation

Challenges in Modeling High-Speed Flows

Modeling supersonic and hypersonic fluid flows involves capturing rapid changes such as shock waves and expansion fans. Traditional fixed time-step methods struggle to represent these dynamics accurately without excessive computation. Adaptive time-stepping is essential to balance simulation accuracy and efficiency by adjusting time steps according to flow changes. However, existing adaptive step selection methods are not directly compatible with neural solvers, which typically depend on coarser space-time approximations.

Advances in Neural PDE Solvers

Recent studies have made progress in learnable spatial re-meshing for solving partial differential equations (PDEs) using supervised and reinforcement learning. Yet, adapting temporal resolution dynamically through time-resolved temporal re-meshing remains underexplored, especially for high-speed flows. Most current models rely on fixed time-step data or require prior knowledge of the time step, limiting their real-world applicability.

Introducing ShockCast: Adaptive Two-Phase Framework

Researchers at Texas A&M developed ShockCast, a two-phase machine learning framework designed to simulate high-speed fluid flows using adaptive time-stepping. Phase one involves a neural model that predicts the optimal timestep based on current flow conditions. Phase two uses this adaptive timestep along with flow fields to advance the simulation. ShockCast integrates physics-inspired timestep prediction and leverages techniques from neural ordinary differential equations (ODEs) and Mixture of Experts to enhance learning.

Neural Conditioning for Improved Timestep Prediction

ShockCast employs several timestep-conditioning strategies to improve the solver's adaptability, including time-conditioned normalization, spectral embeddings, Euler-inspired residuals, and mixture-of-experts layers. These strategies enable the solver to specialize in managing diverse temporal dynamics, ensuring uniform learning across smooth and sharp flow regions.

Experimental Validation on Supersonic Flow Scenarios

The framework was tested on two supersonic datasets: a coal dust explosion and a circular blast wave. The coal dust scenario features shock-dust interactions causing turbulence and mixing, while the circular blast simulates a 2D shock tube with radial shocks. Multiple neural solvers, such as U-Net, F-FNO, CNO, and Transolver, were evaluated with various timestep conditioning techniques. Results highlighted that U-Net with time-conditioned normalization excels in capturing long-term dynamics, whereas F-FNO and U-Net with mixture-of-experts or Euler conditioning significantly reduce turbulence and prediction errors.

Summary of ShockCast's Impact

ShockCast offers a scalable, efficient solution for simulating high-speed fluid flows by adaptively predicting time steps to handle rapid flow changes effectively. The approach advances neural PDE solvers by combining physics-inspired conditioning with adaptive temporal resolution, validated through challenging supersonic flow experiments. The project's codebase is publicly available in the AIRS library for further exploration and development.