Stable neural emulation improves coarse simulation of turbulent flows
Learning the Entropic Relaxation: Stable Coarse-Grid Emulation with Neural Discrete Equilibrium
Machine Learning
Summary
Simulating complex fluid flows like turbulence usually needs lots of computing power because small details must be resolved. The authors show a new neural method called Neural Discrete Equilibrium (NeurDE) that can stably predict these flows even on very coarse grids, which use much less computing. Their approach controls how energy dissipates in the system, keeping the simulation stable for long times, sometimes better than traditional numerical solvers. This means faster, efficient simulations can be done without losing key physical behaviors.
What this means in practice
- •For computational fluid dynamics engineers: Run stable long-term turbulence simulations on coarse grids reducing computation time while preserving physical energy dissipation.
- •For weather modeling teams: Enable faster large-scale weather forecasts by using stable coarse-grid neural emulators that maintain dissipative properties of atmospheric flows.
Authors
Jose Antonio Lara Benitez, Kareem Hegazy, Anastasis Kratsios, Ivan Dokmanić, Maarten V. de Hoop, Michael W. Mahoney
Abstract
The ability to emulate complicated and computationally-expensive physical systems in an efficient and stable manner is a popular motivation for scientific machine learning (SciML). Stable numerical solvers tend to be computationally expensive, as they attempt to resolve small (spatial and temporal) scales that receive and dissipate spectral energy. Learned coarse-grid forecasters remove the dissipative channel, allowing unresolved frequencies to re-emerge as grid-scale noise (aliasing). In this paper, we use the Neural Discrete Equilibrium (NeurDE) method to explore stable emulation at extremely coarse grids, demonstrating physically-principled control over entropy dynamics that reinforces the physical system's dissipative mechanism. Entropically-stabilized NeurDE produces stable long-time rollouts for thousands of forecasting steps on large Reynolds number turbulent flows ($\mathrm{Re}=100{,}000$) with very coarse grids (down to $\mathbb{R}^{16\times16}$). At these very coarse grid scales, entropically-stabilized NeurDE can be more stable than even our stabilized data-generation numerical method.