Training of particle-turbulence sub-grid-scale closures with just particle data

TL;DR

This paper demonstrates that neural networks trained on particle data, focusing on spectra and kinetic energy, can effectively model sub-grid-scale turbulence physics without direct flow field input.

Contribution

It introduces a novel approach to train turbulence closures using only particle data, emphasizing spectral and kinetic energy targets, and addresses stochastic physics aspects.

Findings

Training on spectra improves model effectiveness over full space-time data.

Sub-grid-scale stress models can be learned from particle kinetic energy alone.

Models remain effective even with noisy, partial, or single-component particle data.

Abstract

If sufficient training data are available, neural networks are attractive for representing missing physics in simulations, such as sub-grid scales in the coarse-mesh particle-turbulence system we consider. Physical constraints are known to both increase performance and reduce the need for data; we use the complete physics represented in the discretized governing equations as a constraint. Two-way coupled particles in two-dimensional turbulence provide a sufficiently complex system to assess effectiveness for various training data, all constructed from well-resolved simulations, in cases intentionally degraded to assess robustness. Surprisingly, using the full space-time data actually hinders model effectiveness. Instead, training that targets only spectra -- hence, neglecting phase information -- provides better closures, which is related to the well-known success of non-dissipative discretizations for simulating turbulence. It is found that some of the missing physics that lead to preferential particle concentration errors are fundamentally stochastic on the coarse mesh and therefore uncorrectable by the basic approach; a learning formulation is introduced for a Langevin-type closure to correct this. Most importantly, training just for particle kinetic energy -- without any direct input from the flow field -- also yields effective sub-grid-scale stress models. This holds true even if noise is added to the particle data, if only a sub-sample of particles are used, or if only one component of the particle velocity is used. In sum, these results show a path for inferring sub-grid-scale physics based just on particle data from experiments.