Online Optimisation of Machine Learning Collision Models to Accelerate Direct Molecular Simulation of Rarefied Gas Flows

TL;DR

This paper introduces an online machine learning approach to calibrate collision models in rarefied gas flow simulations, significantly reducing computational costs while maintaining high accuracy compared to direct molecular simulations.

Contribution

It develops an online optimization algorithm for in situ calibration of collision models, replacing costly trajectory calculations with neural networks during simulations.

Findings

Achieves similar accuracy to DMS at 5-15 times lower cost.

Successfully applies to 1D normal shocks in argon across various conditions.

Online calibration improves DSMC collision models' accuracy.

Abstract

We develop an online optimisation algorithm for in situ calibration of collision models in simulations of rarefied gas flows. The online optimised collision models are able to achieve similar accuracy to Direct Molecular Simulation (DMS) at significantly reduced computational cost for 1D normal shocks in argon across a wide range of temperatures and Mach numbers. DMS is a method of simulating rarefied gases which numerically integrates the trajectories of colliding molecules. It often achieves similar fidelity to Molecular Dynamics (MD) simulations, which fully resolve the trajectories of all particles at all times. However, DMS is substantially more computationally expensive than the popular Direct Simulation Monte Carlo (DSMC) method, which uses simple phenomenological models of the collisions. We aim to accelerate DMS by replacing the computationally costly Classical Trajectory Calculations (CTC) with a neural network collision model. A key feature of our approach is that the machine learning (ML) collision model is optimised online during the simulation on a small dataset of CTC trajectories generated in situ during simulations. The online Machine Learning DMS (ML-DMS) is able to reproduce the accuracy of MD and CTC-DMS for 1D normal shocks in argon at a significantly lower computational cost (by a factor of $\sim5$--$15$), at a wide range of physical conditions (Mach numbers $1.55\leq \text{Ma}\leq 50 $, densities $\sim 10^{-4}\text{kg}\text{m}^{-3}$ to $1\text{kg}\text{m}^{-3}$, and temperatures 16K to 300K). We also derive an online optimisation method for calibration of DSMC collision models given a model of the interatomic forces. In our numerical evaluations for 1D normal shocks, the online optimisation method matches or significantly improves the accuracy of VHS (Variable Hard Sphere) DSMC with respect to CTC-DMS (with a $\sim20 \times$ lower computational cost).