Data-Driven Surrogate Modeling of DSMC Solutions Using Deep Neural Networks

TL;DR

This paper develops a deep neural network framework that significantly accelerates DSMC simulations for rarefied-gas flows while maintaining high physical accuracy, enabling rapid and reliable surrogate modeling for complex flow phenomena.

Contribution

It introduces novel neural network techniques including physical constraint injection, Fourier feature mapping, and a modular expert-interpolation scheme for wide-range parametric flow modeling.

Findings

Inference time reduced from minutes to milliseconds.

High accuracy in predicting shock profiles and flow fields.

Robust generalization to unseen flow conditions.

Abstract

This study presents a deep neural network (DNN) framework that accelerates Direct Simulation Monte Carlo (DSMC) computations for rarefied-gas flows, while maintaining high physical fidelity. First, a fully connected deep neural network is trained on high-quality DSMC data for seven temperatures (200-650 K) to reproduce the Maxwell-Boltzmann speed distribution of argon. Injecting the physical boundary point into the training set enforces the correct low-speed limit. It reduces the mean-squared error to below 10^-5, thereby decreasing inference time from tens of minutes per DSMC run to milliseconds. For one-dimensional shock waves, a multi-output network equipped with learnable Fourier features learns the complete profiles of density, velocity, and temperature. Trained only on Mach numbers 1.4-1.9, it predicts a Mach 2 and 2.5 case with near-perfect agreement to DSMC, demonstrating robust out-of-training generalization. In a lid-driven cavity, the large parametric spread in Knudsen number is handled by a "family-of-experts" strategy: separate specialist models are trained at discrete Knudsen (Kn) values, and log-space interpolation fuses their outputs. This hybrid surrogate recovers the full 2-D velocity and temperature fields at unseen Kn with less than 2% spatial error. Key innovations include (i) explicit injection of physical constraints during data preprocessing, (ii) learnable Fourier feature mapping to capture steep shock gradients, and (iii) a modular expert-interpolation scheme to cover wide Knudsen ranges. Together, they establish a general recipe for trustworthy, rapid surrogate models that can be extended to non-equilibrium phenomena, gas mixtures, and design optimization workflows