Machine Learning Accelerated Rarefied Gas Dynamics Calculations Based on DSMC Dataset

This work introduces a deep neural network (DNN) surrogate that accelerates Direct Simulation Monte Carlo (DSMC) for rarefied-gas flows without sacrificing physical accuracy. First, a fully connected network is trained on high-fidelity DSMC data to reproduce argon's Maxwell–Boltzmann speed distribution. By embedding the physical low-speed boundary condition into the training set, the model drives the mean-squared error below 10⁻⁵ and cuts inference time from minutes to milliseconds. Next, for one-dimensional shock waves, a multi-output DNN augmented with trainable Fourier features learns full profiles of density, velocity, and temperature; though only trained on Mach 1.4–1.9, it generalizes effectively to Mach 2 and 2.5. Finally, in a lid-driven cavity study, a "family-of-experts" strategy—training specialist networks at discrete Knudsen numbers and interpolating their log-space outputs—recovers unseen Kn regimes with under 2% spatial error in 2D velocity and temperature fields. Key innovations include (i) injecting physical constraints during preprocessing, (ii) using learnable Fourier mappings to capture steep gradients, and (iii) adopting a modular expert-interpolation scheme to span wide Kn ranges. Together, these elements establish a scalable recipe for fast, trustworthy surrogates applicable to non-equilibrium phenomena previously obtained only through DSMC approach.