Physics-Constrained Deep Learning-Based Model for Non-Equilibrium Flows

In hypersonic applications, the construction of accurate and computationally affordable models for simulating non-equilibrium fluid flows is a challenging task. In particular, designrelevant cases are complex and data availability is poor, de facto hampering the development of constitutive relations of general validity. To circumvent this issue, we propose a methodology for building physics-constrained neural networks providing a correction to the constitutive relation included in the Navier-Stokes model, with a specific focus on rarefied flows. The approach is based on the premise that physical laws should be inherently encoded in robust and accurate closures. By requiring the fulfillment of these laws i.e., by introducing specific constraints to the training process of the neural network, we obtain correction terms coherent with the physics, enhancing the modeling of both the viscous stress tensor and the heat flux vector. The goal is to demonstrate the feasibility of the proposed approach and its potential to benchmark the test case of the 1D shock.