A Machine Learning Approach To Calculating the Non-Equilibrium Diffusion Coefficients in the State-To-State Solution of the Navier–Stokes Equations

Abstract This work considers the application of machine learning methods for approximate determination of diffusion coefficients that are part of extended Navier–Stokes equations solved in a state-by-state approximation. Three methods are suggested: the k-Nearest Neighbors (k-NN) algorithm, a classical neural network (NN) and Physics-Informed Neural Network (PINN). The resulting solution, fully based on data and well-known physics relations, can be used to direct research in more complex cases.

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