Novel Quantitative Analysis of Gas Dynamics Equations using Physics Informed Neural Network (PINN) Raj Rashmi and Kojiro Suzuki (Univ. of Tokyo）

The discovery of governing equations using the Physics Informed Neural Network (PINN) based on spatial-temporal data is revolutionizing the field of statistical physics. This study combines neural network technology with deterministic model equations and molecular simulation to find an appropriate description of stochastic phenomena. Conventional stochastic solvers rely on molecular interactions and enforce basic conservation laws on a microscopic level. Data-driven algorithms like PINN, when combined with molecular simulations, are promising for (i) deterministic model equations consisting of partial derivatives and (ii) data-based discovery of macroscopic field properties for stochastic phenomena, for which we have abundant data but scarce knowledge of physical form. In the present study, as a trial, the diffusion of the gas was simulated by the DSMC method, and the diffusion coefficient was accurately identified by PINN.