Machine learning of hidden variables in multiscale fluid simulation

Abstract Solving fluid dynamics equations often requires the use of closure relations that account for missing microphysics. For example, when solving related to systems with a large Reynolds number, sub-grid effects become important and turbulence is required, in Knudsen kinetic required. By adding an equation governing growth transport quantity requiring relation, it becomes possible capture microphysics through introduction ‘hidden variables’ are non-local space time. The behavior response conditions can be learned from higher fidelity or ab-initio model contains all In our study, partial differential simulator end-to-end differentiable used train judiciously placed neural networks against ground-truth simulations. We show this method enables Euler based approach reproduce non-linear, number plasma physics otherwise only modeled using Boltzmann-like simulators such as Vlasov particle-in-cell modeling.