Machine learning of hidden variables in multiscale fluid simulation
This addresses the need for efficient and accurate fluid simulations in systems with high Reynolds or Knudsen numbers, offering a novel method to bypass traditional closure models, though it is incremental in applying differentiable simulators to this domain.
The authors tackled the problem of modeling multiscale fluid dynamics with missing microphysics by learning hidden variables from high-fidelity simulations, enabling an Euler equation approach to reproduce non-linear, large Knudsen number plasma physics that typically requires more complex simulators.
Solving fluid dynamics equations often requires the use of closure relations that account for missing microphysics. For example, when solving equations related to fluid dynamics for systems with a large Reynolds number, sub-grid effects become important and a turbulence closure is required, and in systems with a large Knudsen number, kinetic effects become important and a kinetic closure is required. By adding an equation governing the growth and transport of the quantity requiring the closure relation, it becomes possible to capture microphysics through the introduction of ``hidden variables'' that are non-local in space and time. The behavior of the ``hidden variables'' in response to the fluid conditions can be learned from a higher fidelity or ab-initio model that contains all the microphysics. In our study, a partial differential equation simulator that is end-to-end differentiable is used to train judiciously placed neural networks against ground-truth simulations. We show that this method enables an Euler equation based approach to reproduce non-linear, large Knudsen number plasma physics that can otherwise only be modeled using Boltzmann-like equation simulators such as Vlasov or Particle-In-Cell modeling.