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 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.

A multifidelity approach to continual learning for physical systems

“…In recent years, a huge research focus has been on scientific machine learning methods for physical systems [14][15][16], for example, fluid mechanics and rheology [17][18][19][20][21][22], metamaterial development [23][24][25], high speed flows [26], and power systems [27][28][29][30][31], among many other applications. In particular, physics-informed neural networks, or PINNs [32], allow for accurately representing differential operators through automatic differentiation, allowing for finding the solution to partial differential equations (PDEs) without explicit mesh generation.…”

Learning the dynamics of a one-dimensional plasma model with graph neural networks

“…These efforts include approaches to accelerate [5] or fully replace [6,7] the field solver block, reduce the computational burden associated with the particle push and grid-particle/particle-grid interpolation [8,9], and the integration of surrogate models into advanced physics extensions [10]. In parallel, PIC simulations and machine learning algorithms have also been used to train fast surrogate models for plasma accelerator setups [11][12][13][14], to learn closures for fluid simulations [15], to model hybrid plasma representations [16], and to recover reduced plasma models [17]. However, obtaining a significant computational gain, while enforcing known physics constraints and reproducing the kinetic effects for a broad range of scenarios, is still an open research question.…”