Stable Machine-Learning Models for Fluid Simulations: A Geometry-Agnostic Approach to Nonlinear Kinetic Effects

For many decades, fusion modeling has struggled with multi-scale physics due to the analytical intractability of certain dynamics and thus, has involved the use of ad-hoc parameters e.g. flux-limiters, frequency-shift scalings, Landau damping fractions. Machine learning offers a new paradigm by which to approximate the functions that describe the nonlinear, kinetic behavior of these phenomena. However, training such models requires careful construction because while some approaches reproduce the correct behavior for a certain parameter regime in a specific geometry over a short time interval, achieving long term stability and generalizing to novel geometries requires retention of all possible physics over the simulation time-scale. The paradigm of differentiable programming enables this retention and allows us to construct simulators that can contain and train neural networks that represent the missing physics. In this work, we acquire a model for nonlinear Landau damping by training a differentiable fluid simulator directly against fully kinetic simulations. Since our model is geometry agnostic by construction, we are able to successfully apply it to 100x larger geometries in space and time, with varying boundary conditions. This exemplifies a promising new direction for the development of reduced models for missing physics in design codes.