Applying Differentiable Programming to Kinetic Plasma Physics Simulations

Plasma supports collective modes and particle-wave interactions that leads to complex behavior in fusion energy, and other applications. While plasma can sometimes be modeled as a charged fluids, the Vlasov-Poisson system of partial differential equations provides a description that is useful towards the study of nonlinear effects in the higher dimensional momentum-position phase-space that describes the full complexity of plasma dynamics. By constructing a Vlasov-Poisson solver using an auto-differentiable framework, we are able to perform gradient-based optimization of arbitrary functions of the simulation results with respect to input parameters. We validate the methodology and implementation by rediscovering resonances in the well-understood linear regime. Then, we use our solver to learn the parameters to a forcing function that reveal new non-linear effects in finite-length electrostatic plasma-wave propagation. We also discuss the effect of neural-reparameterization of the inputs on the optimization process.