Discovering novel nonlinear plasma physics using machine learning and differentiable programming

Differentiable programming enables the calculation of gradients of general-purpose numerical programs with respect to their inputs e.g. of PDE solvers with respect to their forcing functions. We apply this technique to Vlasov-Fokker-Planck (VFP) simulations of driven nonlinear plasma waves relevant to Stimulated Raman Scattering (SRS). By framing parameter discovery as a gradient-based optimization problem, we are able to discover regions of parameter space where novel nonlinear physics occurs. Because our simulation is fully differentiable, we are able to train neural networks to learn the forcing function that results in the novel nonlinear effects in the VFP system. Because we do not use any surrogate models and retain all physics in the VFP system, we simply observe the simulation output to interpret the novel physical mechanism uncovered by the machine-learned ponderomotive driver. The newfound mechanism may inform the minimal distance required between laser speckles in order to minimize speckle-speckle interaction and suppress kinetic nonlinearities in laser-plasma instabilities.