Differentiable Programming for Plasma Physics: From Diagnostics to Discovery and Design

Differentiable programming, enabled by automatic differentiation (AD), provides a robust framework for gradient-based optimization in computational plasma physics. While optimization is often only used towards design, we demonstrate that it can also be used for discovery and bridging the gap towards multi-scale modeling. We discuss four applications: (1) discovering novel nonlinear plasma phenomena, including a previously unknown superadditive wavepacket interaction regime, by optimizing differentiable kinetic simulations; (2) learning hidden variables that capture spatiotemporally non-local kinetic effects in fluid simulations, enabling hydrodynamic models to reproduce large Knudsen number physics typically requiring kinetic solvers; (3) accelerating Thomson scattering analysis by over $140\times$ while enabling extraction of velocity distribution functions with $\mathcal{O}(10^3)$ parameters; and (4) inverse design of spatiotemporal laser pulses that achieve target far-field behavior where full space-time coupling improves performance by $15\times$ over spatial or temporal optimization alone. These examples illustrate that differentiable programming not only accelerates existing design and inference workflows but enables qualitatively new capabilities, from algorithmic physics discovery to high-dimensional inference and design previously considered intractable.