Generative neural networks for designing bandwidth schema that minimize Laser Plasma InstabilitiesΑ

Previous work on the effects of bandwidth on TPD thresholds has quantified the increase in threshold as a function of Δω where Δω is discretized into a finite number of "lines" rather than a continuous distribution. Each of the finite number of lines has 2 free parameters depending on the Δω_i , the amplitude Α_i and an initial phase shift Φ_i. In the previous work, each of these were prescribed in a relatively simple but not necessarily optimal manner. Here, we train a generative neural network to provide optimal bandwidth parameters. To train this neural network, we develop a GPU-native differentiable solver in JAX for the enveloped equations, ADEPT-LPSE, to acquire gradients of TPD simulations with respect to the bandwidth. Using a differentiable solver written in an ML-native framework enables us to train neural networks inline that give the optimal bandwidth parameters as a function of intensity, temperature, and scale length in a relatively small number of simulations (O(1000)) in comparison to a purely supervised neural network (O(N^M) where N is number of parameters and M are the number of samples per parameter))