Exploring higher-order effects in laser-driven ion acceleration via deep learning

Computer models of intense, laser-driven ion acceleration require expensive particle-in-cell (PIC) simulations that may struggle to capture all the multi-scale, multi-dimensional physics involved. We discuss an approach to ameliorate this deficiency, using a physics-informed, multi-fidelity model that can incorporate physical trends and phenomena at different levels. As the base framework for this study, an ensemble of approximately 10,000 1D PIC simulations was generated to buttress a separate ensemble of hundreds of high-fidelity, one- and two-dimensional simulations. Using transfer learning and multi-fidelity modeling in a deep neural network, one can reproduce the more complex physics at a much smaller cost. The networks trained in this fashion can in turn act as a surrogate model for the simulations themselves, allowing for quick and efficient exploration of the parameter space of interest. Standard figures-of-merit were used as benchmarks such as the hot electron temperature and peak ion energy, in addition to higher-order data such as the fields and particle phase space. These surrogate models are also useful for incorporating more complex scenarios, such as pulse shaping, that are challenging to model systematically let alone execute. We can rapidly identify and explore under what conditions dimensionality becomes a predominant effect as well as the transition between acceleration mechanisms.