Learning interpretable ICF hot spot models with deep learning

Simple physics models are often used to infer hot spot conditions, that are not directly measured, from experimental observables in ICF experiments. The multiple achievements of ignition and increasing target gains attained at the National Ignition Facility (NIF) is moving experiments into a paradigm of rapidly evolving hot spots which may violate simple model assumptions and lower model accuracy. Here we present two deep learning methods to predict hot spot conditions from experimental observables and compare performance with the “0D” hot spot model over a massive high yield 2D HYDRA simulation ensemble. The first method uses a "black box" neural network ensemble to predict several hot spot parameters and the second method uses a deep symbolic regression model (Petersen et al. 2021) to train a recurrent neural network (RNN) to sequentially build interpretable mathematical expressions to best fit selected hot spot parameters. We find the trained DeepSymReg model learns expressions that contain the 0D model equations with effective “corrections”, via leveraging more observables in the expression that may encode added hot spot information, to recover near fidelity of HYDRA simulations. Both DL models significantly outperform the 0D model for a variety of hot spot parameters and can help develop high accuracy ICF foundation models for future higher yield designs.