Learning physical unknowns from hydrodynamic shock and material interface features in ICF capsule implosions

In high energy density physics (HEDP) and inertial confinement fusion (ICF), predictive modeling is complicated by uncertainty in parameters that characterize various aspects of the modeled system, such as those characterizing material properties, equation of state (EOS), opacities, and initial conditions. Typically, however, these parameters are not directly observable. What is observed instead is a time sequence of radiographic projections using X-rays. In this work, we define a set of sparse hydrodynamic features derived from the outgoing shock profile and outer material edge, which can be obtained from radiographic measurements, to directly infer such parameters. Our machine learning (ML)-based methodology involves a pipeline of two architectures, a radiograph-to-features network (R2FNet) and a features-to-parameters network (F2PNet), that are trained independently and later combined to approximate a posterior distribution for the parameters from radiographs. We show that the estimated parameters can be used in a hydrodynamics code to obtain density fields and hydrodynamic shock and outer edge features that are consistent with the data. Finally, we demonstrate that features resulting from an unknown EOS model can be successfully mapped onto parameters of a chosen analytical EOS model, implying that network predictions are learning physics, with a degree of invariance to the underlying choice of EOS model.

Reconstructing Richtmyer-Meshkov instabilities from noisy radiographs using low dimensional features and attention-based neural networks

A trained attention-based transformer network can robustly recover the complex topologies given by the Richtmyer-Meshkoff instability from a sequence of hydrodynamic features derived from radiographic images corrupted with blur, scatter, and noise. This approach is demonstrated on ICF-like double shell hydrodynamic simulations. The key component of this network is a transformer encoder that acts on a sequence of features extracted from noisy radiographs. This encoder includes numerous self-attention layers that act to learn temporal dependencies in the input sequences and increase the expressiveness of the model. This approach is demonstrated to exhibit an excellent ability to accurately recover the Richtmyer-Meshkov instability growth rates, even despite the gas-metal interface being greatly obscured by radiographic noise.