On the design and evaluation of generative models in high energy density physics

Understanding high energy density physics (HEDP) is critical for advancements in fusion energy and astrophysics. The computational demands of the computer models used for HEDP studies have led researchers to explore deep learning methods to enhance simulation efficiency. This paper introduces HEDP-Gen, a framework for training and evaluating generative models tailored for HEDP. Central to HEDP-Gen is Geom-WAE-a generalized Wasserstein auto-encoder accommodating both Euclidean and non-Euclidean latent spaces. HEDP-Gen establishes a rigorous evaluation standard, assessing not only reconstruction fidelity but also scientific validity, sample diversity, and latent space utility in geodesic interpolation and attribute traversal. A case study using hyperbolic geometry (Poincaréball prior) demonstrates that non-Euclidean priors yield scientifically valid samples and stronger generalization in downstream tasks, advantages often missed by conventional reconstruction metrics.