Learning closure relations using differentiable programming: An example in radiation transport

Abstract

Reduced order models with a-priori unknown closure relations are ubiquitous in transport problems. In this work, we present a machine-learning approach to finding closure relations utilising differentiable programming. We use the Su Olson radiation transport test problem as an example training data set. We present novel closures for second angular moment (variable Eddington factor), third angular moment and flux-limited diffusion models. We evaluate the improvement of the machine-learnt closures over those from the literature. These improvements are then tested by considering a modification to the Su Olson problem. Comparisons to literature closures show the machine learning models out-perform them in both the trained and unseen problems.