Speaker: Juntao Huang (University of Delaware)

Title: Structure-preserving machine learning moment closure models for kinetic equations

Abstract: The radiative transfer equation (RTE) is a high-dimensional kinetic model with important applications in physics and engineering. Moment methods provide an efficient dimension reduction strategy by evolving finitely many angular moments, but they require a closure for the highest-order moment. Designing closures that are both accurate in non-equilibrium regimes and mathematically well-posed remains a major challenge. In this talk, we develop structure-preserving machine learning approaches for moment closure of the RTE. Instead of learning the unclosed high-order moment directly, we propose a gradient-based moment closure, in which a neural network approximates the spatial gradient of the highest-order moment. This formulation improves accuracy in optically thin regimes and offers additional flexibility for enforcing structural properties. A key difficulty of machine learning closures is the potential loss of hyperbolicity, leading to ill-posedness and long-time instability. To address this, we introduce two mechanisms to enforce hyperbolicity: a symmetrizer-based approach ensuring symmetrizability and consistency with the diffusion limit, and an eigenvalue-based approach that guarantees real characteristic speeds. Numerical experiments demonstrate that the resulting hyperbolic machine learning closures achieve improved accuracy over classical models while maintaining long-time stability across different regimes.

A short bio:
Prof. Juntao Huang is an Assistant Professor in the Department of Mathematical Sciences at the University of Delaware and an affiliated faculty member in Data Science Institute at University of Delaware. He received his Ph.D. in Applied Mathematics in 2018 from Tsinghua University, where he also earned dual Bachelor’s degrees in Mathematics and Engineering Mechanics in 2013. Prior to joining Delaware, he served as a Visiting Assistant Professor at Michigan State University from 2018 to 2022, and subsequently held a faculty position at Texas Tech University from 2022 to 2025.