Juntao Huang, University of Delaware
Event Date
2025-11-19
Event Time
04:00 pm ~ 05:00 pm
Event Location
617 Wachman Hall
In this talk, we take a data-driven approach and apply machine learning to the moment closure problem for the kinetic equations, including radiative transfer equations and Boltzmann BGK equations. Traditional closures often rely on empirical assumptions, while naive machine learning closures can violate structural properties of the PDEs, leading to ill-posedness and numerical instability. To address these challenges, we propose a gradient-based moment closure, where neural networks directly learn the gradient of the high-order moment. Furthermore, we develop two strategies to enforce hyperbolicity, ensuring well-posed and stable evolution of the machine learning model. Extensive benchmark tests demonstrate that our hyperbolic ML closures achieve high accuracy, robust stability, and good generalization beyond training regimes.