63 citations · 357 across the 53 of their papers we have counts for
6 papers · 1 filter
Numerical Robustness of PINNs for Multiscale Transport Equations
Alexander Jesser, Kai Krycki, Ryan G. McClarren +1
We investigate the numerical solution of multiscale transport equations using Physics Informed Neural Networks (PINNs) with ReLU activation functions. Therefore, we study the analo…
A review of low-rank methods for time-dependent kinetic simulations
Lukas Einkemmer, Katharina Kormann, Jonas Kusch +2
Time-dependent kinetic models are ubiquitous in computational science and engineering. The underlying integro-differential equations in these models are high-dimensional, comprised…
The non-equilibrium Marshak wave problem in non-homogeneous media
Nitay Derei, Shmuel Balberg, Shay I. Heizler +3
We derive a family of similarity solutions to the nonlinear non-equilibrium Marshak wave problem for an inhomogeneous planar medium which is coupled to a time dependent radiation d…
A multi-fidelity adaptive dynamical low-rank based optimization algorithm for fission criticality problems
C. Scalone, L. Einkemmer, J. Kusch +1
Computing the dominant eigenvalue is important in nuclear systems as it determines the stability of the system (i.e. whether the system is sub or supercritical). Recently, the work…
A unified theory of the self-similar supersonic Marshak wave problem
Menahem Krief, Ryan G. McClarren
We present a systematic study of the similarity solutions for the Marshak wave problem, in the local thermodynamic equilibrium (LTE) diffusion approximation and in the supersonic r…
Self-similar solutions for the non-equilibrium nonlinear supersonic Marshak wave problem
Menahem Krief, Ryan G. McClarren
Similarity solutions to the nonlinear non-equilibrium Marshak wave problem with a time dependent radiation driving source are presented. The radiation transfer model used is the gr…