63 citations · 347 across the 39 of their papers we have counts for
13 papers · 1 filter
RelaxNet: A structure-preserving neural network to approximate the Boltzmann collision operator
Tianbai Xiao, Martin Frank
This paper addresses a neural network-based surrogate model that provides a structure-preserving approximation for the fivefold collision integral. The notion originates from the s…
A flux reconstruction stochastic Galerkin scheme for hyperbolic conservation laws
Tianbai Xiao, Jonas Kusch, Julian Koellermeier +1
The study of uncertainty propagation poses a great challenge to design numerical solvers with high fidelity. Based on the stochastic Galerkin formulation, this paper addresses the…
Using neural networks to accelerate the solution of the Boltzmann equation
Tianbai Xiao, Martin Frank
One of the biggest challenges for simulating the Boltzmann equation is the evaluation of fivefold collision integral. Given the recent successes of deep learning and the availabili…
Massively Parallel Stencil Strategies for Radiation Transport Moment Model Simulations
Marco Berghoff, Martin Frank, Benjamin Seibold
The radiation transport equation is a mesoscopic equation in high dimensional phase space. Moment methods approximate it via a system of partial differential equations in tradition…
A stochastic kinetic scheme for multi-scale flow transport with uncertainty quantification
Tianbai Xiao, Martin Frank
Gaseous flows show a diverse set of behaviors on different characteristic scales. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist betw…
A low-rank method for two-dimensional time-dependent radiation transport calculations
Zhuogang Peng, Ryan McClarren, Martin Frank
The low-rank approximation is a complexity reduction technique to approximate a tensor or a matrix with a reduced rank, which has been applied to the simulation of high dimensional…