63 citations · 347 across the 39 of their papers we have counts for
45 papers
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…
Constructing relaxation systems for lattice Boltzmann methods
Stephan Simonis, Martin Frank, Mathias J. Krause
We present the first top-down ansatz for constructing lattice Boltzmann methods (LBM) in d dimensions. In particular, we construct a relaxation system (RS) for a given scalar, line…
Predicting continuum breakdown with deep neural networks
Tianbai Xiao, Steffen Schotthöfer, Martin Frank
The multi-scale nature of gaseous flows poses tremendous difficulties for theoretical and numerical analysis. The Boltzmann equation, while possessing a wider applicability than hy…
Multivariate error modeling and uncertainty quantification using importance (re-)weighting for Monte Carlo simulations in particle transport
Pia Stammer, Lucas Burigo, Oliver Jäkel +2
Fast and accurate predictions of uncertainties in the computed dose are crucial for the determination of robust treatment plans in radiation therapy. This requires the solution of…
Neural network-based, structure-preserving entropy closures for the Boltzmann moment system
Steffen Schotthöfer, Tianbai Xiao, Martin Frank +1
This work presents neural network based minimal entropy closures for the moment system of the Boltzmann equation, that preserve the inherent structure of the system of partial diff…
A low-rank power iteration scheme for neutron transport criticality problems
Jonas Kusch, Benjamin Whewell, Ryan McClarren +1
Computing effective eigenvalues for neutron transport often requires a fine numerical resolution. The main challenge of such computations is the high memory effort of classical sol…