37 citations · 133 across the 14 of their papers we have counts for
15 papers
Structure-Preserving Operator Learning: Modeling the Collision Operator of Kinetic Equations
Jae Yong Lee, Steffen Schotthöfer, Tianbai Xiao +2
This work explores the application of deep operator learning principles to a problem in statistical physics. Specifically, we consider the linear kinetic equation, consisting of a…
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…
KiT-RT: An extendable framework for radiative transfer and therapy
Jonas Kusch, Steffen Schotthöfer, Pia Stammer +2
In this paper we present KiT-RT (Kinetic Transport Solver for Radiation Therapy), an open-source C++ based framework for solving kinetic equations in radiation therapy applications…
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…
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 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…
A structure-preserving surrogate model for the closure of the moment system of the Boltzmann equation using convex deep neural networks
Steffen Schotthöfer, Tianbai Xiao, Martin Frank +1
Direct simulation of physical processes on a kinetic level is prohibitively expensive in aerospace applications due to the extremely high dimension of the solution spaces. In this…
A flux reconstruction kinetic scheme for the Boltzmann equation
Tianbai Xiao
It is challenging to solve the Boltzmann equation accurately due to the extremely high dimensionality and nonlinearity. This paper addresses the idea and implementation of the firs…
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…
Modeling and Simulation of Non-equilibrium Flows with Uncertainty Quantification
Tianbai Xiao
In the study of gas dynamics, theoretical modeling and numerical simulation are mostly set up with deterministic settings. Given the coarse-grained modeling in theories of fluids,…
A stochastic kinetic scheme for multi-scale plasma transport with uncertainty quantification
Tianbai Xiao, Martin Frank
In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochasti…
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 velocity-space adaptive unified gas kinetic scheme for continuum and rarefied flows
Tianbai Xiao, Kun Xu, Qingdong Cai
In this paper, a unified gas kinetic scheme with adaptive velocity space (AUGKS) for multiscale flow transport will be developed. In near-equilibrium flow regions, particle distrib…
An investigation of non-equilibrium heat transport in a gas system under external force field
Tianbai Xiao, Kun Xu, Qingdong Cai +1
The gas dynamics under external force field is essentially associated with multiple scale nature due to the large variations of density and local Knudsen number. Single scale fluid…
A Well-Balanced Unified Gas-Kinetic Scheme for Multiscale Flow Transport Under Gravitational Field
Tianbai Xiao, Qingdong Cai, Kun Xu
The gas dynamics under gravitational field is usually associated with the multiple scale nature due to large density variation and a wide range of local Knudsen number. It is chal-…