Tianbai Xiao

Tianbai Xiao
Karlsruhe Institute of Technology | KIT · Institute of Applied and Numerical Mathematics

Ph.D. Peking University
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About

21
Publications
3,510
Reads
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118
Citations
Introduction
Tianbai Xiao (https://xiaotianbai.com) @Department of Mathematics and Steinbuch Centre for Computing in Karlsruhe Institute of Technology. Topics: kinetic theory and related numerical algorithm, uncertainty quantification and neural differential equations. For reproducible science, welcome to check the open-source computational physics and machine learning framework (https://github.com/vavrines/Kinetic.jl).
Additional affiliations
August 2019 - present
Karlsruhe Institute of Technology
Position
  • Research Associate
April 2016 - January 2019
The Hong Kong University of Science and Technology
Position
  • Research Assistant
Education
September 2014 - June 2019
Peking University
Field of study
  • Fluid Mechanics

Publications

Publications (21)
Article
Full-text available
Plasmas present a diverse set of behaviors in different regimes. Given the intrinsic multiscale nature of plasma dynamics, classical theoretical and numerical methods are often employed at separate scales with corresponding assumptions and approximations. Clearly, the coarse-grained modeling may introduce considerable uncertainties between the fiel...
Article
Full-text available
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 availability of efficient tools, it is an obvious idea to try to substitute the calculation of the collision operator by the evaluation of a neural network. However, it is unlcear...
Article
Full-text available
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 first flux reconstruction method for high-order Boltzmann solutions. Based on the Lagrange interpolation and reconstruction, the kinetic upwind flux functions are solved simu...
Preprint
Full-text available
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. The aim of this code framework is to provide a collection of classical deterministic solvers for unstructured meshes that allow for easy extendability. Therefore, KiT-R...
Preprint
Full-text available
The multi-scale nature of gaseous flows poses tremendous difficulties for theoretical and numerical analysis. The Boltzmann equation, while possessing a wider applicability than hydrodynamic equations, requires significantly more computational resources due to the increased degrees of freedom in the model. The success of a hybrid fluid-kinetic flow...
Preprint
Full-text available
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 differential equations, such as entropy dissipation and hyperbolicity. The described method embeds convexity of the moment to entropy map in the neural network approximation...
Preprint
Full-text available
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 idea and implementation of the first flux reconstruction scheme for hyperbolic conservation laws with random inputs. Unlike the finite volume method, the treatments in ph...
Conference Paper
Full-text available
View Video Presentation: https://doi.org/10.2514/6.2021-2895.vid 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 paper, we consider the moment system of the Boltzmann equation, which projects the kinetic physics onto t...
Article
Full-text available
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 between the flow-field solutions and the real physics. To study the emergence, propagation and evolution of uncertainties from molecular to hydrodynamic level poses great opp...
Preprint
Full-text available
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 paper, we consider the moment system of the Boltzmann equation, which projects the kinetic physics onto the hydrodynamic scale. The unclosed moment system can be solved i...
Article
Full-text available
Kinetic.jl is a lightweight finite volume toolbox written in the Julia programming language for the study of computational physics and scientific machine learning. It is an open-source project hosted on GitHub and distributed under the MIT license. The main module consists of KitBase.jl for basic physics and KitML.jl for neural dynamics. The functi...
Preprint
Full-text available
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 first flux reconstruction method for high-order Boltzmann solutions. Based on the Lagrange interpolation and reconstruction, the kinetic upwind flux functions are solved simu...
Preprint
Full-text available
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 availability of efficient tools, it is an obvious idea to try to substitute the evaluation of the collision operator by the evaluation of a neural network. However, it is unlcear w...
Preprint
Full-text available
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, considerable uncertainties may exist between flow-field solutions and real-world physics. To study the emergence, propagation and evolution of uncertainties from molecula...
Preprint
Full-text available
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 stochastic Galerkin and collocation methods. Based on the BGK-type relaxation model of the multi-component Boltzmann equation, a scale-dependent kinetic central-upwind flux functi...
Article
Full-text available
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 distribution function is close to the Chapman-Enskog expansion and can be formulated with a continuous velocity space, where only macroscopic conservative variables are updated....
Preprint
Full-text available
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 between the flow-field solutions and the real physics. To study the emergence, propagation and evolution of uncertainties from molecular to hydrodynamic level poses great opp...
Article
Full-text available
Compressible flows exhibit a diverse set of behaviors, where individual particle transports and their collective dynamics play different roles at different scales. At the same time, the atmosphere is composed of different components that require additional degrees of freedom for representation in computational fluid dynamics. It is challenging to c...
Article
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 governing equations, such as the Boltzmann and Navier-Stokes equations, are valid in their respective modeling scales. Without identifying a physical scale between the above t...
Article
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- lenging to construct a reliable numerical algorithm to accurately capture the non-equilibrium physical effect in different regimes. In this paper, a well-balanced unifie...
Article
Full-text available
The multiple scale non-equilibrium gaseous flow behavior under external force field is investigated. Both theoretical analysis based on the kinetic model equation and numerical study are presented to demonstrate the dynamic effect of external force on the flow evolution, especially on the non-equilibrium heat flux. The current numerical experiment...

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Projects

Projects (3)
Project
To use neural networks as building blocks to solve the unified mechanical-neural models
Project
The goal is to enable reliable knowledge sourcing from data by developing models and methods within the field of uncertainty quantification (UQ).
Project
This project is dedicated to developing novel deep learning-based algorithms for solving the challenging Boltzmann equation