Projects

Currently I'm conducting research on three topics

• Mesoscopic Science
• Uncertainty Quantification
• Scientific Machine Learning

Mesoscopic Science: From Atom to Continuum

The world is multi-scale, multi-layered and multi-physics in nature. David Hilbert's sixth problem let to an intriguing line of research that links the behavior of interacting many-particle systems at different scales through mesoscopic (characteristic scale between micro and macro) modeling. The leap forward in modern advanced computing power provides us with an alternative to study the Hilbert's passage from a simulation point of view. This project is dedicated to modeling the nonlinear behaviors of particle transports (including molecules, plasma, electrons, photons, phonons, skyrmions, etc.) based on kinetic theory, and developing high-performance solution algorithms. Topics include, but are not limited to, direct solvers for the Boltzmann equation and related models, moment models with physics-oriented closures, and particle-based simulation frameworks.

Uncertainty Quantification: From Data to Knowledge

How will the climate develop, how secure is our energy supply, and what chances does molecular medicine offer? The rapidly increasing amount of data offers radically new opportunities to address today’s most pressing questions but also requires novel mathematical and statistical methods to handle them. The uncertainties coming from stochastic data or immature prior knowledge are often considered as an unavoidable burden in real-world applications. By employing probabilistic data science techniques, uncertainty can also be turned into a valuable source of information and a powerful enrichment of black-box approaches from artificial intelligence. To harness this source of information, in this project we identify common challenges between several common use cases and foster translational research at the interface of disciplinary and mathematical research. The goal is to enable more reliable knowledge sourcing from data by developing tools and methods within the field of uncertainty quantification (UQ).

Scientific Machine Learning: From Machine to Reality

The thriving machine learning techniques provide the possibility for solving problems that seemed challenging in the past, e.g., computer vision and natural language processing. The same momentum is beginning to build in computational sciences, leading to a field named scientific machine learning (SciML). While typical classification and regression tasks in classical machine learning applications mostly handle discrete and localized data, in scientific machine learning, information at different locations is expected to be connected by mathematical modeling and physical constraints, e.g., differential equations. The goal of this project is to leverage state-of-the-art machine learning models as building blocks in a numerical method to solve unified mechanical-ML models. Fundamentally, a physical model is a coarse-grained projection of reality that possesses an intricate structure, which a numerical method needs to preserve. Thus, machine learning is likely to be beneficial, but cannot be used out-of-the-box. The project therefore touches upon the applications point of view of machine learning with a focus on interpretability and robustness, and on the mathematical methodologies point of view to solve neural differential and integral equations.

OUTCOME

I can be found on Google Scholar and ResearchGate.

Preprints

Xu Wang, Tianbai Xiao, Yonghao Zhang, and Song Chen. An investigation of thermochemical reaction and aerodynamic ablation model during hypersonic reentry. Submitted to Acta Mechanica Sinica, 2024.

Shiwei Hu, Tianbai Xiao, Mingshuo Han, Zuoxu Li, Erkan Oterkus, Selda Oterkus, and Yonghao Zhang. An Efficient Explicit-Implicit Adaptive Method for Peridynamic Modelling of Quasi-Static Fracture Formation and Evolution. arXiv:2410.12552, 2024. [PDF]

Jae Yong Lee, Steffen Schotthöfer, Tianbai Xiao, Sebastian Krumscheid, and Martin Frank. Structure-Preserving Operator Learning: Modeling the Collision Operator of Kinetic Equations. arXiv:2402.16613, 2024. [PDF]

2024

Mingliang Zhong, Tianbai Xiao, Mathias J. Krause, Martin Frank, and Stephan Simonis. A stochastic Galerkin lattice Boltzmann method for incompressible fluid flows with uncertainties. Journal of Computational Physics, 517:113344, 2024. [PDF]

Jiaqing Kou and Tianbai Xiao. Artificial Intelligence and Machine Learning in Aerodynamics. Metascience in Aerospace, 1(2): 190-218, 2024. [PDF]

Yun Long, Xi'an Guo, and Tianbai Xiao. Research, Application and Future Prospect of Mode Decomposition in Fluid Mechanics. Symmetry, 16(2): 155, 2024. [PDF]

2023

Jonas Kusch, Steffen Schotthöfer, Pia Stammer, Jannick Wolters, and Tianbai Xiao. KiT-RT: An extendable framework for radiative transfer and therapy. ACM Transactions on Mathematical Software, 49(4): 1-24, 2023. [PDF]

Tianbai Xiao and Martin Frank. RelaxNet: A structure-preserving neural network to approximate the Boltzmann collision operator. Journal Computational Physics, 490: 112317, 2023. [PDF]

Tianbai Xiao, Steffen Schotthöfer, and Martin Frank. Predicting continuum breakdown with deep neural networks. Journal Computational Physics, 489: 112278, 2023. [PDF]

Tianbai Xiao, Jonas Kusch, Julian Koellermeier, and Martin Frank. A Flux Reconstruction Stochastic Galerkin Scheme for Hyperbolic Conservation Laws. Journal of Scientific Computing, 95(1): 18, 2023. [PDF]

2022

Tianbai Xiao. A Well-Balanced Unified Gas-Kinetic Scheme for Multicomponent Flows under External Force Field. Entropy, 24(8): 1110, 2022. [PDF]

Tianbai Xiao. An Investigation of Uncertainty Propagation in Non-equilibrium Flows. International Journal of Computational Fluid Dynamics, 36(4): 294-318, 2022. [PDF]

Steffen Schotthöfer, Tianbai Xiao, Martin Frank, and Cory D. Hauck. Structure Preserving Neural Networks: A Case Study in the Entropy Closure of the Boltzmann Equation. Proceedings of the 39th International Conference on Machine Learning, PMLR: 19406-19433, 2022. [PDF][Video][Poster]

Steffen Schotthöfer, Tianbai Xiao, Martin Frank, and Cory D. Hauck. Neural network-based, structure-preserving entropy closures for the Boltzmann moment system. arXiv:2201.10364v1 [math.NA] 25 Jan. 2022. [PDF]

2021

Tianbai Xiao. A flux reconstruction kinetic scheme for the Boltzmann equation. Journal of Computational Physics, 447: 110689, 2021. [PDF]

Tianbai Xiao and Martin Frank. Using neural networks to accelerate the solution of the Boltzmann equation. Journal of Computational Physics, 443: 110521, 2021. [PDF]

Steffen Schotthöfer, Tianbai Xiao, Martin Frank, and Cory D. Hauck. A structure-preserving surrogate model for the closure of the moment system of the Boltzmann equation using convex deep neural networks. AIAA Aviation Forum, 2021. [PDF]

Tianbai Xiao. Kinetic.jl: A portable finite volume toolbox for scientific and neural computing. Journal of Open Source Software, 6(62): 3060, 2021. [PDF]

Tianbai Xiao and Martin Frank. A stochastic kinetic scheme for multi-scale flow transport with uncertainty quantification. Journal of Computational Physics, 437: 110337, 2021. [PDF]

Tianbai Xiao and Martin Frank. A stochastic kinetic scheme for multi-scale plasma transport with uncertainty quantification. Journal of Computational Physics, 432: 110139, 2021. [PDF]

2020

Tianbai Xiao. Modeling and Simulation of Non-equilibrium Flows with Uncertainty Quantification. arXiv:2008.02503v1 [physics.comp-ph] 6 Aug. 2020. [PDF]

Tianbai Xiao, Chang Liu, Kun Xu, and Qingdong Cai. A velocity-space adaptive unified gas kinetic scheme for continuum and rarefied flows. Journal of Computational Physics, 415: 109535, 2020. [PDF]

2019

Tianbai Xiao, Kun Xu, and Qingdong Cai. A unified gas-kinetic scheme for multiscale and multicomponent flow transport. Applied Mathematics and Mechanics, 40(3), 355-372, 2019. [PDF]

2018

Tianbai Xiao, Kun Xu, Qingdong Cai, and Tiezheng Qian. An investigation of non-equilibrium heat transport in a gas system under external force field. International Journal of Heat and Mass Transfer, 126: 362-379, 2018. [PDF]

2017

Tianbai Xiao, Qingdong Cai, and Kun Xu. A well-balanced unified gas-kinetic scheme for multiscale flow transport under gravitational field. Journal of Computational Physics, 332: 475-491, 2017. [PDF]

2016

Tianbai Xiao and Kun Xu. Investigation of multiscale non-equilibrium flow dynamics under external force field. arXiv:1610.05544 [physics.flu-dyn] 19 Oct 2016. [PDF]