| Abstract: |
| In this talk, we will discuss about a class of multi-fidelity numerical methods for solving kinetic models. In the first part, we will address the uncertainty quantification for kinetic problems and development of bi-fidelity or tri-fidelity methods for different models, where some error estimates are studied using the hypocoercivity. In the second part, we will study an efficient asymptotic-preserving scheme for solving the Boltzmann equation with bi-fidelity algorithm designed in the velocity discretization. Lastly, some applications to deep learning approaches for kinetic models will be discussed, with the idea of bi-fidelity introduced. These are joint works with Xueyu Zhu, Lorenzo Pareschi, Nicolas Crouseilles, Zhen Hao. |
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