| Abstract: |
| In this talk, we will first discuss the hypocoercivity analysis for general space-inhomogeous collisional kinetic problems with uncertainties, on the regularity and long-time behavior of the solution in the random space, proved spectral accuracy and long time (exponential decay) error estimates for the stochastic Galerkin method. For the spatially homogenous Boltzmann equation, we will show the spectral convergence for the numerical system with discrete velocity and uncertainty variables. Regarding numerical simulations for kinetic models with uncertainties, we will introduce the multi-fidelity method and asymptotic-preserving neural network approach, then discuss about how to apply the above analyses to obtain convergence and error estimates for the numerical methods. |
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