Reduced order model for kinetic and transport problems

Speaker: Zhichao Peng (MSU)

Dates: 2023/02/24

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Abstract: Numerical simulation plays an important role in various engineering and scientific problems. Reduced order model (ROM), a technique to reduce degrees of freedom needed in numerical simulations, is developed to accelerate today’s simulations.In the first part of this talk, we will discuss a ROM for the radiative transfer equation (RTE) based on the micro-macro decomposition. RTE is a kinetic equation which models particle systems in nuclear engineering and astrophysics. One of the main challenges to numerically solve this equation is due to its high dimensional nature, and standard grid-based method may suffer from the curse of dimensionality. To mitigate the curse of dimensionality, we construct a ROM by projecting the original problem to some low dimensional surrogate spaces, and these spaces are constructed in a way which respects the underlying low-rank structure.

In the second part, we will discuss a ROM for transport problems. Due to the slow decay of Kolmogorov n-width for some transport problems, classical linear ROMs may be inefficient or even inaccurate for these problems. The underlying low rank structure of these problems may be more efficiently captured through some intrinsic transformations, hence we propose to learn a subspace determined by such transformations from data and design a new ROM for transport problems.