691	RWTH Publication No: 1009806        2025
TITLE	Sparse Reconstruction of Multi-Dimensional Kinetic Distributions
AUTHORS	Georgii Oblapenko, Manuel Torrilhon, Michael Herty
ABSTRACT	In the present work, we propose a novel method for reconstruction of multi-dimensional kinetic distributions, based on their representation as a mixture of Dirac delta functions. The representation is found as a solution of an optimization problem. Different target functionals are considered, with a focus on sparsity-promoting regularization terms. The proposed algorithm guarantees non-negativity of the distribution by construction, and avoids an exponential dependence of the computational cost on the dimensionality of the problem. Numerical comparisons with other classical methods for reconstruction of kinetic distributions are provided for model problems, and the role of the different parameters governing the optimization problem is studied.
KEYWORDS	Boltzmann equation, moment method, maximum entropy, sparse reconstruction, numerical optimization