Felix Klein Kolloquium des Fachbereichs

We present how artificial neural networks can be used to substitute the otherwise costly computation of the Boltzmann collision operator, a nonlinear integral operator  modeling collisions between particles in gases. In large scale simulations, this operator needs to be evaluated in each spatial cell at every time step. Specifically, we study how network architectures can be designed that exactly capture crucial analytical properties of the operator. Of particular interest will be entropy decay, which is related to the Second Law of Thermodynamics. Furthermore, we address the question of data sampling. Several numerical results will be shown.