Acceleration of Boltzmann Collision Integral Calculation Using Machine Learning

The Boltzmann equation is essential to the accurate modeling of rarefied gases. Unfortunately, traditional numerical solvers for this are too computationally expensive many practical applications. With modern interest in hypersonic flight and plasma flows, which relevant, there would be immediate value an efficient simulation method. collision integral component main contributor large complexity. A plethora new mathematical approaches have been proposed effort reduce computational cost solving integral, yet it still remains prohibitively problems. This paper aims accelerate computation via machine learning methods. In particular, we build a deep convolutional neural network encode/decode solution vector, enforce conservation laws during post-processing before each time-step. Our preliminary results spatially homogeneous show drastic reduction cost. Specifically, our algorithm requires O(n3) operations, while asymptotically converging direct discretization algorithms require O(n6), where n number discrete velocity points one dimension. method demonstrated speed up 270 times compared these methods maintaining reasonable accuracy.