Tensorisation in the Solution of Smoluchowski Type Equations

We investigate the structure of the non-linear operator featured in the Smoluchowski-type system of ordinary differential equations, and find a way to express it algebraically in terms of the parameters of the problem and a few auxiliary tensors, describing, in a sense, the “shape” of the system. We find compact representations of these auxiliary tensors in terms of a Tensor Train decomposition. Provided the parameters admit a compact representation in this format as well, this allows us to rather straightforwardly reuse standard numerical algorithms for a wide range of associated problems, obtaining \(O(\log N)\) asymptotic complexity.