TENSOR APPROXIMATION OF STATIONARY DISTRIBUTIONS OF CHEMICAL REACTION NETWORKS.

We prove that the stationary distribution of a system of reacting species with a weakly reversible reaction network of zero deficiency in the sense of Feinberg and separable propensity functions admits the tensor-structured approximation in the quantized tensor train (QTT) format. The complexity of the approximation scales linearly with respect to the number of species and logarithmically in the maximum copy numbers as well as in the desired accuracy. Our result covers the classical mass-action and Michaelis--Menten kinetics which correspond to two widely used classes of propensity functions and also to arbitrary combinations of those. New rank bounds for tensor-structured approximations of the probability density function (PDF) of a truncated one-dimensional Poisson distribution are an auxiliary result of the present paper which might be of independent interest. The present work complements recent results obtained by the authors jointly with Khammash and Nip on the tensor-structured numerical simulation of the evolution of system states distributions, driven by the Kolmogorov forward equation of the system, known also as the chemical master equation (CME). For the two kinetics mentioned above and a general reaction network, we also quantify the error of the low-rank tensor-structured approximation of the CME operator in the QTT format. [ABSTRACT FROM AUTHOR]