Speaker
Description
The development of new drugs and therapies increasingly relies on the numerical simulation of the reaction networks inside biological cells. However, the most accurate description of such reaction networks with the chemical master equation (CME) suffers from the curse of dimensionality, meaning that memory and computational cost grow exponentially with the number of dimensions. This renders the simulation of such networks infeasible on currently available computer hardware and it will remain a fundamental limitation in the future.
In this talk, we present a novel numerical solution method for the stochastic description of chemical reaction networks. It is based on the dynamical low-rank approximation with tree tensor networks, which effectively approximates the high-dimensional solution of the CME as a linear combination of low-rank factors.
This low-rank approximation corresponds to a hierarchical separation of the reaction network into smaller partitions. Only reactions that occur between chemical species in different partitions are approximated. The number of low-rank factors, the so-called rank, determines the accuracy of the approximation; typically, 10 to 20 low-rank functions are sufficient for a good solution.
We derive an efficient integration scheme for the low-rank factors that exploits the low-rank tensor structure of the CME. This scheme is based on the projector-splitting integrator for tree tensor networks [Ceruti, Lubich, and Walach, SIAM J. Numer. Anal., vol. 59, 2021]. We apply our method to models from biochemistry and show that the method significantly reduces the memory consumption, while achieving improved computational performance and better runtimes compared to a Monte Carlo method.
Finally, we investigate how the choice of the partitioning affects the required rank. To this end, a heuristic partitioning algorithm is presented that minimizes information entropy and the number of reactions between partitions.