Simultaneous state-time approximation of the chemical master equation using tensor product formats

Tensor-product approach to global time-space-parametric discretization of chemical master equation

We study the application of the novel tensor formats (TT, QTT, QTTTucker) to the solution of d-dimensional chemical master equations, applied mostly to gene regulating networks (signaling cascades, toggle switches, phage-λ). For some important cases, e.g. signaling cascade models, we prove good separability properties of the system operator. The time is treated as an additional variable, with t...

Reduction and solution of the chemical master equation using time scale separation and finite state projection.

The dynamics of chemical reaction networks often takes place on widely differing time scales--from the order of nanoseconds to the order of several days. This is particularly true for gene regulatory networks, which are modeled by chemical kinetics. Multiple time scales in mathematical models often lead to serious computational difficulties, such as numerical stiffness in the case of differenti...

Parallel Tensor-Formatted Numerics for the Chemical Master Equation

Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains

The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionali...

A Multiple Time-Step Finite State Projection Algorithm for the Solution to the Chemical Master Equation

At the mesoscopic scale, chemical processes have probability distributions that evolve according to an infinite set of linear ordinary differential equations known as the chemical master equation (CME). It is commonly believed that the CME cannot be solved except for the most trivial of cases, but recent work has raised questions regarding validity of this belief. For many cases, Finite State P...