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Computing the equilibrium of the chemical master equation using tensors with sliding windows
  • Trang Dinh,
  • Brandon Reid,
  • Roger B. Sidje
Trang Dinh
The University of Alabama
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Brandon Reid
Milwaukee School of Engineering
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Roger B. Sidje
The University of Alabama

Corresponding Author:[email protected]

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Abstract

When studying a system of chemical reactions on the cellular level, it is often helpful to use the chemical master equation (CME) that results from modeling the system using a continuous-time Markov chain. Furthermore, the system’s long-term behavior can be explored by computing the stationary solution to the CME. However, the number of states involved grows exponentially with the number of chemical species tracked. In some cases, the state space may even be countably infinite. To cope with this issue, a potent strategy is to restrict to a finite state projection (FSP) and represent the transition matrix and probability vector in quantized tensor train (QTT) format. Here, we employ our adaptive FSP tensor-based solver with sliding windows as well as the method of using Reaction Rate Equations (RREs) to estimate the probability mass function when the system is in statistical equilibrium. Using RREs, we first cheaply get an approximation of the steady state, which is then fed to our adaptive QTT solver to reach the equilibrium quickly. We refer to this solver as FSP-QTT-SS. We include numerical experiments to show the efficiency of our approach.