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arXiv · 2504.03070

Adaptive Finite State Projection with Quantile-Based Pruning for Solving the Chemical Master Equation

Aditya Dendukuri·Linda Petzold
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Abstract

We present an adaptive Finite State Projection (FSP) method for efficiently solving the Chemical Master Equation (CME) with rigorous error control. Our approach integrates time-stepping with dynamic state-space truncation, balancing accuracy and computational cost. Krylov subspace methods approximate the matrix exponential, while quantile-based pruning controls state-space growth by removing low-probability states. Theoretical error bounds ensure that the truncation error remains bounded by the pruned mass at each step, which is user-controlled, and does not propagate forward in time. Numerical experiments on biochemical systems, including the Lotka-Volterra and Michaelis-Menten and bi-stable toggle switch models.

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Aditya Dendukuri, Linda Petzold. 2025-04-03. Adaptive Finite State Projection with Quantile-Based Pruning for Solving the Chemical Master Equation. https://arxiv.org/abs/2504.03070

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