Abstract:The Finite State Projection (FSP) method approximates the Chemical Master Equation (CME) by restricting the dynamics to a finite subset of the (typically infinite) state space, enabling direct numerical solution with computable error bounds. Adaptive variants update this subset in time, but multiscale systems with widely separated reaction rates remain challenging, as low-probability bottleneck states can carry essential probability flux and the dynamics alternate between fast transients and slowly evolving stiff regimes. We propose a flux-based adaptive FSP method that uses probability flux to drive both state-space pruning and time-step selection. The pruning rule protects low-probability states with large outgoing flux, preserving connectivity in bottleneck systems, while the time-step rule adapts to the instantaneous total flux to handle rate constants spanning several orders of magnitude. Numerical experiments on stiff, oscillatory, and bottleneck reaction networks show that the method maintains accuracy while using substantially smaller state spaces.
| Subjects: | Computational Engineering, Finance, and Science (cs.CE); Statistics Theory (math.ST); Computation (stat.CO) |
| Cite as: | arXiv:2512.17064 [cs.CE] |
| (or arXiv:2512.17064v2 [cs.CE] for this version) | |
| https://doi.org/10.48550/arXiv.2512.17064 arXiv-issued DOI via DataCite |
From: Aditya Dendukuri [view email]
[v1]
Thu, 18 Dec 2025 21:04:12 UTC (809 KB)
[v2]
Sat, 23 May 2026 05:17:57 UTC (927 KB)
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