Interpretable Neural Approximation of Stochastic Reaction Dynamics with Guaranteed Reliability

TL;DR

DeepSKA is a neural framework that provides interpretable, reliable, and computationally efficient estimates of stochastic reaction network outputs, outperforming traditional methods in accuracy and speed across various models.

Contribution

It introduces DeepSKA, a neural approach that guarantees interpretability and reliability while significantly reducing computational costs for stochastic reaction network analysis.

Findings

DeepSKA achieves accurate predictions across nine diverse SRNs.

It provides unbiased, convergent estimates with lower variance than Monte Carlo.

DeepSKA offers orders-of-magnitude efficiency improvements over classical methods.

Abstract

Stochastic Reaction Networks (SRNs) are a fundamental modeling framework for systems ranging from chemical kinetics and epidemiology to ecological and synthetic biological processes. A central computational challenge is the estimation of expected outputs across initial conditions and times, a task that is rarely solvable analytically and becomes computationally prohibitive with current methods such as Finite State Projection or the Stochastic Simulation Algorithm. Existing deep learning approaches offer empirical scalability, but provide neither interpretability nor reliability guarantees, limiting their use in scientific analysis and in applications where model outputs inform real-world decisions. Here we introduce DeepSKA, a neural framework that jointly achieves interpretability, guaranteed reliability, and substantial computational gains. DeepSKA yields mathematically transparent representations that generalise across states, times, and output functions, and it integrates this structure with a small number of stochastic simulations to produce unbiased, provably convergent, and dramatically lower-variance estimates than classical Monte Carlo. We demonstrate these capabilities across nine SRNs, including nonlinear and non-mass-action models with up to ten species, where DeepSKA delivers accurate predictions and orders-of-magnitude efficiency improvements. This interpretable and reliable neural framework offers a principled foundation for developing analogous methods for other Markovian systems, including stochastic differential equations.