Simulation-based inference using splitting schemes for partially observed diffusions in chemical reaction networks

2025-08-15

AI Summary

This work addresses the dual challenge of numerically solving high-dimensional, nonlinear stochastic differential equations (SDEs) arising from the chemical Langevin equation (CLE) for partially observed diffusion processes in chemical reaction networks—where multiplicative, non-commutative noise and partial state observability impede inference. We propose a structure-preserving splitting numerical scheme that reformulates the CLE as a perturbed Cox–Ingersoll–Ross (CIR)-type SDE to ensure state non-negativity and numerical stability. Integrating data-conditional simulation with sequential summary statistic learning, our framework embeds approximate Bayesian computation (ABC) within a sequential Monte Carlo (SMC) framework for robust parameter inference. Validated on benchmark systems—including the Repressilator and Lotka–Volterra models—our method achieves significantly higher numerical accuracy, improved parameter estimation fidelity, and enhanced computational efficiency compared to the standard Euler–Maruyama scheme.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

We address the problem of simulation and parameter inference for chemical reaction networks described by the chemical Langevin equation, a stochastic differential equation (SDE) representation of the dynamics of the chemical species. This is challenging for two main reasons. First, the (multi-dimensional) SDEs cannot be explicitly solved and are driven by multiplicative and non-commutative noise, requiring the development of advanced numerical schemes for their approximation and simulation. Second, not all components of the SDEs are directly observed, as the available discrete-time data are typically incomplete and/or perturbed with measurement error. We tackle these issues via three contributions. First, we show that these models can be rewritten as perturbed conditionally Cox-Ingersoll-Ross-type SDEs, i.e., each coordinate, conditioned on all other coordinates being fixed, follows an SDE with linear drift and square root diffusion coefficient perturbed by additional Brownian motions. Second, for this class of SDEs, we develop a numerical splitting scheme that preserves structural properties of the model, such as oscillations, state space and invariant distributions, unlike the commonly used Euler-Maruyama scheme. Our numerical method is robust for large integration time steps. Third, we propose a sequential Monte Carlo approximate Bayesian computation algorithm incorporating "data-conditional" simulation and sequential learning of summary statistics, allowing inference for multidimensional partially observed systems, further developing previous results on fully observed systems based on the Euler-Maruyama scheme. We validate our approach on models of interest in chemical reaction networks, such as the stochastic Repressilator, Lotka-Volterra, and two-pool systems, demonstrating its effectiveness, in terms of both numerical and inferential accuracy, and reduced computational cost.

Problem

• Simulating chemical reaction networks with multiplicative noise SDEs
• Inferring parameters from incomplete, noisy diffusion observations
• Developing robust numerical schemes preserving model structural properties

Innovation

• Rewriting models as perturbed Cox-Ingersoll-Ross-type SDEs
• Developing robust numerical splitting scheme preserving model properties
• Proposing sequential Monte Carlo ABC algorithm for inference