Linear Noise Approximation Assisted Bayesian Inference on Mechanistic Model of Partially Observed Stochastic Reaction Network
Wandi Xu, Wei Xie
TL;DR
This paper tackles Bayesian inference for partially observed, nonlinear stochastic reaction networks (SRNs) described by diffusion-approximated SDEs, motivated by the need for online mechanism learning and digital twins in biomanufacturing. It introduces a Bayesian updating Linear Noise Approximation (LNA) metamodel to approximate the observation likelihood using the known mechanistic SRN structure and develops a gradient-based Metropolis-adjusted Langevin Algorithm (MALA) for efficient posterior sampling, with reinitialization of the LNA to control approximation error across observation intervals. The main contributions are the interpretable LNA metamodel for likelihood construction and the MALA sampler that leverages posterior gradients (via a recursive procedure) to accelerate convergence, demonstrated on synthetic data. The results indicate improved convergence and parameter accuracy under data-poor, partially observed settings, highlighting the method’s potential for online learning and digital twin applications in bioprocess development and control.
Abstract
To support mechanism online learning and facilitate digital twin development for biomanufacturing processes, this paper develops an efficient Bayesian inference approach for partially observed enzymatic stochastic reaction network (SRN), a fundamental building block of multi-scale bioprocess mechanistic model. To tackle the critical challenges brought by the nonlinear stochastic differential equations (SDEs)-based mechanistic model with partially observed state and having measurement errors, an interpretable Bayesian updating linear noise approximation (LNA) metamodel, incorporating the structure information of the mechanistic model, is proposed to approximate the likelihood of observations. Then, an efficient posterior sampling approach is developed by utilizing the gradients of the derived likelihood to speed up the convergence of Markov Chain Monte Carlo (MCMC). The empirical study demonstrates that the proposed approach has a promising performance.