Exploiting network topology for large-scale inference of nonlinear reaction models

Abstract

The development of chemical reaction models aids system design and optimization, along with fundamental understanding, in areas including combustion, catalysis, electrochemistry, and biology. A systematic approach to building reaction network models uses available data not only to estimate unknown parameters, but also to learn the model structure. Bayesian inference provides a natural approach to this data-driven construction of models. Traditional Bayesian model inference methodology is based on evaluating a multidimensional integral for each model. This approach is often infeasible for nonlinear reaction network inference, as the number of plausible models can be combinatorially large. An alternative approach based on model-space sampling can enable large-scale network inference, but its efficient implementation presents many challenges. In this paper, we present new computational methods that make large-scale nonlinear network inference tractable. Firstly, we exploit the network-based interactions of species to design improved "between-model" proposals for Markov chain Monte Carlo (MCMC). We then introduce a sensitivity-based determination of move types which, when combined with the network-aware proposals, yields further sampling efficiency. These algorithms are tested on example problems with up to 1024 plausible models. We find that our new algorithms yield significant gains in sampling performance, thus providing a means for tractable inference over a large number reaction models with physics-based nonlinear species interactions.