Bayesian inference using an adaptive neuro-fuzzy inference system

Abstract

For most Bayesian inference problems that are of interest, solving for the model parameter posterior probability distribution remains to be the main challenge. A typical technique entails using Markov chain Monte Carlo (MCMC), in order to obtain an approximation of the posterior distribution. However, one drawback of MCMC is that it usually requires solving the forward problem multiple times, which could be infeasible, if the forward model is computationally expensive. In this paper, a computationally cheap surrogate model is developed using the adaptive neuro-fuzzy inference system with a fuzzy c-means initialization (ANFIS-FCM). The optimal number of fuzzy rules is chosen via a proposed algorithm based on the pairing frequency clustering validity index. The effectiveness of the ANFIS-FCM model is tested on inferring reaction rate parameters in a 3-node network toy problem, which mimics idealized combustion reaction networks. Using multiple error measures, it is shown that the developed ANFIS-FCM model is capable of constructing accurate surrogate models at a minimal computational cost. © 2022 Elsevier B.V.