Artificial neural network-based Hamiltonian Monte Carlo for high-dimensional Bayesian Inference of reaction kinetics models

Bayesian inference plays a pivotal role in optimizing reaction kinetics models, with Markov Chain Monte Carlo (MCMC) methods being a critical implementation. However, MCMC is constrained with low acceptance rates in high-dimensional scenarios. Conversely, Hamiltonian Monte Carlo (HMC) has high acceptance rates, albeit at the expense of computing first-order log-posterior gradients, thus limiting its application in model optimization. This study introduces an Artificial Neural Network-based HMC (ANN-HMC) approach, wherein gradient computation is accelerated through automatic differentiation. Unlike previous models that depend on early HMC samples for training surrogate models to predict the Hamiltonian, our ANN-HMC employs prediction samples for training an ANN. This ANN predicts targets used in the Hamiltonian computation, hence significantly streamlines the training process. The experimental data of ignition delay time and laminar flame velocity are utilized to optimize the methanol, ammonia and JetSurF1.0 models. The optimization results show that ANN-HMC outperforms ANN-MCMC, enhancing the sampling efficiency by three to four orders of magnitude after neural network training. Additionally, we investigate the influence of active parameter selection on model optimization under uncertainty constraints. The global sensitivity analysis typically identifies fewer total parameters than the local sensitivity analysis, resulting in more stringent parameter constraints. This can amplify the sampling challenge for ANN-HMC as some parameters approach boundary limits, thereby increasing the overall sampling time. In addition, more stringent parameter constraints may potentially limit the model performance on the optimization dataset. Appropriately increasing the number of active parameters can improve the model prediction accuracy, while maintaining prediction uncertainty within the limits of experimental uncertainty. The ANN-HMC demonstrates its unique advantages in reaction kinetics model optimization.