As various value-added products such as pharmaceuticals, smart polymers, and batteries, attract more attention by society, design and optimization of processes that produce these products are becoming increasingly active research areas. These processes are often characterized by a distributed parameter system, such as crystallization, polydispersity, or degradation, which typically involves a significant amount of uncertainty [1-3]. Bayesian inference is a key method for accounting for system uncertainty, estimating the parameter posterior distribution learned from the observed data, and enabling model-based stochastic design and control. However, most Bayesian inference methods require the explicit likelihood function or a large number of simulations, which are prohibitive for first-principle based models. Here, we propose an automated algorithm for the efficient Bayesian inference of the parameters in a computationally expensive, first-principles simulation. Our algorithm is a novel combination of two effective methods: we use Automated Learning of Algebraic MOdels (ALAMO) [4] to construct a low-complexity surrogate model, and adversarial variational Bayes (AVB) [5] to flexibly represent and learn the posterior distribution. Our ALAMO-AVB algorithm is computationally efficient, yet is flexible enough to infer complex models that involve multimodal posterior distributions. Being a Bayesian method, the algorithm also aptly characterizes the uncertainties and correlations in the parameter space. We demonstrate the performance of our ALAMO-AVB algorithm in three problems. The second and third problems involve kinetic Monte Carlo and computational fluid dynamics, respectively, allowing extensive application of kinetics and reaction studies to account for atom-to-reactor scale interactions. The results reveal that the proposed model can capture the true parameter posterior distribution to the level of state-of-the-art Hamiltonian Monte Carlo (HMC) sampling with a much lower computational cost. Unlike Monte Carlo sampling, our approach allows for an arbitrary number of output responses through its generative network. Thus, the present study also sheds light on modeling the stochastic systems for robust design and control under uncertainty using generative model based on deep learning techniques.
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[2] Lee Y, Jeon K, Cho J, Na J, Park J, Jung I, Park, J, Park MJ, Lee WB. Multicompartment Model of an EthyleneâVinyl Acetate Autoclave Reactor: A Combined Computational Fluid Dynamics and Polymerization Kinetics Model. Industrial & Engineering Chemistry Research 2019;58(36):16459â16471.
[3] Ramadesigan V, Northrop PWC, De S, Santhanagopalan S, Braatz RD, Subramanian VR. Modeling and Simulation of Lithium-Ion Batteries from a Systems Engineering Perspective. Journal of The Electrochemical Society 2012;159(3):R31âR45.
[4] Mescheder L, Nowozin S, Geiger A. Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networks. arXiv e-prints 2017 Jan;p. arXiv:1701.04722
[5] Cozad A, Sahinidis NV, Miller DC. Learning surrogate models for simulation-based optimization. AIChE Journal 2014;60(6):2211â2227.