2022 Annual Meeting

(624h) Optimization Under Uncertainty with Bayesian Hybrid Models

Authors

Eugene, E. - Presenter, University of Notre Dame
Dowling, A., University of Notre Dame
Multiscale computer models are used in science, (chemical) engineering, and beyond to guide discovery, optimize systems, and facilitate decision making in important application areas including carbon capture[1-3] and life sciences[4]. The complex nature of multiscale modeling, however, often requires approximations to ensure computational tractability, which also introduces model-form, i.e., epistemic, uncertainty. Harnessing the full predictive potential of these models requires a comprehensive framework to quantify this uncertainty. While machine learning has catalyzed tremendous progress in science and engineering, these techniques are often best suited for problems with readily available, rich datasets. At the intersection of so-called black box ML models and glass-box equation-oriented models are Kennedy-O’Hagan (KOH) or “hybrid” models[5,6] which use data-driven ML constructs to quantify epistemic (i.e. model-form) uncertainty associated with a simplified or reduced order often physics-based glass-box model. While KOH frameworks are popular in the broader computational science and engineering research community[7-11], they remain niche in chemical engineering[3,12]. Moreover, a majority of KOH focuses on uncertainty quantification and propagation. It remains unclear how to most efficiently perform optimization under uncertainty for decision-making using KOH Bayesian hybrid models of the following form:

yi = η(xi; θ) + δ(xi; φ) + εi

Here, observation yi is modeled with three components: a white-box model η(·,·) with global parameters θ and inputs xi for experiment i, a stochastic discrepancy function δ(·), and random measurement error ε ∼ N(0, Iσ2).

In this presentation, we compare these Bayesian hybrid models to black-box and glass-box alternatives in the context of chemical kinetics modeling and reactor optimization. Using a complex series reaction, we demonstrate how hybrid models overcome systematic bias introduced by a reduced order kinetic model to correctly predict the operating temperature and reaction time of an objective function of the intermediate (desired) product yield. Pragmatically, the hybrid model enables reaction engineering decision-making for reactor design and optimization despite model inadequacy. We conclude by discussing stochastic programming formulations to facilitate optimization under uncertainty considering both aleatoric uncertainty obtained from the posterior of Bayesian parameter estimation and epistemic uncertainty quantified by Gaussian Processes in the KOH model[13].

References:

[1] D. C. Miller, M. Syamlal, D. S. Mebane, C. Storlie, D. Bhattacharyya, N. V. Sahinidis, D. Agarwal, C. Tong, S. E. Zitney, A. Sarkar, X. Sun, S. Sundaresan, E. Ryan, D. Engel, and C. Dale, “Carbon capture simulation initiative: A case study in multiscale modeling and new challenges,” Annual Review of Chemical and Biomolecular Engineering, vol. 5, no. 1, pp. 301–323, 2014. PMID: 24797817.

[2] K. S. Bhat, D. S. Mebane, P. Mahapatra, and C. B. Storlie, “Upscaling uncertainty with dynamic discrepancy for a multi-scale carbon capture system,” Journal of the American Statistical Association, vol. 112, no. 520, pp. 1453–1467, 2017.

[3] J. Kalyanaraman, Y. Fan, Y. Labreche, R. P. Lively, Y. Kawajiri, and M. J. Realff, “Bayesian estimation of parametric uncertainties, quantification and reduction using optimal design of experiments for co2 adsorption on amine sorbents,” Computers and Chemical Engineering, vol. 81, 2015.

[4] M. Alber, A. Buganza Tepole, W. R. Cannon, et al., “Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences.,” npj Digital Medicine, vol. 2.

[5] M. C. Kennedy and A. O’Hagan, “Bayesian calibration of computer models,” Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol. 63, no. 3, pp. 425–464, 2001.

[6] R. Gramacy, Surrogates: Gaussian Process Modeling, Design, and Optimization for the Applied Sciences. Chapman & Hall/CRC Texts in Statistical Science, CRC Press, 2020.

[7] A. van Griensven and T. Meixner, “A global and efficient multi-objective auto-calibration and uncertainty estimation method for water quality catchment models,” Journal of Hydroinformatics, vol. 9, no. 4, pp. 277–291, 2007.

[8] Y. Xiong, W. Chen, K.-L. Tsui, and D. Apley, “A better understanding of model updating strategies invalidating engineering models,” Computer Methods in Applied Mechanics and Engineering, vol. 198, no. 15-16, pp. 1327–1337, 2009.

[9] W. Chen, Y. Xiong, K. Tsui, and S. Wang, “A design-driven validation approach using bayesian prediction models,” Journal of Mechanical Design - Transactions of the ASME, vol. 130, no. 2, 2008.

[10] P. M. Tagade, B.-M. Jeong, and H.-L. Choi, “A gaussian process emulator approach for rapid contaminant characterization with an integrated multizone-cfd model,” Building and Environment, vol. 70, pp. 232–244, 2013.

[11] G. B. Arhonditsis, D. Papantou, W. Zhang, G. Perhar, E. Massos, and M. Shi, “Bayesian calibration of mechanistic aquatic biogeochemical models and benefits for environmental management,” Journal of Marine Systems, vol. 73, no. 1, pp. 8–30, 2008.

[12] J. Kalyanaraman, Y. Kawajiri, R. P. Lively, and M. J. Realff, “Uncertainty quantification via bayesian inference using sequential monte carlo methods for co2 adsorption process,” AIChE Journal, vol. 62, no. 9, pp. 3352–3368, 2016.

[13] J. Wang, E. Eugene, and A. Dowling, “Scalable stochastic programming with bayesian hybrid models,” in Proceedings of the 14th International Symposium on Process System Engineering, 2022.