(95b) Bayesian Optimization for Nonlinear Model and Force Field Calibration

The phase-out of high global warming potential (GWP) hydrofluorocarbon refrigerants has been mandated by over 160 countries as part of the Kigali amendment to the Montreal protocol. Estimates suggest that this could lead to a $270 billion dollar industry by 2050 [1]. Many refrigerants are near azeotropic mixtures, which makes it difficult to separate them into their high and low GWP components [2]. We are investigating the use of ionic liquids as entrainers that can be used in extractive distillation to perform this separation. This requires accurate thermophysical properties of the refrigerants and ionic liquids. Molecular simulation methods can be used alongside experimental measurement to determine these properties, but this requires accurate intermolecular potentials (force fields (FFs). Unfortunately, calibrating FFs is difficult. Hand tuning to match experimental data has been the conventional approach for developing FFs, but recent work has shown that machine learning [3,4] and Gaussian process Bayesian optimization (GPBO) [5,6] can be particularly effective. In standard GPBO, convergence limitations arise through use of a Gaussian process (GP) surrogate model that emulates an error-based objective function. There is no GPBO method that can tune a FF by directly emulating simulation results, but there is evidence that using GPBO with a function emulator will be successful for FF optimization applications [7].

Therefore, in this work, we proposed and compared five optimization formulations calibrating expensive computational models using Gaussian process surrogates and benchmark their accuracy against classical nonlinear least-squares. The first two methods use a GP to model either the error or the logarithmic error between the simulation and experimental results. The last three methods use a GP to emulate the molecular model using an independence approximation, an independence approximation and logarithmic scaling, and a sparse grid approximation. The results suggest that the emulator based GPBO methods can potentially converge 10x faster than current GPBO methods and provide greater insight into function behavior without sacrificing accuracy or reproducibility. This improved behavior is attributed to the added robustness of the newly derived expected improvement acquisition functions and particularly, we find that a sparse grid approximation leads to the quickest convergence. Future work aims to benchmark performance for all formulations in higher dimensions and apply them to develop a general force field for hydrofluorocarbons. The force fields calibrated by this method can be used to generate data in cases where experiments are difficult to perform and can be used in computer aided design. The methods generated in this work can then be extended to other systems including reaction kinetics [8], pharmaceutics [9], and additive manufacturing [10].

References

1. United States Environmental Protection Agency U.S. Will Dramatically Cut Climate-Damaging Greenhouse Gases with New Program Aimed at Chemicals Used in Air Conditioning, Refrigeration, 2021.
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3. Unke, O. T., Chmiela, S., Sauceda, H. E., Gastegger, M., Poltavsky, I., Schütt, K. T., Tkatchenko, A., & Müller, K. R. (2021). Machine Learning Force Fields. Rev., 121(16), 10142–10186. https://doi.org/10.1021/acs.chemrev.0c01111
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7. Befort, B. J., Defever, R. S., Maginn, E. J., & Dowling, A. W. (2022). Machine Learning-Enabled Optimization of Force Fields for Hydrofluorocarbons. Aided Chem. Eng., 49, 1249–1254.
8. Heijmans, K., Tranca, I. C., Smeulders, D. M. J., Vlugt, T. J. H., & Gaastra-Nedea, S. v. (2021). Gibbs Ensemble Monte Carlo for Reactive Force Fields to Determine the Vapor-Liquid Equilibrium of CO2and H2O. Chem. Theory Comput., 17(1), 322–329. https://doi.org/10.1021/acs.jctc.0c00876
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10. Wang, K., Zeng, M., Wang, J., Shang, W., Zhang, Y., Luo, T., & Dowling, A. W. (2023). When Physics-Informed Data Analytics Outperforms Black-Box Machine Learning: A Case Study in Thickness Control for Additive Manufacturing. Digital Chemical Engineering, 6, 100076. https://doi.org/10.1016/J.DCHE.2022.100076