Bayesian Design of Experiments: Implementation, Validation and Application to Chemical Kinetics

Bayesian experimental design (BED) is a tool for guiding experiments founded on the principle of expected information gain. I.e., which experiment design will inform the most about the model can be predicted before experiments in a laboratory are conducted. BED is also useful when specific physical questions arise from the model which are answered from certain experiments but not from other experiments. BED can take two forms, and these two forms are expressed in three example models in this work. The first example takes the form of a Bayesian linear regression, but also this example is a benchmark for checking numerical and analytical solutions. One of two parameters is an estimator of the synthetic experimental data, and the BED task is choosing among which of the two parameters to inform (limited experimental observability). The second example is a chemical reaction model with a parameter space of informed reaction free energy and temperature. The temperature is an independent experimental design variable explored for information gain. The second and third examples are of the form of adjusting an independent variable in the experimental setup. The third example is a catalytic membrane reactor similar to a plug-flow reactor. For this example, a grid search over the independent variables, temperature and volume, for the greatest information gain is conducted. Also, maximum information gain is conducted is optimized with two algorithms: the differential evolution algorithm and steepest ascent, both of which benefitted in terms of initial guess from the grid search.

[1]  Michael Habeck,et al.  Bayesian evidence and model selection , 2014, Digit. Signal Process..

[2]  Heather J Kulik,et al.  Predicting electronic structure properties of transition metal complexes with neural networks† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c7sc01247k , 2017, Chemical science.

[3]  K. Chaloner,et al.  Bayesian design for accelerated life testing , 1992 .

[4]  J. Oden,et al.  Selection and Validation of Predictive Models of Radiation Effects on Tumor Growth Based on Noninvasive Imaging Data. , 2017, Computer methods in applied mechanics and engineering.

[5]  J. Hrbek,et al.  Activity of CeOx and TiOx Nanoparticles Grown on Au(111) in the Water-Gas Shift Reaction , 2007, Science.

[6]  J. Oden,et al.  A Posteriori Error Estimation in Finite Element Analysis , 2000 .

[7]  A. Basile,et al.  Methane Conversion to Syngas in a Composite Palladium Membrane Reactor with Increasing Number of Pd Layers , 2002 .

[8]  Youssef M. Marzouk,et al.  Bayesian inference of chemical kinetic models from proposed reactions , 2015 .

[9]  A. O'Hagan,et al.  Bayesian calibration of computer models , 2001 .

[10]  H. Scott Fogler,et al.  Essentials of Chemical Reaction Engineering , 2011 .

[11]  R. D. Berry,et al.  DATA-FREE INFERENCE OF UNCERTAIN PARAMETERS IN CHEMICAL MODELS , 2014 .

[12]  Jan Galuszka,et al.  Methane conversion to syngas in a palladium membrane reactor , 1998 .

[13]  Karl W. Schulz,et al.  The Parallel C++ Statistical Library 'QUESO': Quantification of Uncertainty for Estimation, Simulation and Optimization , 2011, Euro-Par Workshops.

[14]  P. Bauman,et al.  Computational Modeling of Laser Absorption in Reacting Flows , 2019, Journal of Thermophysics and Heat Transfer.

[15]  B. Freeman,et al.  Modeling gas permeability and diffusivity in HAB-6FDA polyimide and its thermally rearranged analogs , 2017 .

[16]  Y. S. Lin,et al.  Modeling and analysis of ceramic-carbonate dual-phase membrane reactor for carbon dioxide reforming with methane , 2011 .

[17]  Y. Marzouk,et al.  Uncertainty quantification in chemical systems , 2009 .

[18]  Venkat Venkatasubramanian,et al.  Bayesian Framework for Building Kinetic Models of Catalytic Systems , 2009 .

[19]  Ryan P. Lively,et al.  Bayesian estimation of parametric uncertainties, quantification and reduction using optimal design of experiments for CO2 adsorption on amine sorbents , 2015, Comput. Chem. Eng..

[20]  H. Kulik,et al.  Density functional theory for modelling large molecular adsorbate–surface interactions: a mini-review and worked example , 2016 .

[21]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[22]  Roy H. Stogner,et al.  GRINS: A Multiphysics Framework Based on the libMesh Finite Element Library , 2015, SIAM J. Sci. Comput..

[23]  T. Merkel,et al.  50th Anniversary Perspective: Polymers and Mixed Matrix Membranes for Gas and Vapor Separation: A Review and Prospective Opportunities , 2017 .

[24]  Zachary W. Ulissi,et al.  To address surface reaction network complexity using scaling relations machine learning and DFT calculations , 2017, Nature Communications.

[25]  R. Moser,et al.  The Parallel C++ Statistical Library for Bayesian Inference: QUESO , 2015, 1507.00398.

[26]  Michael M. McKerns,et al.  Building a Framework for Predictive Science , 2012, SciPy.

[27]  J. Tinsley Oden,et al.  Problem decomposition for adaptive hp finite element methods , 1995 .

[28]  Hazzim F. Abbas,et al.  Dry reforming of methane: Influence of process parameters—A review , 2015 .

[29]  Sai Hung Cheung,et al.  Bayesian uncertainty analysis with applications to turbulence modeling , 2011, Reliab. Eng. Syst. Saf..

[30]  Raul Tempone,et al.  Fast estimation of expected information gains for Bayesian experimental designs based on Laplace approximations , 2013 .

[31]  Huaiyu Zhu.  On Information and Sufficiency , 1997 .

[32]  Terry Z. H. Gani,et al.  Unifying Exchange Sensitivity in Transition-Metal Spin-State Ordering and Catalysis through Bond Valence Metrics. , 2017, Journal of chemical theory and computation.

[33]  K. Chaloner,et al.  Bayesian Experimental Design: A Review , 1995 .

[34]  Christine M. Anderson-Cook,et al.  Computational Enhancements to Bayesian Design of Experiments Using Gaussian Processes , 2016 .

[35]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[36]  Tiangang Cui,et al.  Goal-Oriented Optimal Approximations of Bayesian Linear Inverse Problems , 2016, SIAM J. Sci. Comput..

[37]  Ralph E. White,et al.  Comparison of a particle filter and other state estimation methods for prognostics of lithium-ion batteries , 2015 .

[38]  Thomas Bligaard,et al.  Assessing the reliability of calculated catalytic ammonia synthesis rates , 2014, Science.

[39]  Michael Frenklach,et al.  Comparison of Statistical and Deterministic Frameworks of Uncertainty Quantification , 2016, SIAM/ASA J. Uncertain. Quantification.

[40]  Jonathan E. Sutton,et al.  Effect of errors in linear scaling relations and Brønsted–Evans–Polanyi relations on activity and selectivity maps , 2016 .

[41]  Osman G. Mamun,et al.  Prediction of Adsorption Energies for Chemical Species on Metal Catalyst Surfaces Using Machine Learning , 2018, The Journal of Physical Chemistry C.

[42]  Andreas Heyden,et al.  Identifying Active Sites of the Water-Gas Shift Reaction over Titania Supported Platinum Catalysts under Uncertainty , 2017, 1710.03672.

[43]  Sai Hung Cheung,et al.  PARALLEL ADAPTIVE MULTILEVEL SAMPLING ALGORITHMS FOR THE BAYESIAN ANALYSIS OF MATHEMATICAL MODELS , 2012 .

[44]  Sebastian Matera,et al.  Addressing global uncertainty and sensitivity in first-principles based microkinetic models by an adaptive sparse grid approach. , 2018, The Journal of chemical physics.

[45]  Markos A Katsoulakis,et al.  Effects of correlated parameters and uncertainty in electronic-structure-based chemical kinetic modelling. , 2016, Nature chemistry.

[46]  Gabriel Terejanu,et al.  Uncertainty Quantification Framework Applied to the Water–Gas Shift Reaction over Pt-Based Catalysts , 2016 .

[47]  Gabriel Terejanu,et al.  Bayesian experimental design for the active nitridation of graphite by atomic nitrogen , 2011, ArXiv.