BASC: Applying Bayesian Optimization to the Search for Global Minima on Potential Energy Surfaces

We present a novel application of Bayesian optimization to the field of surface science: rapidly and accurately searching for the global minimum on potential energy surfaces. Controlling molecule-surface interactions is key for applications ranging from environmental catalysis to gas sensing. We present pragmatic techniques, including exploration/exploitation scheduling and a custom covariance kernel that encodes the properties of our objective function. Our method, the Bayesian Active Site Calculator (BASC), outperforms differential evolution and constrained minima hopping--two state-of-the-art approaches-- in trial examples of carbon monoxide adsorption on a hematite substrate, both with and without a defect.

[1]  Karsten W. Jacobsen,et al.  An object-oriented scripting interface to a legacy electronic structure code , 2002, Comput. Sci. Eng..

[2]  Kristian Sommer Thygesen,et al.  Localized atomic basis set in the projector augmented wave method , 2009, 1303.0348.

[3]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[4]  Martin F. Luna,et al.  A Bayesian Approach to Run-to-Run Optimization of Animal Cell Bioreactors Using Probabilistic Tendency Models , 2014 .

[5]  Anubhav Jain,et al.  The Materials Application Programming Interface (API): A simple, flexible and efficient API for materials data based on REpresentational State Transfer (REST) principles , 2015 .

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

[7]  Ian H. Sloan,et al.  QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere , 2012, Math. Comput..

[8]  Jasper Snoek,et al.  Practical Bayesian Optimization of Machine Learning Algorithms , 2012, NIPS.

[9]  John D. Hunter,et al.  Matplotlib: A 2D Graphics Environment , 2007, Computing in Science & Engineering.

[10]  S. Goedecker Minima hopping: an efficient search method for the global minimum of the potential energy surface of complex molecular systems. , 2004, The Journal of chemical physics.

[11]  Kristin A. Persson,et al.  Commentary: The Materials Project: A materials genome approach to accelerating materials innovation , 2013 .

[12]  Andrew A. Peterson,et al.  Global Optimization of Adsorbate–Surface Structures While Preserving Molecular Identity , 2014, Topics in Catalysis.

[13]  Janet E. Jones On the determination of molecular fields. —II. From the equation of state of a gas , 1924 .

[14]  K. Jacobsen,et al.  Real-space grid implementation of the projector augmented wave method , 2004, cond-mat/0411218.

[15]  Jorge Nocedal,et al.  On the limited memory BFGS method for large scale optimization , 1989, Math. Program..

[16]  Wang,et al.  Accurate and simple analytic representation of the electron-gas correlation energy. , 1992, Physical review. B, Condensed matter.

[17]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[18]  Chunshan Song Global challenges and strategies for control, conversion and utilization of CO2 for sustainable development involving energy, catalysis, adsorption and chemical processing , 2006 .

[19]  G. Zeng,et al.  Use of iron oxide nanomaterials in wastewater treatment: a review. , 2012, The Science of the total environment.

[20]  Heping Chen,et al.  Robot learning for complex manufacturing process , 2015, 2015 IEEE International Conference on Industrial Technology (ICIT).

[21]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[22]  Christopher J. Paciorek,et al.  Nonstationary Gaussian Processes for Regression and Spatial Modelling , 2003 .

[23]  Michael Grätzel,et al.  Solar water splitting: progress using hematite (α-Fe(2) O(3) ) photoelectrodes. , 2011, ChemSusChem.

[24]  Yat Li,et al.  Oxygen-deficient metal oxide nanostructures for photoelectrochemical water oxidation and other applications. , 2012, Nanoscale.

[25]  Eric Jones,et al.  SciPy: Open Source Scientific Tools for Python , 2001 .

[26]  S. Berman Isotropic Gaussian Processes on the Hilbert Sphere , 1980 .

[27]  Brian E. Granger,et al.  IPython: A System for Interactive Scientific Computing , 2007, Computing in Science & Engineering.

[28]  Nando de Freitas,et al.  A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning , 2010, ArXiv.

[29]  Alexander B. Pacheco Introduction to Computational Chemistry , 2011 .

[30]  N. A. Romero,et al.  Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[31]  Heping Chen,et al.  Welding parameter optimization based on Gaussian process regression Bayesian optimization algorithm , 2015, 2015 IEEE International Conference on Automation Science and Engineering (CASE).

[32]  Iain Murray Introduction To Gaussian Processes , 2008 .

[33]  Nancy Wilkins-Diehr,et al.  XSEDE: Accelerating Scientific Discovery , 2014, Computing in Science & Engineering.

[34]  David Duvenaud,et al.  Automatic model construction with Gaussian processes , 2014 .

[35]  J. Doye,et al.  Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms , 1997, cond-mat/9803344.