(376bf) Development of a Generic Mathematical Optimization-Based Nanomaterial Design Toolkit

Advances in nanotechnology are enabling the synthesis of increasingly complex nanostructured materials [1]. Concurrently, there are significant efforts in the areas of density functional theory (DFT) and machine learning to predict which nanomaterials are expected to have superior properties [2]. However, these approaches constitute heuristic searches and provide no guarantees on the quality of identified designs. To address the lack of guarantees on global optimality, we have previously demonstrated several approaches for modeling nanostructured crystalline material design problems via mixed integer linear programming (MILP) [3,4]. Using our experiences from these past works, we attempt to abstract the search for the best nanostructured crystalline material, formalize this as a rigorous design problem, and provide a common optimization framework for choosing the optimal nanostructuring decisions.

We present a new Python-based software tool for generically formulating and solving nanostructured material optimization problems. The tool takes input information about the crystal structure of the material, general forms of simplified structure-function relationships, and an objective function from which it automatically casts an MILP model. The latter can then be solved directly via standard optimization solvers available through Pyomo [5], or via customized decomposition approaches.

Part of the IDAES Multi-Scale Process Systems Engineering Framework [6-7], the tool provides interfaces to input material information via several levels of detail and customization. In the simplest case, standard crystal data files and predefined structure-function relationships can be used to instantiate the models. Conversely, in the spirit of open-source code, we also provide access to the modelling elements from which users can write highly customized scripts for building materials optimization models. In this way, we aim to support a wide range of applications and user expectations. This tool aims to effectively lower the barrier for applying mathematical optimization by materials experts while simultaneously codifying the material design problems for further development by mathematical optimization researchers.

References

[1] Xia, Y., Y. Xiong, B. Lim, & S.E. Skrabalak. (2009). Shape-Controlled Synthesis of Metal Nanocrystals: Simple Chemistry Meets Complex Physics? Angewandte Chemie International Edition, 48(1), 60–103.

[2] Saal, J. E., S. Kirklin, M. Aykol, B. Meredig, & C. Wolverton. (2013). Materials design and discovery with high-throughput density functional theory: The open quantum materials database (OQMD). Jom, 65(11), 1501–1509.

[3] Hanselman, C. L., & C.E. Gounaris. (2016) A mathematical optimization framework for the design of nanopatterned surfaces. AIChE Journal, 62(9), 3250-3263.

[4] Hanselman, C. L., D.N. Tafen, D.R. Alfonso, J.W. Lekse, C. Matranga, D.C. Miller, & C.E. Gounaris, (2018). Design of doped perovskite oxygen carriers using mathematical optimization. In Proceedings of the 13th International Symposium on Process Systems Engineering. San Diego, USA, 2461-2466.

[5] Hart, W.E., J. Watson, & D.L. Woodruff, "Pyomo: modeling and solving mathematical programs in Python." Mathematical Programming Computation 3(3) (2011): 219-260.

[6] Miller, D.C., J. Siirola, D. Agarwal, A.P. Burgard, A. Lee, J.C. Eslick, B. Nicholson, C. Laird, L.T. Biegler, D. Bhattacharyya, N.V. Sahinidis, I.E. Grossmann, C.E. Gounaris, and D. Gunter, “Next Generation Multi-Scale Process Systems Engineering Framework”, Proceedings of the 13th International Symposium on Process Systems Engineering (PSE 2018), Computer-Aided Chemical Engineering, 44, pp. 2209-2214, Elsevier, Amsterdam, M. R. Eden, M. Ierapetritou and G. P. Towler (eds.) (2018).

[7] Institute for the Design of Advanced Energy Systems (IDAES) https://idaes.org/