(235g) Impacts of Modeling Error on Optimization-Based Materials Design

Materials development has often relied on experimentation or experience. In an attempt to accelerate this process, a variety of computational approaches are being pursued which utilize, for example, artificial intelligence techniques for discovering materials which are expected to meet certain requirements based on prior data [1], or optimization-based approaches that seek to find the optimal structure of a material for meeting a property target given a structure-function relationship developed from data [2]. In any computational approach for materials development, a model of material behavior must be utilized, whether it is data-driven or an attempt to simulate from first-principles (as in, for example, density functional theory [3]). Modeling approaches may fail to be fully accurate; however, for performing computational development of new materials, it is desirable to understand how these inaccuracies could impact the optimal solution (i.e., which material ends up being selected) of the optimization-based materials design problem. This could be particularly important to understand for a long-term vision of an optimization-based materials design framework being used in selecting materials which both meet product requirements and also are cheapest in terms of manufacturing or process design.

This work explores this question through simulation and mathematical studies. First, we will probe the effects of modeling error by developing multiple optimization-based materials design simulations with varying degrees of model error for different modeling frameworks (e.g., data-driven and first-principles) to analyze how these errors impact what material is determined to be optimal with respect to a target property. Subsequently, taking an approach inspired by our prior work which characterized the impact of model approximations in an optimization-based control framework on closed-loop stability considerations [4], we will explore mathematically how the solution of the optimization-based materials design problem is impacted by approximations of the material behavior.

References

[1] Pilania, G., C. Wang, X. Jiang, S. Rajasekaran and R. Ramprasad. "Accelerating materials property predictions using machine learning." Scientific Reports 3, pp: 1-6 (2013).

[2] Hanselman, C. L. and C. E. Gounaris. “A mathematical optimization framework for the design of nanopatterned surfaces.” AIChE Journal 62, pp: 3250-3263 (2016).

[3] Sholl, D. and J. A. Steckel., "Density Functional Theory: A Practical Introduction," John Wiley & Sons, Hoboken, NJ (2011).

[4] Rangan, K. K. and H. Durand, "Lyapunov-based economic model predictive control with Taylor series state approximations," In: The Proceedings of the American Control Conference, in press, Denver, CO (July 1-3, 2020).