Turning statistical physics models into materials design engines

Abstract

Despite the success statistical physics has enjoyed at predicting the properties of materials for given parameters, the inverse problem, identifying which material parameters produce given, desired properties, is only beginning to be addressed. Recently, several methods have emerged across disciplines that draw upon optimization and simulation to create computer programs that tailor material responses to specified behaviors. However, so far the methods developed either involve black-box techniques, in which the optimizer operates without explicit knowledge of the material's configuration space, or require carefully tuned algorithms with applicability limited to a narrow subclass of materials. Here we introduce a formalism that can generate optimizers automatically by extending statistical mechanics into the realm of design. The strength of this approach lies in its capability to transform statistical models that describe materials into optimizers to tailor them. By comparing against standard black-box optimization methods, we demonstrate how optimizers generated by this formalism can be faster and more effective, while remaining straightforward to implement. The scope of our approach includes possibilities for solving a variety of complex optimization and design problems concerning materials both in and out of equilibrium.omputer programs that can design material properties have led to exciting, new directions for materials science (1-3). Computational methods have been used to predict crystal (4) and protein (5, 6) structures, yielding the toughest crystals known to mankind (4) and de novo protein configurations unseen in nature (5). Applied to polymers, Monte Carlo methods (7-9) and evolutionary algorithms (10, 11) have paved the way toward optimizing directed self-assembly. Similar methods have been used to identify the crystal structures of patchy, colloidal particles (12). For far-from-equilibrium systems like jammed, metastable aggregates of particles (3), simulation-based optimization has been successfully used to design bulk properties like stiffness (13) and packing density (14) by way of tuning complicated microscale features like particle shape.However, despite these successes, most of the existing methods work only for narrowly defined classes of materials: Optimization techniques that prove successful at designing one class of materials may struggle or fail on other systems. Thus, designing new materials can require a large investment in trial and error at the level of the algorithm itself, even if, for given parameters, the material's behavior can be simulated easily.In black-box approaches, the algorithm tunes the material by adjusting control parameters without considering the likelihood of finding the material in microscale configurations. Instead, the optimizer operates in some auxiliary space, defined outside the physical model, and remains ignorant of the statistics in the physical configuration space. On the other hand, for the overwhelming majority of materials, an accurate description of m...

Perspective: Evolutionary design of granular media and block copolymer patterns

“…More recently, design approaches using inverse methods have been implemented. [8][9][10][11]18 In these cases, the forward simulation consists of a numerical engine to solve various trial morphologies by implementing, e.g., a self-consistent field theory, 69 a mean field model based on the Cahn-Hilliard equation, 10 or a theoretically informed coarse-grain model for block copolymers. 70 As before, the forward simulation is coupled to an inverse process that optimizes the parameter set in order to achieve a solution that closely approximates the targeted design.…”

“…70 As before, the forward simulation is coupled to an inverse process that optimizes the parameter set in order to achieve a solution that closely approximates the targeted design. In this regard, our recent work 10,11,18 has shown that evolutionary strategies such as CMA-ES can be significantly faster and more efficient in finding optimized solutions than inverse methods based on Monte Carlo searches. 8,9 In a typical design task corresponding to Fig.…”

“…71 An alternative approach is to use a physics based model, be it a self-consistent field theory or a molecular simulation, to interpret the data. While such a consideration would be overly demanding for traditional Monte Carlo-based strategies, by relying on CMA-ES versions and our more recently proposed variants, 10,11,18 it is possible to interpret scattering in terms of a fully three-dimensional particle based model that includes fluctuations. 72 Again, we highlight the fact here that, from a computational point of view, a computational engine is charged with designing a material that scatters x-rays in a manner dictated by the experiments.…”

“…We recently were able to show that the answer is yes, at least for design problems where the underlying physics can be described by models based on statistical mechanics. 18 Specifically, in situations where the macro-level outcome depends on the likelihood for a system to be in a particular micro-level configuration, knowledge of the probability distribution for these microstates can be used to derive an "equation of motion" for the parameters that encode these microstates. This equation deterministically calculates updates along directions of small entropy change in order to find new, improved parameter values.…”

“…It is able to use information about how fluctuations in configurations correspond to fluctuations in quality because it has been built to exploit the extra fact that the simulation data were generated from a known distribution. 18 Importantly, to create the probability distribution, the microstate statistics have to be evaluated only once during this evolution toward the design goal.…”