Discovery and Optimization of Materials Using Evolutionary

May 12, 2016 - ... akin to Darwinian evolution: survival of the fittest. Somewhat surprisingly, the materials science research community has not made ...
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Discovery and Optimization of Materials Using Evolutionary Approaches Tu C. Le† and David A. Winkler*,†,‡,§,∥ †

CSIRO Manufacturing, Bag 10, Clayton South MDC, Victoria 3169, Australia Monash Institute of Pharmaceutical Sciences, 381 Royal Parade, Parkville 3052, Australia § Latrobe Institute for Molecular Science, La Trobe University, Bundoora 3046, Australia ∥ School of Chemical and Physical Sciences, Flinders University, Bedford Park 5042, Australia ‡

ABSTRACT: Materials science is undergoing a revolution, generating valuable new materials such as flexible solar panels, biomaterials and printable tissues, new catalysts, polymers, and porous materials with unprecedented properties. However, the number of potentially accessible materials is immense. Artificial evolutionary methods such as genetic algorithms, which explore large, complex search spaces very efficiently, can be applied to the identification and optimization of novel materials more rapidly than by physical experiments alone. Machine learning models can augment experimental measurements of materials fitness to accelerate identification of useful and novel materials in vast materials composition or property spaces. This review discusses the problems of large materials spaces, the types of evolutionary algorithms employed to identify or optimize materials, and how materials can be represented mathematically as genomes, describes fitness landscapes and mutation operators commonly employed in materials evolution, and provides a comprehensive summary of published research on the use of evolutionary methods to generate new catalysts, phosphors, and a range of other materials. The review identifies the potential for evolutionary methods to revolutionize a wide range of manufacturing, medical, and materials based industries.

CONTENTS 1. Introduction 2. Evolutionary Algorithms 2.1. Genetic Algorithms 2.1.1. Overview of the Process 2.1.2. Materials Genomes 2.1.3. Fitness Functions 2.1.4. Fitness Landscapes 2.1.5. Genetic Operators 2.2. Structure−Property Model Methods as in Silico Fitness Functions 2.3. Genetic Algorithm Software and Optimization Parameter Choices 3. Examples of Materials Discovery and Optimization Using Evolutionary Algorithms 3.1. Catalytic Materials 3.1.1. Catalyst Evolution Using Experimental Fitness Functions 3.1.2. Catalyst Evolution Using Computational Models as Fitness Functions 3.2. Phosphors 3.3. Other Materials 4. Optimization Using Structure−Property Models of Materials Evolutionary Landscapes 5. Conclusions and Perspective Author Information

Corresponding Author Notes Biographies References

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1. INTRODUCTION The vastness of materials structure space is still not widely recognized in the materials science community. Estimating how many new materials could be made from the elements in the periodic table using the laws of chemical valence and reactivity is very difficult. However, most studies have agreed on a number of close to 10100, considerably larger than the estimated number of particles of matter in the Universe. For all intents and purposes, the number of possible materials we could synthesize is infinite. This realization immediately raises a threat and an opportunity. The threat revolves around the impossibility of exhaustively exploring such vast space using even the most optimistic projections of the capabilities of robotics and automation. Although these high throughput materials synthesis and characterization capabilities are being developed at a rapid pace,1,2 and they will undoubtedly improve the efficiency of discovery of new and useful materials, they do not provide an answer to the materials space problem. The

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and effectively by performing a reasonable number of experiments. We trust that this comprehensive and timely review will be useful to a broad materials science audience and will inspire scientists to use these very efficient, state-of-the-art computational tools to make major discoveries in materials design and development. This paper is organized as follows. Section 2 gives a brief introduction to evolutionary methodologies. This is followed by a comprehensive review of studies on materials optimization using genetic algorithms, the most widely used technique, in section 2.1. The use of models of materials structure property (genotype−phenotype) relationships as surrogate fitness functions is described in section 2.2. Section 3 reviews the literature on the application of evolutionary algorithms to identify and optimize new materials. Sections 3.1, 3.2, and 3.3 are devoted to catalysts, phosphors, and other materials, respectively. Section 3.1 provides a thorough review of catalyst discovery and optimization using genetic algorithms, the largest body of published work. It also describes the use of both experimental and computational fitness functions to evolve materials into promising areas of catalyst space. Catalyst optimization studies that use genetic algorithms and, for example, models of catalyst structure−property relationships as surrogate fitness functions, offer benefits in time and cost savings compared to carrying out experiments alone and are reviewed in sections 3.2 and 3.3. Materials optimization using quantitative structure−property relationships models trained on data derived during evolutionary optimization is reviewed in section 4. Conclusions and prospects for the future of evolutionary methods in materials discovery and optimization are given in section 5.

opportunity that vast materials spaces offer is that, even if this space is sparsely populated by regions with useful properties, there will be an almost inexhaustible number of them, providing rich areas for research and application in the future. Exploration of materials spaces by computational rather than experimental means can be much faster and more efficient, and a growing body of published work supports the utility of computational methods in materials design and optimization.3−5 The key question is, how do we explore vast materials structure and property spaces as efficiently as possible using very fast computational methods? By drawing on resources from other areas of research, namely evolutionary mathematical methods, we have a rational and viable means of tackling this extremely challenging but also very important problem. These methods are some of the most effective ways of searching extremely large search spaces consisting of multiple dimensions.6−9 Evolutionary methods, where a population of promising materials is altered (mutated) to increase some useful property (fitness), are akin to Darwinian evolution: survival of the fittest. Somewhat surprisingly, the materials science research community has not made significant use of these very promising methods, possibly because much of the work is published in engineering and computer science journals, but also because the experimental methods to implement them (high throughput synthesis and characterization technologies) have only recently been developed and applied. Innovations in combinatorial chemistry in the pharmaceutical industries, high throughput peptide and oligonucleotide synthesis methods, and robotics and automation in general10−12 have stimulated recent efforts to automate materials synthesis and characterization. These are also important enabling technologies for wider and more effective utilization of evolutionary methods. Genetic algorithms have been used to solve optimization problems in some computational tools used in drug design, for example. Since the early 1990s there have been successful applications of evolutionary methods to docking of small molecules to protein targets,13 conformational analysis,14 drug dosing strategies,15 pharmacophore identification, similarity searching, derivation of quantitative structure−activity models, feature selection,16 and combinatorial library design.17 However, direct structural mutation of populations of druglike molecules or more complex materials, to optimize specific useful properties, is still in its relative infancy. Similarly, evolutionary methods, such as particle swarm optimization, have been applied successfully to de novo crystal structure prediction in various materials.18 Once structures have been derived, conventional electronic structure calculations can predict useful materials properties such as superconductivity or hardness.19 The application of evolutionary methods to these areas is not within the scope of the current review. Interested readers can consult the listed publications for more information on these applications of evolutionary methods. We have also not reviewed the application of evolutionary algorithms to the design of drugs, as this topic was covered recently in a mini-review.20 This review describes the most commonly used evolutionary methods for materials discovery and optimization and summarizes published examples of their application to identification of new and useful materials, or optimization of properties of existing materials. Using evolutionary approaches, the optimal conditions for chemical and materials synthesis, as well as the optimal materials properties, can be found quickly

2. EVOLUTIONARY ALGORITHMS Evolutionary algorithms (EAs) are generic, population-based, metaheuristic optimization methods. Metaheuristics are higherlevel procedures that generate approximate solutions to problems in parameter spaces, such as materials spaces, that are too large to be exhaustively sampled. The mechanisms by which EAs operate are inspired by biological evolutionary operations such as selection, mutation, recombination, and reproduction. Candidate solutions to the optimization problem play the role of population members, and a fitness function ranks the quality of the solutions. The evolutionary operators are applied to the top ranked members of the population, selection pressure is applied by a fitness function, and the evolutionary cycle is repeated until specified performance criteria are satisfied. Evolutionary algorithms are generic, as they do not make any assumptions about the nature of the fitness landscape. They have been applied widely across many areas of science and technology21 and in some engineering aspects of materials science22 but, paradoxically, not in materials design and optimization to a large extent. The main types of evolutionary algorithms are genetic algorithms (GAs), particle swarm optimization,23 genetic swarm optimization,23 ant colony optimization,24 evolutionary programming,25 and evolutionary strategies (more suitable for real value data). Whitley published an overview of evolutionary algorithms that describes practical issues and common pitfalls.26 Genetic algorithms dominate the applications of evolutionary algorithms in materials science, so we provide a more detailed summary of the method. 6108

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Figure 1. Steps in an evolutionary process.

2.1. Genetic Algorithms

The population size depends on the nature of the problem and, in the studies reviewed, varied between tens and several hundreds of materials. The way in which materials are presented in the genome can have a significant effect on the performance of the evolutionary algorithm, as was illustrated recently by Gobin and Schuth.28 An example of a materials genome used to optimize a property using genetic algorithms is given in Figure 2.

2.1.1. Overview of the Process. Genetic algorithms (GAs) were proposed by Holland9 and Rechenberg27 to solve combinatorial problems. As members of the broader class of evolutionary algorithms, they use techniques inspired by natural evolution, such as inheritance, mutation, selection, and crossover, to solve optimization problems. In the context of materials science, a genetic algorithm evolves a population of materials toward improved solutions to the optimization problem under study. Each material is represented mathematically by a set of properties (its chromosomes or genotype) that can be mutated and modified using specific operators. The initial population of individuals (materials) is often generated randomly but can also incorporate prior knowledge about suitable materials. This and subsequent populations (generations) are mutated to generate the next population in an iterative manner. The fitness of every individual in a given population is evaluated by means of a fitness or objective function, usually a desired and measurable property of the materials, but may also include undesirable properties to be avoided. The “fittest” materials are selected from the population, and their genomes are subjected to mutation operations to generate the new generation. A stochastic process is used to apply the mutational operations to selected population members. This iterative cycle continues until a maximum number of generations have been produced, or until some members of a population have properties that have exceeded an acceptance threshold. The basic steps in an evolutionary approach are summarized in Figure 1. The variables in a genetic optimization process include the materials genomes, the population sizes, the mutation operators used, the number of generations in the optimization, and the nature of the fitness function. 2.1.2. Materials Genomes. The evolutionary procedure starts with a population of different entities such as molecules or materials that are represented by genomes that encode compositional or structural parameters, but may also include information on how the material was manufactured or processed (provenance). Examples of elements of genomes include the mole fraction of individual components of the materials, the processing (e.g., calcination) temperature, presence or absence of specific promoter materials or acidity enhancers, polymer block sizes, monomer compositions, degree of cross-linking, and polydispersities. The elements of the genome can be continuous or integer or binary numbers. Most genetic representations of materials have a fixed length, although variable length representations are not precluded.

Figure 2. Example of a materials genome. Each of four metals used in a catalyst is represented by a binary string of seven bits. Converting the binary to decimal, the percentage contribution to the mole fraction can be calculated, and the material composition can be represented. Adapted from Umegaki et al.29 Copyright 2003 American Chemical Society.

2.1.3. Fitness Functions. The objective of any evolutionary optimization is to generate successive, relatively small populations of materials exhibiting substantial improvements in one or more specific, useful properties (the fitness or objective function(s)). The fitness function used to select the best performing population members is problem dependent and, for materials, is usually a property like catalyst efficiency, phosphor brightness or color, bioactivity, hardness, etc. As the evolutionary process proceeds, only a fraction of a given population is selected to breed the next generation. Selections are made by assessing the fitness of individuals, and a stochastic process (often a roulette wheel) is used to choose a mix of population members for the next generation, with fitter individuals being selected more frequently. The average fitness of each population generally increases because most of the best individuals from the preceding generation are selected for breeding. In some cases, multiple rather than single fitness functions are optimized. This usually leads to a compromise between the optimization objectives. In this scenario, there may exist a large number of nondominated or Pareto optimal solutions (those in which it is impossible to make any 6109

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or materials where it is possible to specify an appropriate genome that permits free movement on the fitness landscape.32 2.1.5. Genetic Operators. Genetic algorithms involve a set of operations: replication, mutation, and crossover. The mutation operations are applied to “parent” materials (individuals) selected for breeding from the pool. These genetic operators generate “child” materials that share characteristics of the “parents” but that are distinctly different. The replication (elitism) operator copies a genome into the next generation unchanged, a mutation operator sets one gene in the genome to a different value to obtain a new genome, and a crossover operator takes two or more genomes, splits them at some randomly defined point and then exchanges the pieces to build new genomes by mixing them according to certain rules (Figure 5). As there is a direct and deterministic relationship between the materials genome and its composition, structure, and provenance (e.g., processing conditions), it is a simple matter to translate the fittest “genotype” to the equivalent materials “phenotype”. The selection and mutation operations continue until a new population of materials of appropriate size is generated. The best (fittest) members of the population are selected and either carried forward unchanged into the next generation (elitism) or modified in some major or minor way by mutating the genomes of the materials before including them in the next generation. This new population of molecules or materials is then assessed against the fitness criteria and the cycle repeats until some stopping criteria (e.g., the materials have the desired property) are met. Other genetic algorithm “tuning” parameters include the mutation probability and the crossover probability

component better without making at least one other component worse, see Figure 3).

Figure 3. Illustration of a Pareto optimal surface. Any of the red points represents optimal choices. Other subjective factors may be used to choose between the points on the Pareto surface. Creative Commonsby-SA license (https://en.wikipedia.org/wiki/Pareto_efficiency).

2.1.4. Fitness Landscapes. A fitness landscape is a function in multidimensional space that describes the relationship between the fitness function and the genome. It is essentially a picture of the genotype−phenotype relationship, or an evaluation of a fitness function for all candidate solutions, a type of structure−property relationship. It is the surface that the evolutionary algorithms such as GAs explore when they optimize a fitness function by mutating a materials genome. It is also the surface that is approximated by machine learning models of the materials composition−fitness function relationship discussed below. The properties of fitness landscapes30,31 are usually dependent on two assumptions: the property used as the fitness function is physically well-defined; the genomes permit adequate movement on the landscape. Upon satisfaction of both assumptions, mathematical analysis shows that the topology (i.e., number and location of maxima, minima, and saddle points) of any fitness landscape should be monotonic; i.e., the landscape contains extremes only at globally maximal and/or minimal property values (as well as saddles at intermediate property values). Figure 4 illustrates fitness landscapes with two variables where the landscape contains multiple local maxima with different property values and is monotonic. Thus, evolutionary algorithms are applicable to any well-defined chemical or physical property and to all molecules

2.2. Structure−Property Model Methods as in Silico Fitness Functions

In many real-world optimization problems, the evaluation of the fitness of the population, essential for efficient optimization, is often performed experimentally. The time and expense of carrying out these experiments can sometimes dominate the optimization cost. The optimization process can be made faster and more cost efficient if prior information gained during the optimization process is used. The most obvious way to use this prior information is by building a model of the fitness function to assist in the selection of candidate solutions for evaluation. Such models are also called surrogates, metamodels, or approximation models and can be generated by any of the quantitative structure−property relationship (QSPR) methods commonly used for materials.5 These include linear and nonlinear regression, artificial neural networks (ANNs), support vector machines (SVMs), and various flavors of decision tree methods. ANNs have been used almost exclusively as surrogate fitness functions in the materials evolution literature, so we will discuss this modeling method in more detail. Artificial neural networks are versatile machine learning methods that have been widely used to predict diverse materials properties.5 They are supervised methods that use a set of training data to model the relationship between the composition, structures and processing parameters of materials (genotype) and their properties (phenotype). They are most useful when a relatively large amount of information is available to train them, such as data from high throughput experiments or prior information from genetic optimization experiments. The most commonly used ANNs are the feed-forward networks, which usually consist of three processing layers.

Figure 4. Visualization of a two-dimensional (two genes in the genome) fitness landscape. Different paths that the population could follow while mutating and evolving on the fitness landscape are shown in color. Creative Commons-by-SA license (https://en.wikipedia.org/ wiki/Fitness_landscape). 6110

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Figure 5. Example of materials genome encoding (e.g., Pn are process variables, Cn are composition variables), and common genetic algorithm operators.

Figure 6. Three-layer artificial neural network with five input nodes, three hidden layers, and one output node. More than one hidden layer can be used (deep neural network) and multiple output nodes can be specified where there is more than one property being modeled. The lower figure shows the structure of each nodeinputs are summed and passed through a linear or nonlinear transfer function to the next layer. Creative Commons-by-SA license 3.0. Stack Exchange (www.stackexchange.com).

The structure of a typical artificial neural network is shown in Figure 6. The input layer receives input data such as the composition, structure, or processing conditions of the materials or the materials genome, one or more hidden layers

perform nonlinear computation, and one or more output layers generate the predicted value of the property or fitness function (phenotype). It is common for the networks to have only one hidden layer, and the architecture of these networks is often 6111

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MATLAB implementation is available at http://www.mathworks.com/matlabcentral/fileexchange/10429-nsga-ii--amulti-objective-optimization-algorithm; C version is available at http://www.iitk.ac.in/kangal/codes.shtml MATLAB implementation is available on request from http://faculty.sites.uci.edu/jasper/sample/

http://dev.heuristiclab.com HeuristicLab

AMALGAM

examples of a simple genetic evolution problem codes in many different programming languages fast, nondominated multiobjective genetic algorithm; the metacode for the algorithm is presented by Deb et al.39 efficient version of NSGA-II; the metacode and description by Vrugt and Robinson40 package of many popular evolutionary and machine learning codes RosettaCode

NSGA-II

genetic programming toolbox for MATLAB GPLab

https://rosettacode.org/wiki/Evolutionary_algorithm

http://www.wardsystems.com/genehunter.asp

Ward Systems Group public domain public domain public domain public domain GNU public domain

http://gplab.sourceforge.net/features.html

http://au.mathworks.com/help/gads/genetic-algorithm.html Mathworks

global optimization toolbox; contains useful functions for developing MATLAB code for evolutionary optimization problems Microsoft Excel add-in that performs genetic optimization

https://sourceforge.net/directory/development/algorithms/genetic-algorithms/ public domain comprehensive list of largely public domain genetic algorithm software libraries, frameworks, and packages

SourceForge genetic algorithms MATLAB neural network GeneHunter

supplier

As the application of evolutionary algorithms such as genetic algorithms is at an early stage, almost all of the literature examples discussed below have used bespoke software to conduct the evolutional process. There are, however, a number of quite useful frameworks or packages that researchers interested in materials evolution might employ. Table 1 summarizes some of the more accessible evolutionary algorithm packages, many of which are in the public domain. A few of the literature studies that have not hand-coded their algorithms used the NSGA algorithm. Choice of parameters for genetic algorithm optimizations is problem dependent and is influenced by a number of factors. The optimum size of the population depends on factors such as the scale of experimentation, cost of materials and experiments, time and other resources, etc., and is a critical factor. Populations that are too large lead to a low convergence, while those that are too small are prone to converge toward a local optimum.35 The choice of mutation operators can also affect the search spaces. Crossover alters the materials genomes more drastically and can move searches into new areas of materials space, while point mutations tend to explore more local regions. The degree of discretization of the genomes is also an important parameter that is clearly also related to population sizes. For example, if the genome of a catalyst or phosphor is described by the mole fractions of the components and the processing temperature of the calcination, small step sizes in these parameters imply small search spaces (the ranges over which the parameters are varied) if the populations are kept small, and large populations if the search space is expanded. A useful strategy that is discussed at length below is the complementary use of quantitative structure−property

description

2.3. Genetic Algorithm Software and Optimization Parameter Choices

software

Table 1. Genetic Algorithm Computational Frameworks or Packages That Could Be Used in Materials Evolution Projects

described by the notation Nin − Nhidden − Nout, where Nin, Nhidden, and Nout are the numbers of nodes in the input, hidden, and output nodes, respectively. Deep neural networks with more than one hidden layer have also appeared recently, and they may offer significant advantages over traditional backpropagation neural networks.33,34 In all cases, care must be taken to avoid overtraining or overfitting problems. Nodes in the successive layers of the ANNs are connected to each other by weights. The inputs to the hidden and output nodes consist of the sum of the values of each input variable multiplied by the weight of all connections leading into the node. This sum is presented to a transfer function (linear for input and output nodes and sigmoidal for hidden nodes) to generate the output for that node. The difference between the measured value of the materials property and the network output is fed backward through the network to adjust the weights and minimize the error in the output. All materials in the data set are presented repeatedly to the network until the prediction performance is acceptable. Using an initial set of experimental data, ANNs can be trained and used to predict properties for all possible combinations so that the material with the optimum property value can be found, within the domain of applicability (DOA) of the models. The DOA is the parameter and property space in which the training data resides and in which the model makes the most reliable predictions. ANN models can therefore be very useful surrogate fitness functions that can be used to select the best members of populations of materials for mutation and progressing to the next evolutionary cycle.

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relationship models embodied, for example, in a neural network. The model is trained on data generated over a useful range of materials space using a coarse discretization. The model can then interpolate in this region of space, effectively allowing a fine level of discretization to be used for subsequent evolutionary steps. As we discussed above, the materials search spaces are typically extremely large and not accessible by “brute force” combinatorial approaches. Although evolutionary methods such as genetic algorithms are among the most efficient methods to explore these potentially vast spaces, they clearly cannot explore all of it. Solutions will most likely be high fitness local optima on very complex response surfaces and are unlikely to be global optima. Nonetheless, like natural selection in biology, almost all of the local optima can be very useful and constitute substantial improvements over previous solutions. In addition, the size of search spaces and the potential complexity of response surfaces means that we cannot be sure that there is not a better local optimum relatively close by, unless we explore more widely. It is also important to consider constraints on evolution. Compositions clearly cannot have mole fractions that do not add up to 1, there are usually upper and lower bounds on processing temperatures or other parameters, abrupt phase or compositional changes may occur in some regions of composition space, and some materials may not be able to be synthesized at all. Some simple rules for synthetic accessibility have been proposed for small organic molecules,36 organometallics,37 etc. that could be used as constraints. In the case of phosphors discussed below,38 one of the constraints or fitness objectives used in the optimization was proximity to known phosphor compositions and the patent space embodied by these. Use of these factors allows the novelty of populations to be improved.

Figure 7. Selectivity of propene as a function of propane conversion for the first generation of catalytic materials (T = 500 °C, C3H8/O2/ N2 = 3/1/6). OF, objective function as criterion of catalyst quality to be minimized in the next generations. Reproduced with permission from Wolf et al.41 Copyright 2000 Elsevier.

The performance of all catalysts is summarized in Figure 8. The mean value of the objective function decreased (improved) from 107.7 to 98.3, and the propene yield increased from the first to the fourth generation. These authors reported an additional study on oxidative dehydrogenation of propane using catalysts containing other elements.42 The oxides they employed were V2O5, MoO3, MnO2, Fe2O3, ZnO, Ga2O3, GeO2, Nb2O5, WO3, Co3O4, CdO, In2O3, and NiO. The first generation consisted of 20 catalytic materials, each of which was composed of three elements. In the subsequent three generations, only 10 catalytic materials, seven of which were generated by mutation and three by crossover, were prepared and tested. The performance of the best four catalytic materials in each generation is illustrated in Figure 9, clearly illustrating the substantial increase in propene yield as the evolutionary procedure progressed. A similar study on optimizing catalysts for the oxidative dehydrogenation of propane was reported by Buyevskaya et al.43 Eight metal oxides, V2O5, MoO3, MnO2, Fe2O3, Ga2O3, La2O3, B2O3, and MgO, were used as primary components, and the genome consisted of a vector of the mole fractions used in the catalyst. Materials in the first generation consisted of four individual metal oxides deposited on α-alumina. The subsequent four generations of catalytic materials were created using mutation and crossover operators after assessing the fitness (propene yield) of each population member. Each of the generations consisted of 56 catalyst materials with different compositions. Figure 10 shows that the average propene yields increased from 3 to 6%, and the propene yields from the best catalysts increased from 7 to 9%, from the first to fifth generation, respectively. Evolutionary methods were also used by Rodemerck et al. to develop low-temperature catalysts for the total combustion of low-concentration propane in air.44 Such processes are essential for the fractional distillation of air to ensure that dangerous mixtures of liquid propane and liquid oxygen do not occur. The first generations of catalysts were created from two 60-member libraries of TiO2 supported and α-Fe2O3 supported catalysts generated by randomly mixing solutions of eight compounds (H2[PtCl6]·xH2O, (NH4)2PdCl6, RhCl3·2H2O, RuCl3·H2O, H[AuCl4]·3H2O, Ag lactate, Cu(NO3)2, Mn(NO3)2). Two subsequent generations, with population sizes of 45, were generated by applying mutation and crossover operators to the

3. EXAMPLES OF MATERIALS DISCOVERY AND OPTIMIZATION USING EVOLUTIONARY ALGORITHMS 3.1. Catalytic Materials

3.1.1. Catalyst Evolution Using Experimental Fitness Functions. The research area that has most frequently applied evolutionary approaches is that of catalyst identification and optimization. A relatively large number of research groups have reported using genetic algorithms to optimize the performance of these materials. The seminal paper on using the evolutionary approaches to optimize heterogeneous catalysts was that of Wolf et al.41 They aimed to optimize the conversion of propane to propene. Eight oxides (V2O5, MoO3, Fe2O3, GaO, MgO, B2O3, and La2O3) were chosen as primary catalyst components which, when randomly mixed and calcined, provided the first of four generations containing 56 catalysts each. Experiments showed that materials composed of four elements gave higher catalytic performance than materials with a greater or fewer number of elements. The objective (fitness) function used was the distance between a given catalyst performance (propene generated relative to propane consumed) to a hypothetical perfect catalyst (100% conversion of propane to propene), The selectivity of propene plotted against the propane conversion for all tested catalytic materials is given in Figure 7, together with an illustration of the objective function. Subsequent generations were created using mutation and crossover operators on the catalyst genomes, with vectors specifying the relative fraction of each element in the catalyst. 6113

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Figure 8. Left: Selectivity of propene as a function of propane conversion for all tested materials (T = 500 °C, C3H8/O2/N2 = 3/1/6). Mean OF: 107.7 (first generation), 105.5 (second generation), 100.3 (third generation), and 98.3 (fourth generation). Right: Propene yields of the 10 best catalysts in each generation. Reproduced with permission from Wolf et al.41 Copyright 2000 Elsevier.

compared to catalysts containing little or no Ru (30% CO yield were selected and their performances experimentally validated. The catalyst life was also optimized and ANNs were retrained using an additional three data points. The optimum catalyst suggested by the ANN model with fitted parameters a, b, and c as inputs had a much longer lifespan than the one found previously. A study aimed at developing catalysts for dry reforming of methane under pressure was also reported by the same research group. They used catalysts composed of cobalt and strontium carbonate with 10 different additives (B, K, Sc, Mn, Zn, Nb, Ag, Nd, Re, and Tl).85 The catalytic activities of 10 mol % Co + 1 mol % X/SrCO3 (X is one of the 10 additive elements) and 16 physicochemical properties of the 10 elements comprised the training data used to generate a neural network model for CO yield. The models predicted CO yield after 15 min or after 4 h 6128

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Figure 40. Results of the grid search for (a) CO conversion as functions of Co loading and pretreatment temperature (× is the maximum conversion) and (b) O2 conversion by H2 oxidation as a function of CO conversion. Adapted with permission from Omata et al.86 Copyright 2005 Elsevier.

selectivity for preferential oxidation at 200 °C and over 99% conversion of CO with the assistance of methanation of CO at 220 °C (Figure 40). The development of Co/SrCO 3 based catalysts for preferential oxidation of CO in excess H2 was also reported by Kobayashi et al.87 The catalysts consisted of 17 mol % Co + 1.7 mol % X/SrCO3 catalyst, where X was one of 10 elements (B, K, Sc, Mn, Zn, Nb, Ag, Nd, Re, and Tl). Sixteen physicochemical properties for 10 elements and the catalytic performance (CO conversion and O2 conversion by H2) were used to train a neural network model. The model was then used to predict the performance for 53 other additive elements. The effect of different additives was also analyzed using a multivariate data mining technique. The study identified a catalyst consisting of 17 mol % Co and 5.1 mol % B/SrCO3 catalyst that provided 99% CO conversion and 52% selectivity at 200 °C. Fine grained virtual screening of membrane disk catalysts for oxidative reforming of methane has been reported by Omata et al.88 They employed two porous alumina membrane filter disks in their catalysis rig, with one catalyst disk for methane combustion and one for methane reforming. The disks contained additives selected from nine elements (B, Ca, P, Mn, Fe, Cd, Ce, Gd, and Re). Experimental catalyst performance and 15 physicochemical properties for the additives were used to train the neural network models mapping catalyst composition to performance. The neural networks predicted the CH4 conversion and H2 selectivity. For the first disk, the model was used to predict the catalytic performance of NiZ, where Z was one additive element not used in training the model. Experiments confirmed that the predicted conversion and selectivity were close to those predicted by the neural network model. Among the predicted combinations, NiSc, NiY, and NiTb showed the highest conversion and selectivity. Similarly, for the second NiPr + CoMgZ based disks, the neural network was trained to predict their catalytic performance. An optimum composite for this disk consisted of NiPr plus CoMgLi that produced a CH4 conversion of 67%, an H2 selectivity of 82%, and a CO selectivity of 80%, almost the same level as two sheets of Rh alumina disk catalyst. Neural network models of objective functions and the NSGA-II genetic algorithm were used by Scott, Manos, and

Coveney to design electroceramic materials.89 They trained the neural network using literature data and that from a ceramic materials database. The structure−property models of permittivity, proximity to known ceramic compositions, and stoichiometry were used as multiobjective functions in a process where an evolutionary algorithm was used to “invert” the model to identify Pareto fronts for electroceramic materials with favorable properties. Very recently, a different quasi-evolutionary approach was reported by Thornton et al. They explored the performance limits for hydrogen storage for a very large virtual library of porous materials such as metal−organic frameworks, zeolitic imidazolate frameworks, and covalent organic frameworks.90 They employed computationally expensive grand canonical Monte Carlo methods using appropriate force fields to generate the structures and performances of a subset of the 850 000 possible structures, and then used neural networks to model the relationships between structural descriptors and performance. The neural network objective function models were then used to predict the evolutionary landscape and the fittest points in structure space used to generate new populations of improved porous materials. This process was iterated over three generations to identify porous materials with optimal hydrogen storage properties.

5. CONCLUSIONS AND PERSPECTIVE Evolutionary algorithms have found relatively wide applications in areas other than chemistry and materials. The increasing application of robotic and other high throughput methods for synthesis and characterization of materials provides a strongly enabling capability that will allow these very efficient methods to be applied to the discovery of new materials. These optimization methods are applicable to almost any type of materials that can be encoded into a genome, and they represent a fundamentally different approach to the general problem of materials design, identification, and optimization. Evolutionary algorithms should find increasing application in both the discovery and optimization of novel materials structures, and the optimization of synthesis and processing conditions that often play an important role in the properties of the final materials. The synergistic coupling of these powerful methods of exploring very large and multidimensional spaces with empirical machine learning models of fitness landscapes in 6129

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the short to medium term, or high throughput ab initio calculations that predict materials properties in the long term, will allow materials scientists to find regions of very useful property space more quickly and effectively than by using high throughput synthesis and testing of materials alone. As Bohr (among others) once stated, it is difficult to make predictions, especially about the future. It is conceivable that evolutionary methods will have an impact on the large amount of research on self-assembling systems, resulting in methods to evolve self-assembling “smart” materials with unprecedented capabilities as delivery or targeting vehicles, sensors, etc. A glimpse of this future was provided by the work of Schulman,91 who used evolutionary methods to evolve the self-assembly of nano tiles, made from deterministically assembled DNA origami methods, into specific shapes. The Cronin group is also taking evolutionary methods in materials to a new level in their work on primordial chemistry, self-assembly, and evolution of oil droplets as model biochemical machines or to probe the pathways from complex chemical mixtures to autonomously evolving systems.92 The direction of this materials evolution research is taking generates a nice intellectual symmetry, given that powerful evolutionary search methods that mimic natural selection are being applied to materials that make up the biological genome (DNA) and the study of processes at the core of the development of life itself.

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AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. Biographies Tu C. Le is a research scientist at CSIRO Manufacturing, Australia. She is working with Prof. David A. Winkler on modeling diverse materials properties, such as aqueous solubility, nanophase behavior of drug delivery systems, and flash points using machine-learning-based quantitative structure−property relationship modeling techniques. She is also involved in simulating guest−host systems and bioactive peptides using molecular dynamics methods. She completed her Ph.D. on hyperbranched polymer melt simulations at Swinburne University of Technology, Australia, in 2010 under the supervision of Prof. Billy D. Todd (Swinburne University of Technology), Prof. Peter Daivis (RMIT University), and Dr. Alfred Uhlherr (CSIRO). David A. Winkler is a senior principal research scientist with CSIRO Manufacturing and an adjunct professor at Monash, Latrobe, and Flinders Universities. His research interests have involved computational molecular design and complex systems. His recent research has focused on the effects of polymers, bioglasses, small bioactive species, and nanomaterials on biological systems. He works in regenerative medicine and collaborates with international stem cell biologists and tissue engineers. He employs computational methods developed for small molecule research to probe and predict the interactions of materials with complex biological systems. He was awarded traveling fellowships to Kyoto and Oxford and a Newton Turner Fellowship in 2009, and a Royal Academy of Engineering fellowship in 2015. He is a past board chairman of the Royal Australian Chemical Institute, past president of the Asian Federation for Medicinal Chemistry, and president-elect of the Federation of Asian Chemical Societies, and represents Australia on the organizing committee for Pacifichem. He has published over 200 scientific papers and patents. 6130

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