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Is Automated Materials Design and Discovery Possible?

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Materials Discovery and Design

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 280))

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Abstract

In materials design, we typically want to answer questions such as “Can we optimize the probability that a structure will produce the desired properties within some tolerance?” or “Can we optimize the probability that a transition will occur between the desired initial and final states?” In the vast majority of cases, these problems are addressed indirectly, and with a reduced-dimensional model that approximates the actual system. Why? The tools and techniques traditionally used are not sufficient to provide a general rigorous algorithmic approach to determining and/or validating models of the system. Solving for the structure that maximizes some property very likely will be a global optimization over a nonlinear surface with several local minima and nonlinear constraints, while the tools generally used are linear (or at best quadratic) solvers. This approximation is made to handle the large dimensionality of the problem and be able to apply some basic constraints on the space of possible solutions. Unfortunately, constraints from data, measurements, theory, and other physical information are often only applied post-optimization as a binary form of model validation. Additionally, sampling techniques like Monte Carlo, as well as machine learning and Bayesian inference (which strongly rely on existing observed data to infer the form of the solution), will not perform well when, in terms of structural configurations, discovering the materials in the state that produces the desired property is a rare-event. This is unfortunately the rule, rather than the exception—and thus most searches either require the solution to already have been observed, or at least to be in the locality of the optimum. Fortunately, recent developments in applied mathematics and numerical optimization provide a new suite of tools that should overcome the existing limitations, and make rigorous automated materials discovery and design possible.

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Notes

  1. 1.

    \(\delta _x\) is the Dirac delta mass on x, i.e. the measure of probability on Borel subsets \(A \subset \mathbb {R}\) such that \(\delta _x(A)=1\) if \(x\in A\) and \(\delta _x(A)=0\) otherwise. The first Dirac delta mass is located at the minimum of the interval \([a,\infty ]\) (since we are interested in maximizing the probability of the event \(\mu [f(X)\ge a]\)). The second Dirac delta mass is located at \(x = a - D\) because we seek to maximize \(p_{\max }\) under the constraints \(p_{\max } a + (1 - p_{\max }) x \le b\) and \(a - x \le D\).

  2. 2.

    This technical requirement is not a serious restriction in practice, since it is satisfied by most common parameter and function spaces. A Radon space is a topological space on which every Borel probability measure \(\mu \) is inner regular in the sense that, for every measurable set E, \(\mu (E) = \sup \{ \mu (K) \mid K \subseteq E \text { is compact} \}\). A simple example of a non-Radon space is the unit interval [0, 1] with the lower limit topology [78, Example 51]: this topology generates the same \(\sigma \)-algebra as does the usual Euclidean topology, and admits the uniform (Lebesgue) probability measure, yet the only compact subsets are countable sets, which necessarily have measure zero.

  3. 3.

    This is a “philosophically reasonable” position to take, since one can verify finitely many such inequalities in finite time.

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  1. The Uncertainty Quantification Foundation, 300 Delaware Ave. Ste. 210, Wilmington, DE, 19801, USA

    Michael McKerns

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  1. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA

    Turab Lookman

  2. Los Alamos National Laboratory, Los Alamos, NM, USA

    Stephan Eidenbenz

  3. Brookhaven National Laboratory, Brookhaven, NY, USA

    Frank Alexander

  4. Los Alamos National Laboratory, Los Alamos, NM, USA

    Cris Barnes

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McKerns, M. (2018). Is Automated Materials Design and Discovery Possible?. In: Lookman, T., Eidenbenz, S., Alexander, F., Barnes, C. (eds) Materials Discovery and Design. Springer Series in Materials Science, vol 280. Springer, Cham. https://doi.org/10.1007/978-3-319-99465-9_2

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