Efficient Exploration of Microstructure-Property Spaces via Active Learning

In materials design, supervised learning plays an important role for optimization and inverse modeling of microstructure-property relations. To successfully apply supervised learning models, it is essential to train them on suitable data. Here, suitable means that the data covers the microstructure and property space sufficiently and, especially for optimization and inverse modeling, that the property space is explored broadly. For virtual materials design, typically data is generated by numerical simulations, which implies that data pairs can be sampled on demand at arbitrary locations in microstructure space. However, exploring the space of properties remains challenging. To tackle this problem, interactive learning techniques known as active learning can be applied. The present work is the first that investigates the applicability of the active learning strategy query-by-committee for an efficient property space exploration. Furthermore, an extension to active learning strategies is described, which prevents from exploring regions with properties out of scope (i.e., properties that are physically not meaningful or not reachable by manufacturing processes)

Exploring and Exploiting Models of the Fitness Landscape: a Case Against Evolutionary Optimization

In recent years, the theories of natural selection and biological evolution have proved popular metaphors for understanding and solving optimization problems in engineering design. This thesis identifies some fundamental problems associated with this use of such metaphors. Key objections are the failure of evolutionary optimization techniques to represent explicitly the goal of the optimization process, and poor use of knowledge developed during the process. It is also suggested that convergent behaviour of an optimization algorithm is an undesirable quality if the algorithm is to be applied to multimodal problems. An alternative approach to optimization is suggested, based on the explicit use of knowledge and/or assumptions about the nature of the optimization problem to construct Bayesian probabilistic models of the surface being optimized and the goal of the optimization. Distinct exploratory and exploitative strategies are identified for carrying out optimization based on such models—exploration based on attempting to reduce maximally an entropy-based measure of the total uncertainty concerning the satisfaction of the optimization goal over the space, exploitation based on evalutation of the point judged most likely to achieve the goal—together with a composite strategy which combines exploration and exploitation in a principled manner. The behaviour of these strategies is empirically investigated on a number of test problems. Results suggest that the approach taken may well provide effective optimization in a way which addresses the criticisms made of the evolutionary metaphor, subject to issues of the computational cost of the approach being satisfactorily addressed