path optimization

Data-driven design shows the promise of accelerating materials discovery but is challenging due to the prohibitive cost of searching the vast design space of chemistry, structure, and synthesis methods. Bayesian Optimization (BO) employs uncertainty-aware machine learning models to select promising designs to evaluate, hence reducing the cost. However, BO with mixed numerical and categorical variables, which is of particular interest in materials design, has not been well studied. In this work, we survey frequentist and Bayesian approaches to uncertainty quantification of machine learning with mixed variables. We then conduct a systematic comparative study of their performances in BO using a popular representative model from each group, the random forest-based Lolo model (frequentist) and the latent variable Gaussian process model (Bayesian). We examine the efficacy of the two models in the optimization of mathematical functions, as well as properties of structural and functional materials, where we observe performance differences as related to problem dimensionality and complexity. By investigating the machine learning models' predictive and uncertainty estimation capabilities, we provide interpretations of the observed performance differences. Our results provide practical guidance on choosing between frequentist and Bayesian uncertainty-aware machine learning models for mixed-variable BO in materials design.

Inspired by the recent achievements of machine learning in diverse domains, data-driven metamaterials design has emerged as a compelling paradigm that can unlock the potential of multiscale architectures. The model-centric research trend, however, lacks principled frameworks dedicated to data acquisition, whose quality propagates into the downstream tasks. Often built by naive space-filling design in shape descriptor space, metamaterial datasets suffer from property distributions that are either highly imbalanced or at odds with design tasks of interest. To this end, we present t-METASET: an active-learning-based data acquisition framework aiming to guide both diverse and task-aware data generation. Distinctly, we seek a solution to a commonplace yet frequently overlooked scenario at early stages of data-driven design of metamaterials: when a massive (~O(10^4 )) shape-only library has been prepared with no properties evaluated. The key idea is to harness a data-driven shape descriptor learned from generative models, fit a sparse regressor as a start-up agent, and leverage metrics related to diversity to drive data acquisition to areas that help designers fulfill design goals. We validate the proposed framework in three deployment cases, which encompass general use, task-specific use, and tailorable use. Two large-scale mechanical metamaterial datasets are used to demonstrate the efficacy. Applicable to general image-based design representations, t-METASET could boost future advancements in data-driven design.

Inspired by the recent achievements of machine learning in diverse domains, data-driven metamaterials design has emerged as a compelling paradigm that can unlock the potential of multiscale architectures. The model-centric research trend, however, lacks principled frameworks dedicated to data acquisition, whose quality propagates into the downstream tasks. Often built by naive space-filling design in shape descriptor space, metamaterial datasets suffer from property distributions that are either highly imbalanced or at odds with design tasks of interest. To this end, we present t-METASET: an active-learning-based data acquisition framework aiming to guide both diverse and task-aware data generation. Distinctly, we seek a solution to a commonplace yet frequently overlooked scenario at early stages of data-driven design of metamaterials: when a massive (~O(10^4 )) shape-only library has been prepared with no properties evaluated. The key idea is to harness a data-driven shape descriptor learned from generative models, fit a sparse regressor as a start-up agent, and leverage metrics related to diversity to drive data acquisition to areas that help designers fulfill design goals. We validate the proposed framework in three deployment cases, which encompass general use, task-specific use, and tailorable use. Two large-scale mechanical metamaterial datasets are used to demonstrate the efficacy. Applicable to general image-based design representations, t-METASET could boost future advancements in data-driven design.

Bayesian optimization is normally performed within fixed variable bounds. In cases like hyperparameter tuning for machine learning algorithms, setting the variable bounds is not trivial. It is hard to guarantee that any fixed bounds will include the true global optimum. We propose a Bayesian optimization approach that only needs to specify an initial search space that does not necessarily include the global optimum, and expands the search space when necessary. However, over-exploration may occur during the search space expansion. Our method can adaptively balance exploration and exploitation in an expanding space. Results on a range of synthetic test functions and an MLP hyperparameter optimization task show that the proposed method out-performs or at least as good as the current state-of-the-art methods.

Many engineering problems require identifying feasible domains under implicit constraints. One example is finding acceptable car body styling designs based on constraints like aesthetics and functionality. Current active-learning based methods learn feasible domains for bounded input spaces. However, we usually lack prior knowledge about how to set those input variable bounds. Bounds that are too small will fail to cover all feasible domains; while bounds that are too large will waste query budget. To avoid this problem, we introduce Active Expansion Sampling (AES), a method that identifies (possibly disconnected) feasible domains over an unbounded input space. AES progressively expands our knowledge of the input space, and uses successive exploitation and exploration stages to switch between learning the decision boundary and searching for new feasible domains. We show that AES has a misclassification loss guarantee within the explored region, independent of the number of iterations or labeled samples. Thus it can be used for real-time prediction of samples’ feasibility within the explored region. We evaluate AES on three test examples and compare AES with two adaptive sampling methods — the Neighborhood-Voronoi algorithm and the straddle heuristic — that operate over fixed input variable bounds.

To solve a design problem, sometimes it is necessary to identify the feasible design space. For design spaces with implicit constraints, sampling methods are usually used. These methods typically bound the design space; that is, limit the range of design variables. But bounds that are too small will fail to cover all possible designs, while bounds that are too large will waste sampling budget. This paper tries to solve the problem of efficiently discovering (possibly disconnected) feasible domains in an unbounded design space. We propose a data-driven adaptive sampling technique—ε-margin sampling, which learns the domain boundary of feasible designs and also expands our knowledge on the design space as available budget increases. This technique is data-efficient, in that it makes principled probabilistic trade-offs between refining existing domain boundaries versus expanding the design space. We demonstrate that this method can better identify feasible domains on standard test functions compared to both random and active sampling (via uncertainty sampling). However, a fundamental problem when applying adaptive sampling to real world designs is that designs often have high dimensionality and thus require (in the worst case) exponentially more samples per dimension. We show how coupling design manifolds with ε-margin sampling allows us to actively expand high-dimensional design spaces without incurring this exponential penalty. We demonstrate this on real-world examples of glassware and bottle design, where our method discovers designs that have different appearance and functionality from its initial design set.