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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(104)) 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.

Deep generative models have demonstrated effectiveness in learning compact and expressive design representations that significantly improve geometric design optimization. However, these models do not consider the uncertainty introduced by manufacturing or fabrication. The past work that quantifies such uncertainty often makes simplifying assumptions on geometric variations, while the “real-world,” “free-form” uncertainty and its impact on design performance are difficult to quantify due to the high dimensionality. To address this issue, we propose a generative adversarial network-based design under uncertainty framework (GAN-DUF), which contains a deep generative model that simultaneously learns a compact representation of nominal (ideal) designs and the conditional distribution of fabricated designs given any nominal design. This opens up new possibilities of (1) building a universal uncertainty quantification model compatible with both shape and topological designs, (2) modeling free-form geometric uncertainties without the need to make any assumptions on the distribution of geometric variability, and (3) allowing fast prediction of uncertainties for new nominal designs. We can combine the proposed deep generative model with robust design optimization or reliability-based design optimization for design under uncertainty. We demonstrated the framework on two real-world engineering design examples and showed its capability of finding the solution that possesses better performance after fabrication.

Deep generative models have demonstrated effectiveness in learning compact and expressive design representations that significantly improve geometric design optimization. However, these models do not consider the uncertainty introduced by manufacturing or fabrication. Past work that quantifies such uncertainty often makes simplifying assumptions on geometric variations, while the “real-world”, “free-form” uncertainty and its impact on design performance are difficult to quantify due to the high dimensionality. To address this issue, we propose a Generative Adversarial Network-based Design under Uncertainty Framework (GAN-DUF), which contains a deep generative model that simultaneously learns a compact representation of nominal (ideal) designs and the conditional distribution of fabricated designs given any nominal design. This opens up new possibilities of 1) building a universal uncertainty quantification model compatible with both shape and topological designs, 2) modeling free-form geometric uncertainties without the need to make any assumptions on the distribution of geometric variability, and 3) allowing fast prediction of uncertainties for new nominal designs. We can combine the proposed deep generative model with robust design optimization or reliability-based design optimization for design under uncertainty. We demonstrated the framework on two real-world engineering design examples and showed its capability of finding the solution that possesses better performances after fabrication.

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 the multiscale architectures. The model-centric research trend, however, lacks principled frameworks dedicated to data acquisition, whose quality propagates into the downstream tasks. 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 balanced and task-aware data generation. Uniquely, we seek a solution to a commonplace yet frequently overlooked scenario at early stages of data-driven design: when a massive 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 (∼ O(104)) are used to demonstrate the efficacy. Applicable to general design representations, t-METASET can boost future advancements in data-driven design.

Graph databases capture richly linked domain knowledge by integrating heterogeneous data and metadata into a unified representation. Here, we present the use of bespoke, interactive data graphics (bar charts, scatter plots, etc.) for visual exploration of a knowledge graph. By modeling a chart as a set of metadata that describes semantic context (SPARQL query) separately from visual context (Vega-Lite specification), we leverage the high-level, declarative nature of the SPARQL and Vega-Lite grammars to concisely specify web-based, interactive data graphics synchronized to a knowledge graph. Resources with dereferenceable URIs (uniform resource identifiers) can employ the hyperlink encoding channel or image marks in Vega-Lite to amplify the information content of a given data graphic, and published charts populate a browsable gallery of the database. We discuss design considerations that arise in relation to portability, persistence, and performance. Altogether, this pairing of SPARQL and Vega-Lite—demonstrated here in the domain of polymer nanocomposite materials science—offers an extensible approach to FAIR (findable, accessible, interoperable, reusable) scientific data visualization within a knowledge graph framework.

Data-driven design of mechanical metamaterials is an increasingly popular method to combat costly physical simulations and immense, often intractable, geometrical design spaces. Using a precomputed dataset of unit cells, a multiscale structure can be quickly filled via combinatorial search algorithms, and machine learning models can be trained to accelerate the process. However, the dependence on data induces a unique challenge: An imbalanced dataset containing more of certain shapes or physical properties than others can be detrimental to the efficacy of the approaches and any models built on those sets. In answer, we posit that a smaller yet diverse set of unit cells leads to scalable search and unbiased learning. To select such subsets, we propose METASET, a methodology that 1) uses similarity metrics and positive semi-definite kernels to jointly measure the closeness of unit cells in both shape and property space, and 2) incorporates Determinantal Point Processes for efficient subset selection. Moreover, METASET allows the trade-off between shape and property diversity so that subsets can be tuned for various applications. Through the design of 2D metamaterials with target displacement profiles, we demonstrate that smaller, diverse subsets can indeed improve the search process as well as structural performance. We also apply METASET to eliminate inherent overlaps in a dataset of 3D unit cells created with symmetry rules, distilling it down to the most unique families. Our diverse subsets are provided publicly for use by any designer.

The data-driven approach is emerging as a promising method for the topological design of the multiscale structure with greater efficiency. However, existing data-driven methods mostly focus on a single class of unit cells without considering multiple classes to accommodate spatially varying desired properties. The key challenge is the lack of inherent ordering or “distance” measure between different classes of unit cells in meeting a range of properties. To overcome this hurdle, we extend the newly developed latent-variable Gaussian process (LVGP) to creating multi-response LVGP (MRLVGP) for the unit cell libraries of metamaterials, taking both qualitative unit cell concepts and quantitative unit cell design variables as mixed-variable inputs. The MRLVGP embeds the mixed variables into a continuous design space based on their collective effect on the responses, providing substantial insights into the interplay between different geometrical classes and unit cell materials. With this model, we can easily obtain a continuous and differentiable transition between different unit cell concepts that can render gradient information for multiscale topology optimization. While the proposed approach has a broader impact on the concurrent topological and material design of engineered systems, we demonstrate its benefits through multiscale topology optimization with aperiodic unit cells. Design examples reveal that considering multiple unit cell types can lead to improved performance due to the consistent load-transferred paths for micro- and macrostructures.