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Abstract In engineering design, global sensitivity analysis (GSA) is used for analyzing the effects of inputs on the system response and is commonly studied with analytical or surrogate models. However, such models fail to capture nonlinear behaviors in complex systems and involve several modeling assumptions. Besides model-focused methods, a data-driven GSA approach, rooted in interpretable machine learning, would also identify the relationships between system components. Moreover, a special need in engineering design extends beyond performing GSA for input variables individually, but instead evaluating the contributions of variable groups on the system response. In this article, we introduce a flexible, interpretable artificial neural network model to uncover individual as well as grouped global sensitivity indices for understanding complex physical interactions in engineering design problems. The proposed model allows the investigation of the main effects and second-order effects in GSA according to functional analysis of variance (FANOVA) decomposition. To draw a higher-level understanding, we further use the subset decomposition method to analyze the significance of the groups of input variables. Using the design of a programmable material system (PMS) as an example, we demonstrate the use of our approach for examining the impact of material, architecture, and stimulus variables as well as their interactions. This information lays the foundation for managing design space complexity, summarizing the relationships between system components, and deriving design guidelines for PMS development. 

Abstract Multifunctional metamaterials (MMM) bear promise as next‐generation material platforms supporting miniaturization and customization. Despite many proof‐of‐concept demonstrations and the proliferation of deep learning assisted design, grand challenges of inverse design for MMM, especially those involving heterogeneous fields possibly subject to either mutual meta‐atom coupling or long‐range interactions, remain largely under‐explored. To this end, a data‐driven design framework is presented, which streamlines the inverse design of MMMs involving heterogeneous fields. A core enabler is implicit Fourier neural operator (IFNO), which predicts heterogeneous fields distributed across a metamaterial array, thus in general at odds with homogenization assumptions. Additionally, a standard formulation of inverse problem covering a broad class of MMMs is presented, together with gradient‐based multitask concurrent optimization identifying a set of Pareto‐optimal architecture‐stimulus (A‐S) pairs. Fourier multiclass blending is proposed to synthesize inter‐class meta‐atoms anchored on a set of geometric motifs, while enjoying training‐free dimension reduction and built‐it reconstruction. Interlocking the three pillars, the framework is validated for light‐by‐light programmable nanoantenna, whose design involves vast space jointly spanned by quasi‐freeform supercells, maneuverable incident phase distributions, and conflicting figure‐of‐merits (FoM) involving on‐demand localization patterns. Accommodating all the challenges, the framework can propel future advancements of MMM. 

Abstract Metamaterials are artificial materials designed to exhibit effective material parameters that go beyond those found in nature. Composed of unit cells with rich designability that are assembled into multiscale systems, they hold great promise for realizing next‐generation devices with exceptional, often exotic, functionalities. However, the vast design space and intricate structure–property relationships pose significant challenges in their design. A compelling paradigm that could bring the full potential of metamaterials to fruition is emerging: data‐driven design. This review provides a holistic overview of this rapidly evolving field, emphasizing the general methodology instead of specific domains and deployment contexts. Existing research is organized into data‐driven modules, encompassing data acquisition, machine learning‐based unit cell design, and data‐driven multiscale optimization. The approaches are further categorized within each module based on shared principles, analyze and compare strengths and applicability, explore connections between different modules, and identify open research questions and opportunities. 

Abstract 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. 

Metamaterials with functional responses can exhibit varying properties under different conditions (e.g., wave‐based responses or deformation‐induced property variation). This work addresses rapid inverse design of such metamaterials to meet target qualitative functional behaviors, a challenge due to its intractability and nonunique solutions. Unlike data‐intensive and noninterpretable deep‐learning‐based methods, this work proposes the random‐forest‐based interpretable generative inverse design (RIGID), a single‐shot inverse design method for fast generation of metamaterials with on‐demand functional behaviors. RIGID leverages the interpretability of a random forest‐based “design → response” forward model, eliminating the need for a more complex “response → design” inverse model. Based on the likelihood of target satisfaction derived from the trained random forest, one can sample a desired number of design solutions using Markov chain Monte Carlo methods. RIGID is validated on acoustic and optical metamaterial design problems, each with fewer than 250 training samples. Compared to the genetic algorithm‐based design generation approach, RIGID generates satisfactory solutions that cover a broader range of the design space, allowing for better consideration of additional figures of merit beyond target satisfaction. This work offers a new perspective on solving on‐demand inverse design problems, showcasing the potential for incorporating interpretable machine learning into generative design under small data constraints. 

Mechanical cloaks are materials engineered to manipulate the elastic response around objects to make them indistinguishable from their homogeneous surroundings. Typically, methods based on material-parameter transformations are used to design optical, thermal, and electric cloaks. However, they are not applicable in designing mechanical cloaks, since continuum-mechanics equations are not form invariant under general coordinate transformations. As a result, existing design methods for mechanical cloaks have so far been limited to a narrow selection of voids with simple shapes. To address this challenge, we present a systematic, data-driven design approach to create mechanical cloaks composed of aperiodic metamaterials using a large precomputed unit cell database. Our method is flexible to allow the design of cloaks with various boundary conditions, multiple loadings, different shapes and numbers of voids, and different homogeneous surroundings. It enables a concurrent optimization of both topology and properties distribution of the cloak. Compared to conventional fixed-shape solutions, this results in an overall better cloaking performance and offers unparalleled versatility. Experimental measurements on additively manufactured structures further confirm the validity of the proposed approach. Our research illustrates the benefits of data-driven approaches in quickly responding to new design scenarios and resolving the computational challenge associated with multiscale designs of functional structures. It could be generalized to accommodate other applications that require heterogeneous property distribution, such as soft robots and implants design. 

Paper received the best paper award in the 48th ASME Design Automation Conference.