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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 Shape morphing that transforms morphologies in response to stimuli is crucial for future multifunctional systems. While kirigami holds great promise in enhancing shape-morphing, existing designs primarily focus on kinematics and overlook the underlying physics. This study introduces a differentiable inverse design framework that considers the physical interplay between geometry, materials, and stimuli of active kirigami, made by soft material embedded with magnetic particles, to realize target shape-morphing upon magnetic excitation. We achieve this by combining differentiable kinematics and energy models into a constrained optimization, simultaneously designing the cuts and magnetization orientations to ensure kinematic and physical feasibility. Complex kirigami designs are obtained automatically with unparalleled efficiency, which can be remotely controlled to morph into intricate target shapes and even multiple states. The proposed framework can be extended to accommodate various active systems, bridging geometry and physics to push the frontiers in shape-morphing applications, like flexible electronics and minimally invasive surgery. 

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. 

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.