Metamaterials

Machine learning surrogates based on neural operators have shown broad applicability in solving forward PDE problems. However, eigenvalue problems, in which an eigenparameter and one of several valid eigenmodes must be simultaneously solved, remain difficult because standard operator learning formulations assume a unique input-output map. This work demonstrates that Fourier Neural Operators (FNOs), combined with wavelet-based encodings of PDE inputs, can learn and predict multiple eigenmodes of the elastic wave equation, corresponding to deformation modes of acoustic waves propagating through arbitrary metamaterial geometries. We provide a mechanistic explanation and experimental evidence for why wavelet encodings are well matched to the dual spatial-spectral structure of the FNO, enabling deterministic mode selection on both continuous-valued and binary-valued geometries within a single model, and for why prediction accuracy varies with geometric discontinuities. For metamaterial design, the resulting surrogate accelerates the simulation stage of the design cycle by three orders of magnitude relative to finite element analysis on a consumer-grade CPU, while preserving high fidelity. These results also carry broader implications for designing input encodings in other multi-mode PDE solvers based on spectral neural operators.

Future wireless systems are expected to transform the surrounding space from a passive propagation medium into a smart electromagnetic environment, where engineered surfaces control wave propagation, support wireless sensing, and create programmable electromagnetic fingerprints. A key challenge in realizing this vision is the inverse design of metasurfaces for tailored electromagnetic propagation. While forward analysis evaluates the response of a known geometry, the inverse task starts from a prescribed scattering signature and seeks a physically realizable structure that produces it. This inverse task is inherently nonlinear and often high-dimensional, while candidate solutions may be non-unique and provide no direct indication of practical realizability. Here, we introduce a conditional diffusion framework for inverse design of dielectric resonator metasurfaces from target angular scattering patterns. Trained on T-matrix simulated geometry-response pairs, the model learns a conditional distribution of geometries instead of a deterministic mapping, enabling multiple candidate designs for the ill-posed inverse problem. The best generated metasurface achieves a mean percentage error of 1.39%, outperforming CMA-ES optimization (4.1% after 10 h) while requiring only about one minute for after-training inference. The model also produces lower error distributions than deterministic neural baselines for out-of-distribution spectra, highlighting the potential of diffusion models for efficient metasurface design.

Data-driven inverse design enables efficient generation of nanophotonic structures with prescribed optical responses, but spectrum-to-geometry mapping remains challenging due to non-uniqueness and fine geometric features. This work presents a two-stage deformable-convolutional framework for reconstructing metal--insulator--metal resonator geometries from 80-dimensional absorption spectra. The spectrum is projected to a $150\times4\times4$ latent representation and decoded into a $64\times64$ resonator mask. Training combines supervised reconstruction with least-squares adversarial refinement initialized from the best supervised checkpoint. A three-run ablation compares deformable convolution with plain convolution, involution, Dynamic Conv, and ODConv under the same architecture. The proposed model achieves $20.79\pm0.31$dB PSNR and $0.8501\pm0.0082$ SSIM, improving over plain convolution by 2.16dB and 0.0831, respectively. It further achieves Dice $0.9623\pm0.0027$, IoU $0.9342\pm0.0038$, and boundary F-score $0.9550\pm0.0027$. Spectral consistency evaluated using a frozen forward surrogate yields RMSE $0.0805\pm0.0013$ and $R^2=0.7923\pm0.0065$. Learned offsets show stronger adaptive sampling at coarse and intermediate decoder stages. Overall, deformable sampling with supervised initialization and adversarial refinement improves spectrum-conditioned geometry reconstruction.

Kirigami turns stiff sheets into compliant, shape-morphing structures, but its reliance on periodic cut patterns comes at a cost: correlated panel rotations couple extension to shear, so stretching one axis drives a parasitic shear that cannot be suppressed, and also confine anisotropic stiffness to a narrow, discrete set of responses that cannot be tuned independently. Biological tissues overcome an analogous constraint through controlled disorder, such as graded fiber orientations in skin and hierarchical anisotropy in myocardium, achieving direction-dependent mechanics unavailable to regular architectures. Here, we show that engineered disorder is a design degree of freedom for kirigami, with stochastic kirigami accessing a continuous and far broader region of mechanical response than periodic patterns. This includes programmable anisotropy with near-complete elimination of extension-shear coupling. Because disordered patterns lack a simple parameterization, we navigate this design space with a geometry-aware graph neural network (GNN) that maps cut topology to the full nonlinear, bidirectional stress-strain response, coupled to a genetic algorithm that inverse-designs patterns reproducing target responses along two perpendicular axes. The GNN trains an order of magnitude faster and more accurately than image-based models. Fabricated elastomer samples reproduce the predicted nonlinear, anisotropic responses, closing the loop from design to physical component. By turning disorder into a variable to control directional stiffness, this work develops architected materials that stretch without parasitic shear, from soft actuators to tissue-interfacing devices matched to the anisotropy of living tissue.

Disordered metamaterials feature microstructures with inherent randomness and irregularity, enabling them to achieve broader property coverage and superior performance unavailable in their regular counterparts. Despite their promise, designing disordered microstructures is substantially harder than designing regular ones. Their design remains trapped between manual parameterizations with limited expressiveness, and generative AI that is data-hungry and struggles to generalize. To address these limitations, we propose a generative design framework based on Neural Cellular Automata that dynamically grows complex microstructures through learned local interaction rules, inspired by the self-organizing processes in natural materials. This framework requires only a single training template, yet accommodates diverse disordered microstructures and adapts to irregular domains and arbitrary discretizations. By manipulating the learned local rules, we can steer the growth process to generate microstructures unseen during training, providing control over orientation, anisotropy, and directional thickness without retraining. As a dynamic, local growth process, it naturally produces spatially varying microstructures that transition smoothly to enable location-specific mechanical properties. We demonstrate this in a multiscale mechanical cloaking design, where microstructures vary across the space to meet an optimized heterogeneous property distribution. Our design enables excellent cloaking performance without complicated post-processing and incompatible assembly common in existing methods. This data-efficient, generalizable approach opens access to previously intractable disordered materials for biomedical implants and soft robotics.

Soft metamaterials provide a promising platform for robotics, biomedical devices, and flexible electronics. The localized mechanical responses by nonuniform excitation are ubiquitous in soft materials, yet their controlled transmission across assemblies remains largely overlooked in metamaterial design, which critically constrains nontrivial functionalities with end-to-end and long-range deformation transmission. Here, we introduce an impedance-guided design framework that enables programmable transmission of localized deformation in modular soft metamaterials, achieving behaviors unattainable by intuitive design. By establishing a nonlinear model considering position-dependent interactions and integrating the concept of mechanical impedance within metamaterials, we regulate assembly-level transmission solely through unit-cell topology optimization. The resulting framework enables effective synthesis of module families, allowing both homogeneous and heterogeneous assemblies to be custom-built with markedly enhanced transmission characteristics. Leveraging the highly combinatorial and extensible design space, we physically realize diverse on-demand displacement manipulation architectures, including obstacle-bypassing modular soft-metamaterial assemblies, defect-tolerant soft gripping, and embodied signal processing. Beyond deformation programming, the reconfigurability and reassemblability of these soft modules can embed electric logic signals, enabling energy-efficient and low-latency information processing through compliant-switch-controlled mechanical LED displays and wearable finger-motion-sensing controllers. Our method provides fundamental insights into localized deformation transmission in modular soft metamaterials and establishes a scalable route toward embodied-intelligence material systems, particularly for soft-metamaterial-centric actuation, sensing, and collective computing.

Inverse design of mechanical metamaterials seeks a periodic unit cell whose homogenized elastic properties meet a prescribed target, but current learning-based methods are data-hungry, mostly interpolative, and provide no guarantee that the generated design satisfies the specification. We introduce CertMix, a data-efficient framework that represents each exemplar unit cell as a small periodic neural implicit field, specifically a SIREN signed-distance decoder overfit from a shared anchor, so that exemplar weight vectors become aligned and directly comparable. The key observation is that, in this aligned weight space, the homogenized elasticity tensor is approximately linear in the mixing coefficients. Targeted design therefore reduces to a small constrained affine-mixing problem solved with a differentiable periodic homogenizer in the loop. Negative coefficients enable extrapolation beyond the exemplar range, a linearity-mismatch trust region keeps blends valid, and split-conformal calibration converts the mismatch signal into a distribution-free certificate on achieved-property error. From as few as 50 exemplars, CertMix attains a scaled property error of $10^{-4}$, roughly two to three orders of magnitude below conditional generative baselines trained on 1000 cells. It remains accurate far outside the exemplar range, is $57\times$ faster than per-target topology optimization while avoiding checkerboards and enclosed voids, and extends to spatially graded fields, 3D triply periodic surfaces, and a certified running-shoe midsole application.

Conventional machine-vision pipelines typically rely on high-quality optics that produce clean, human-interpretable images, and optical design has therefore been driven by image-level criteria such as resolution, aberration correction, and pixel fidelity. However, such optics are often impractical for size-, cost-, or form-factor-constrained applications, where compact meta-optics offer an attractive alternative but operate under strict physical efficiency limits. We propose CODA, a co-design framework that optimizes a continuous-density meta-optic front-end for frozen-model recognition using differentiable image formation and adjoint-gradient updates of Maxwell-based simulations. CODA directly optimizes the cross-entropy loss of a fixed zero-shot CLIP classifier without learned reconstruction, image signal processing, or image-fidelity auxiliary objectives. In a two-dimensional simulated imaging benchmark on ImageNet-100, CODA improves CLIP ViT-L/14 zero-shot accuracy from 53.75 $\pm$ 3.57$\%$ with a focal-concentration baseline to 65.41 $\pm$ 3.99$\%$. The optimized optics further transfer without re-optimization across CLIP, SigLIP, and DINOv2 on ImageNet-100, CIFAR-100, and Food-101. These results demonstrate that, under constrained meta-optic imaging, downstream recognition can be improved by aligning optical design with frozen vision-model objectives rather than conventional image-formation criteria.

Skin cancer is among the most prevalent malignancies worldwiAdbe satnradcitts early detection is essential for improving patient survival and reducing treatment costs Conventional dermoscopic and visual imaging techniques are primarily limited to the visible spectrum and often fail to capture subtle spectral signatures associated with early stage malignancies This study proposes an innovative framework that integrates a multispectral metasurface for imaging with a hybrid deep learning architecture based on Convolutional Neural Networks and Vision Transformers The designed metasurface enables noninvasive acquisition of rich spectral information highly sensitive to tissue alterations while the hybrid CNN ViT model simultaneously extracts local and global features to robustly classify skin lesions Simulation-based evaluations demonstrate that the proposed method achieves approximately 98 accuracy 95 percentages sensitivity and 99 perentage specificity surpassing conventional RGB-based and single-architecture approaches Qualitative analyses using attention maps reveal that the model focuses on clinically relevant lesion regions improving interpretability Overall the results indicate that combining metasurface based multispectral imaging with hybrid deep learning can introduce a new generation of diagnostic tools in dermatology and pave the way for portable fast and highly accurate clinical systems

Acoustic metamaterial (AMM) inverse design is particularly challenging for broadband target responses due to acoustic dispersion: a structure that matches the desired response at one frequency may deviate at others, and modifying geometry to improve one sub-band often perturbs neighboring sub-bands. Yet existing broadband inverse-design approaches are either constrained by predefined templates, or rely on image representations that fail to preserve the geometric precision and structural connectivity required by acoustic structures. We present MetaSeq, a physics-guided, sequence-based generative framework for acoustic metamaterial inverse design. At its core, MetaSeq introduces a language that represents each AMM as a structured sequence, rather than as a pixel grid or fixed template. This representation preserves precise geometry, explicitly encodes connectivity, and casts inverse design as a sequence-to-sequence task from target response to structure sequence. MetaSeq further constructs a balanced, high-fidelity dataset with efficient calibration and complexity-based sampling. To address the one-to-many nature of inverse design, MetaSeq combines supervised pretraining with reinforcement learning fine-tuning guided by a physics-based solver and validity checker. Extensive evaluations against COMSOL and five baselines show that MetaSeq reduces response error by 45% over the best baseline.

Designing 3D metamaterial microstructures that meet the intended functions remains a major challenge, as it typically requires domain expertise, iterative simulations, and extensive manual tuning. Existing work on inverse design that automatically generates microstructures based on desired target properties often suffers from limited design diversity and faces challenges in ensuring the physical feasibility of the generated structures. To address this issue, a property-informed diffusion-based network is proposed that enables the generation of 3D microstructures directly from textual descriptions. Unlike traditional property conditioning methods, our approach leverages rich guidance in terms of semantics and physical properties in the text input to support diverse structure synthesis. To enforce consistency between the generated structures and the target textual prompts, a dual alignment strategy is adopted, including contrastive text-structure alignment and test-time reward-guided alignment. Experimental results show that the model is capable of generating semantically meaningful and physically plausible structures across a wide range of material categories. Our approach has good potential for interactive microstructure design and opens up new directions for combining language-based interfaces with inverse material discovery. Code is available at: https://github.com/hongsong-wang/PropDiff-TMG

Metasurfaces enable precise manipulation of electromagnetic waves for applications such as beam steering, sensing, and stealth technology. However, inverse design of metasurfaces with targeted EM responses remains challenging due to the computational expense of iterative full wave simulation driven optimization and the limited conditioning fidelity and diversity of existing generative approaches. To address these challenges, this paper presents a generative inverse design framework for controllable and physically consistent metasurface synthesis under continuous spectral constraints. The proposed approach employs a progressively growing Wasserstein generative adversarial network with gradient penalty integrated with feature wise linear modulation based conditioning for stable propagation of continuous spectral and fabrication constraints. EM consistency is embedded directly into the generative learning process through a surrogate assisted spectral alignment loss, enabling physics constrained generation during training. Further, a determinantal point process based diversity regularization strategy is incorporated to generate geometrically diverse yet spectrally consistent realizations for the same target response. The effectiveness of the proposed framework is demonstrated through the generation of practically realizable metasurface absorbers exhibiting diverse reflection characteristics in the frequency range of 2 to 18 GHz. EM simulations validate that the generated designs meet the target specifications with high accuracy. The final proposed framework achieved an average mean squared error of 0.0052, diversity score of 0.8730, band alignment accuracy of 0.8533, and a valid EM design generation percentage of 89.57, clearly demonstrating its capability to generate highly accurate, diverse, electromagnetically consistent and fabrication realizable metasurface configurations.

We address the challenge of engineering distributed haptic displays capable of reproducing multiple localized, independently addressable vibrations -- representing virtual tactile pixels -- at arbitrary locations on a surface. Our technique is based on the focusing of mechanical waves in a flexural plate using a sparse set of actuators. At tactile frequencies, wave diffraction prevents the formation of localized virtual tactile pixels at spatial scales relevant for multi-digit touch interactions. We overcome this limitation by augmenting the plate with a lattice of mechanical resonators, forming a locally resonant metamaterial plate. Coupling between the plate's dynamic modes and those of the resonators alters the dispersion relation governing wave transmission, introducing a slow-wave branch that enables focusing beyond the diffraction limit imposed by the unmodified plate. We use numerical simulations to engineer the dispersion relation of the metamaterial system for high-resolution focusing at tactile frequencies. We then fabricate a metamaterial tactile display and experimentally demonstrate virtual pixels that are far more localized than those generated on an otherwise identical plate without resonators, resulting in a tenfold reduction in virtual-pixel area. In behavioral experiments, we show that this system can deliver perceptually localized single- and multi-point tactile feedback and moving tactile sources while maintaining independent control over temporal waveforms at multiple display locations. The methods reported here can enable high-resolution haptic displays for widespread applications using a small number of actuated degrees of freedom.

We argue that governance must transition from a normative discipline to an engineering discipline, and we develop a formal framework, inspired by the physics of metamaterials, to make this transition quantitative and testable. Artificial General Intelligence affects civilization primarily by increasing decision velocity while human verification capacity remains bounded. When the cost of validating AI-generated outputs exceeds the expected utility of acting on them, rational agents default to inaction: a stable but catastrophic Nash equilibrium we term the Freezing Equilibrium. Drawing on metamaterials, where emergent macro-properties arise from designed microstructure, we develop a phenomenological constitutive law for institutional coordination: $R_{\mathrm{eff}} = β\cdot (1-ρ) \cdot (1-τ) \cdot (1-γρτ)$, where $β$ is the decision branching factor, $ρ$ is provenance fidelity, $τ$ is the verification rate, and $γ\in [0,1]$ captures correlated-detection synergy between provenance and verification failures. The model predicts a sharp phase transition between self-healing ($R_{\mathrm{eff}} < 1$) and self-destabilizing ($R_{\mathrm{eff}} > 1$) regimes. We introduce a three-class provenance taxonomy: cryptographic, institutional, and context binding, and derive four falsifiable hypotheses with a proposed 12-week stepped-wedge cluster-randomized trial in government grant review panels. The framework bridges AI alignment theory and institutional design.

Inverse design of metasurfaces under continuous electromagnetic constraints requires generation of geometries that simultaneously satisfy stringent spectral specifications and remain manufacturable. Conventional approaches based on iterative full wave simulations are computationally prohibitive for large design spaces, while existing generative models often suffer from poor conditional controllability and limited fabrication awareness. In this regard, we propose a physics guided condition quality enhanced diffusion framework for the inverse design of metasurface based absorbers. Fabrication-aware constraints are incorporated to ensure practical realizability of the generated designs. The framework introduces a conditioning mechanism for continuous spectral specifications, wherein feature-wise linear modulation propagates the condition across the denoising hierarchy, enabling stable and accurate generation with improved spectral controllability. Further, to embed EM consistency directly into the generative learning process, a pre trained surrogate EM simulator is integrated within the diffusion training pipeline. The proposed framework generated physically realizable metasurface designs for diverse reflection characteristics in the frequency range of 2 to 18 GHz, achieving a very low average spectral mean squared error of 0.0006 and a high band alignment accuracy of 0.958. The framework also addresses the fundamentally non-unique nature of inverse EM design by enabling structured multimodal generation of geometrically distinct yet spectrally consistent metasurface designs for the same target response. The proposed model produces the suitable design in approximately 30 seconds, whereas the conventional approach can take several months under comparable computational resources. The efficiency of the model is also established via experimental measurements.

In biological systems, sensing is not performed by the brain alone: the body deforms, vibrates, and filters external stimuli before they are transduced into neural signals. In engineered systems, this processing burden is placed largely on electronics and computation, while the mechanical body is usually designed only for strength and stability. Here, we present sensing intelligence as a trainable property of the body. We show that the geometry of a metamaterial can be optimized to reshape external stimuli into internal signals that are easier for a neural network to interpret. Rather than hand-designing this physical preprocessing, we let the neural network train its own body for sensing by backpropagating the sensing loss to the body's design parameters through differentiable simulation. Across numerical and experimental sensing scenarios, the optimized body improves sensing accuracy by up to fivefold or reduces the number of required electronic sensors by nearly an order of magnitude.

Metamaterial discovery seeks microstructured materials whose geometry induces targeted mechanical behavior. Existing inverse-design methods can efficiently generate candidates, but they typically require explicit numerical property targets and are less suitable for early-stage exploration, where researchers often begin with incomplete constraints and qualitative intents expressed in natural language. Large language models can interpret such intents, but they lack geometric awareness and physical property validity. To address this gap, we propose MetaSymbO, a multi-agent framework for language-guided Metamaterial discovery via Symbolic-driven latent evOlution. Specifically, MetaSymbO contains three agents: a Designer that interprets free-form design intents and retrieves a semantically consistent scaffold, a Generator that synthesizes candidate microstructures in a disentangled latent space, and a Supervisor that provides fast property-aware feedback for iterative refinement. To move beyond the limitations of reproducing known samples from literature and training data, we further introduce symbolic-driven latent evolution, which applies programmable operators over disentangled latent factors to compose, modify, and refine structures at inference time. Extensive experiments demonstrate that (i) MetaSymbO improves structural validity by up to 34% in symmetry and nearly 98% in periodicity compared to state-of-the-art baselines; (ii) MetaSymbO achieves about 6-7% higher language-guidance scores while maintaining superior structure novelty compared to advanced reasoning LLMs; (iii) qualitative analyses confirm the effectiveness of symbolic logic operators in enabling programmable semantic alignment; and (iv) realworld case studies on auxetic, high-stiffness metamaterial design further validate its practical capability.

Voiceprints are widely used for authentication; however, they are easily captured in public settings and cannot be revoked once leaked. Existing anonymization systems operate inside recording devices, which makes them ineffective when microphones or software are untrusted, as in conference rooms, lecture halls, and interviews. We present EchoMask, the first practical physical-layer system for real-time voiceprint anonymization using acoustic metamaterials. By modifying sound waves before they reach the microphone, EchoMask prevents attackers from capturing clean voiceprints through compromised devices. Our design combines three key innovations: frequency-selective interference to disrupt voiceprint features while preserving speech intelligibility, an acoustic-field model to ensure stability under speaker movement, and reconfigurable structures that create time-varying interference to prevent learning or canceling a fixed acoustic pattern. EchoMask is low-cost, power-free, and 3D-printable, requiring no machine learning, software support, or microphone modification. Experiments conducted across eight microphones in diverse environments demonstrate that EchoMask increases the Miss-match Rate, i.e., the fraction of failed voiceprint matching attempts, to over 90%, while maintaining high speech intelligibility.

Kirigami is an increasingly useful fabrication method to produce shape-programmable metamaterial structures. However, inverse design remains difficult because deployment is nonlinear, and feasible cut layouts must satisfy discrete compatibility rules, avoid overlap, and map one target shape to valid designs. We present RL-Kirigami, an inverse design framework that combines optimal-transport conditional flow matching (OT-CFM) with reinforcement learning to generate compatible ratio fields for compact reconfigurable parallelogram quad kirigami. A marching decoder enforces global geometric compatibility, and Group Relative Policy Optimization (GRPO) aligns the generator with nondifferentiable rewards for silhouette matching, feasibility, and ratio-field regularity. Across procedurally generated target shape instances, a single sample from the pretrained OT-CFM prior reached $94.2$ sIoU and outperformed solver baselines while reducing forward simulator evaluations from hundreds to 1. GRPO improved accuracy to $94.91$ sIoU and, with regularity included, reduced $\mathrm{TV}(\mathbf{x})$ from 0.95 to 0.81 while maintaining $94.83$ sIoU. Generated layouts were exported to DXF and laser-cut in $50~μ\mathrm{m}$ polymeric sheets to produce deployable prototypes in $8.0 \pm 1.0$ minutes per part. These results support a manufacturing-aware inverse design workflow for deployable kirigami metamaterials under hard geometric feasibility constraints.