Nonlinear response-driven inverse design of tubular metamaterials

Machine learning-accelerated inverse design of programmable bi-functional metamaterials

Machine learning (ML)-based data-driven approaches are extensively employed in forward and inverse acoustic metamaterial design, as evidenced by numerous research papers published in recent years. These studies require advanced ML knowledge and coding skills. Furthermore, the proposed ML models lack generalizability, being tailored to specific structures and hard to apply broadly, limiting practical applications. To address these issues, this study establishes two data-driven design strategies—agent interaction and large language model (LLM) fine-tuning—based on LLMs, eliminating the need for specialized ML knowledge. This approach provides a universal user-friendly strategy for acoustic metamaterial design. The agent interaction strategy enables ChatGPT to act as an independent agent, mapping structural parameters to sound absorption coefficients through simple text interactions, thereby facilitating both forward and inverse design. The LLM fine-tuning strategy involves retraining DeepSeek using acoustic metamaterial datasets, adjusting specific model parameters to enable performance prediction or inverse design. Results indicate that the agent interaction strategy can design acoustic metamaterials within one minute solely through dialogue and instruction. The fine-tuned LLM strategy yields design outcomes with higher accuracy compared to the conventional ML model. Additionally, the fine-tuned LLM can evolve into a specialized LLM for the metamaterial domain through continuous fine-tuning. The proposed strategies validate the application potential of LLMs in data-driven metamaterial design and provide significant guidance for advancing this field.

As typical mechanical metamaterials with negative Poisson’s ratios, auxetic metamaterials exhibit counterintuitive auxetic behaviors that are highly dependent on their geometric arrangements. The realization of the geometric arrangement required to achieve a negative Poisson’s ratio relies considerably on the experience of designers and trial-and-error approaches. This report proposes an inverse design method for auxetic metamaterials using deep learning, in which a batch of auxetic metamaterials with a user-defined Poisson’s ratio and Young’s modulus can be generated by a conditional generative adversarial network without prior knowledge. The network was trained based on supervised learning using a large number of geometrical patterns generated by Voronoi tessellation. The performance of the network was demonstrated by verifying the mechanical properties of the generated patterns using finite element method simulations and uniaxial compression tests. The successful realization of user-desired properties can potentially accelerate the inverse design and development of mechanical metamaterials.

Metamaterials, thoughtfully designed, have demonstrated remarkable success in the manipulation of electromagnetic waves. More recently, deep learning can advance the performance in the field of metamaterial inverse design. However, existing inverse design methods based on deep learning often overlook potential trade-offs of optimal design and outcome diversity. To address this issue, in this work we introduce contrastive learning to implement a simple but effective global ranking inverse design framework. Viewing inverse design as spectrum-guided ranking of the candidate structures, our method creates a resemblance relationship of the optical response and metamaterials, enabling the prediction of diverse structures of metamaterials based on the global ranking. Furthermore, we have combined transfer learning to enrich our framework, not limited in prediction of single metamaterial representation. Our work can offer inverse design evaluation and diverse outcomes. The proposed method may shrink the gap between flexibility and accuracy of on-demand design.

Electromagnetic (EM) metamaterials have a wide range of applications due to their unique properties, but their design is often based on specific topological structures, which come with certain limitations. Designing with stochastic topologies can provide more diverse EM properties. However, this requires experienced designers to search and optimise in a vast design space, which is time-consuming and requires substantial computational resources. In this paper, we employ a deep learning network agent model to replace time-consuming full-wave simulations and quickly establish the mapping relationship between the metamaterial structure and its electromagnetic response. The proposed framework integrates a Convolutional Block Attention Module-enhanced Variational Autoencoder (CBAM-VAE) with a Transformer-based predictor. Incorporating CBAM into the VAE architecture significantly enhances the model’s capacity to extract and reconstruct critical structural features of metamaterials. The Transformer predictor utilises an encoder-only configuration that leverages the sequential data characteristics, enabling accurate prediction of electromagnetic responses from latent variables while significantly enhancing computational efficiency. The dataset is randomly generated based on the filling rate of unit cells, requiring only a small fraction of samples compared to the full design space for training. We employ the trained model for the inverse design of metamaterials, enabling the rapid generation of two cells for 1-bit coding metamaterials. Compared to a similarly sized metallic plate, the designed coding metamaterial radar cross-section (RCS) reduces by over 10 dB from 6 to 18 GHz. Simulation and experimental measurement results validate the reliability of this design approach, providing a novel perspective for the design of EM metamaterials.

Customizable metamaterial design for desired strain-dependent Poisson’s ratio using constrained generative inverse design network

A hybrid deep learning approach for the design of 2D low porosity auxetic metamaterials

Deep learning-based inverse design of lattice metamaterials for tuning bandgap

Mechanical and phononic metamaterials exhibiting negative elastic moduli, gapped vibrational spectra, or topologically protected modes enable precise control of structural and acoustic functionalities. While much progress has been made in their experimental and theoretical characterization, the inverse design of mechanical metamaterials with arbitrarily programmable spectral properties and mode localization remains an unsolved problem. Here, we present a flexible computational inverse-design framework that allows the efficient tuning of one or more gaps at nearly arbitrary positions in the spectrum of discrete phononic metamaterial structures. The underlying algorithm optimizes the linear response of elastic networks directly, is applicable to ordered and disordered structures, scales efficiently in 2D and 3D, and can be combined with a wide range of numerical optimization schemes. We illustrate the broad practical potential of this approach by designing mechanical bandgap switches that open and close pre-programmed spectral gaps in response to an externally applied stimulus such as shear or compression. We further show that the designed structures can host topologically protected edge modes, and validate the numerical predictions through explicit 3D finite element simulations of continuum elastica with experimentally relevant material parameters. Generally, this network-based inverse design paradigm offers a direct pathway towards manufacturing phononic metamaterials, DNA origami structures and topolectric circuits that can realize a wide range of static and dynamic target functionalities.

Machine learning (ML) is emerging as a transformative tool for the design of mechanical metamaterials, offering properties that far surpass those achievable through lab‐based trial‐and‐error methods. However, a major challenge in current inverse design strategies is their reliance on extensive computational and/or experimental datasets, which becomes particularly problematic for designing micro‐scale stochastic architected materials that exhibit nonlinear mechanical behaviors. Here, a comprehensive end‐to‐end scientific ML framework, leveraging deep neural operators (including DeepONet and its variants) is introduced, to directly learn the relationship between the complete microstructure and mechanical response of architected metamaterials from sparse but high‐quality in situ experimental data. Various neural operators and standard neural networks are systematically compared to identify the model that offers better interpretability and accuracy. The approach facilitates the efficient inverse design of structures tailored to specific nonlinear mechanical behaviors. Results obtained from stochastic spinodal microstructures, printed using two‐photon lithography, reveal that the prediction error for mechanical responses is within a range of 5 ‐ 10%. This work underscores that by employing neural operators with advanced nano‐ and micro‐mechanical experiments, the design of complex micro‐architected materials with desired properties becomes feasible, even in scenarios constrained by data scarcity. This work marks a significant advancement in the field of materials‐by‐design, potentially heralding a new era in the discovery and development of next‐generation metamaterials with unparalleled mechanical characteristics derived directly from experimental insights.

The design of plasmonic stack metamaterials (PSMs) is critical due to their promising potentials in the fields of optical absorbers, sensors, and thermal irradiation. Compared with the classical circuit‐based optimization, the design by deep learning (DL) has attracted greater attention, since it is not essential to obtain their equivalent circuit parameters. Currently, a DL model for their higher‐precision design, especially with complicated spectral features, is still quite in demand. Here, a divide‐and‐conquer DL model based on a bidirectional artificial neural network is proposed. As proof‐of‐concept examples, the PSMs consisting of two metal/dielectric/metal/dielectric subwavelength stacks are adopted to demonstrate the validity of the paradigm. It demonstrates a significant prediction error reduction of 37.5% with the 47.8% decrease of training parameters than the conventional method in the forward network, which supports a powerful inverse design from spectra to PSM structures. Furthermore, a flexible tool based on the free customer definition, which facilitates the real‐time design of PSMs with various circuit‐analog functions, is developed. The fabrication and measurement experiments verify the design performance of the method. The study enhances the precision and convenience of on‐demand circuit‐analog PSMs and will provide a guide for fast high‐performance inverse design of many other metamaterials.

A data enhanced iterative few-sample (DEIFS) algorithm is proposed to achieve the accurate and efficient inverse design of multi-shaped 2D chiral metamaterials. Specifically, three categories of 2D diffractive chiral structures with different geometrical parameters, including widths, separation spaces, bridge lengths, and gold lengths are studied utilising both the conventional rigorous coupled wave analysis (RCWA) approach and DEIFS algorithm, with the former approach assisting the training process for the latter. The DEIFS algorithm can be divided into two main stages, namely data enhancement and iterations. Firstly, some "pseudo data" are generated by a forward prediction network that can efficiently predict the circular dichroism (CD) response of 2D diffractive chiral metamaterials to reinforce the dataset after necessary denoising. Then, the algorithm uses the CD spectra and the predictions of parameters with smaller errors iteratively to achieve accurate values of the remaining parameters. Meanwhile, according to the impact of geometric parameters on the chiroptical response, a new functionality is added to interpret the experimental results of DEIFS algorithm from the perspective of data, improving the interpretability of the DEIFS. In this way, the DEIFS algorithm replaces the time-consuming iterative optimization process with a faster and simpler approach that achieves accurate inverse design with dataset whose amount is at least one to two orders of magnitude less than most previous deep learning methods, reducing the dependence on simulated spectra. Furthermore, the fast inverse design of multiple shaped metamaterials allows for different light manipulation, demonstrating excellent potentials in applications of optical coding and information processing. This work belongs to one of the first attempts to thoroughly characterize the flexibility, interpretability, and generalization ability of DEIFS algorithm in studying various chiroptical effects in metamaterials and accelerating the inverse design of hypersensitive photonic devices.

Metamaterial design often relies on empirical methods, limiting tunability and customization. This study introduces a data-driven approach for the inverse design of double-arrow honeycomb auxetic metamaterials, enabling tailored auxeticity. Parametric modeling defined the structure using key geometric parameters, and a numerical model under tensile conditions was validated experimentally. Correlation analysis revealed relationships between parameters and Poisson’s ratio. Forward and inverse prediction models using BPNN and GA-BPNN demonstrated high accuracy and robustness. The results highlight the effectiveness of the proposed method in achieving precise auxeticity customization, advancing the design of auxetic metamaterials.

A deep learning approach for inverse design of gradient mechanical metamaterials

Inverse band gap design of elastic metamaterials for P and SV wave control