Enhanced posterior sampling via diffusion models for efficient metasurfaces inverse design

The conventional approach to nanophotonic metasurface design and optimization for a targeted electromagnetic response involves exploring large geometry and material spaces. This is a highly iterative process based on trial and error, which is computationally costly and time consuming. Moreover, the non-uniqueness of structural designs and high non-linearity between electromagnetic response and design makes this problem challenging. To model this unintuitive relationship between electromagnetic response and metasurface structural design as a probability distribution in the design space, we introduce a framework for inverse design of nanophotonic metasurfaces based on cyclical deep learning (DL). The proposed framework performs inverse design and optimization mechanism for the generation of meta-atoms and meta-molecules as metasurface units based on DL models and genetic algorithm. The framework includes consecutive DL models that emulate both numerical electromagnetic simulation and iterative processes of optimization, and generate optimized structural designs while simultaneously performing forward and inverse design tasks. A selection and evaluation of generated structural designs is performed by the genetic algorithm to construct a desired optical response and design space that mimics real world responses. Importantly, our cyclical generation framework also explores the space of new metasurface topologies. As an example application of the utility of our proposed architecture, we demonstrate the inverse design of gap-plasmon based half-wave plate metasurface for user-defined optical response. Our proposed technique can be easily generalized for designing nanophtonic metasurfaces for a wide range of targeted optical response.

Numerical simulations have revolutionized material design. However, although simulations excel at mapping an input material to its output property, their direct application to inverse design has traditionally been limited by their high computing cost and lack of differentiability. Here, taking the example of the inverse design of a porous matrix featuring targeted sorption isotherm, we introduce a computational inverse design framework that addresses these challenges, by programming differentiable simulation on TensorFlow platform that leverages automated end-to-end differentiation. Thanks to its differentiability, the simulation is used to directly train a deep generative model, which outputs an optimal porous matrix based on an arbitrary input sorption isotherm curve. Importantly, this inverse design pipeline leverages the power of tensor processing units (TPU)—an emerging family of dedicated chips, which, although they are specialized in deep learning, are flexible enough for intensive scientific simulations. This approach holds promise to accelerate inverse materials design.

With the rapid growth in intelligent metasurfaces in the recent years, deep learning has attracted attention to transform the ways in which metasurfaces are simulated and designed. The unique advantages of deep learning lie in the powerful data‐driven modality, which allows a computational model to learn useful information using hierarchically structured layers. Among the various successful examples, there are forward and inverse designs. However, such designs are inherently data‐hungry. Thus, the data utilization efficiency must be maximized, and green metasurface design must be achieved. Here, the authors propose heterogeneous transfer learning to allow transferrable and data‐efficient metasurface design. The key to this method is a flexible network framework, which integrates feature augmentation and dimensionality reduction. The concept is demonstrated through three scenarios, i.e., metasurfaces with different parameterizations, different physical sizes, and completely different geometries, where the relative error reduction reaches up to 50%. Furthermore, an inverse metasurface design is proposed, which combines the forward predicted network and heuristic algorithm. This work considerably reduces the workload on data collection and overcomes the limitation that previous works only focused on fixed physical structures. The authors have also envisioned a “global metasurface gene bank,” in which researchers can freely “withdraw and save data” for various applications.

Controlling stress and deformation induced by thermo-mechanical stimulation in high-precision mechanical systems can be achieved by mechanical metamaterials (MM) exhibiting negative thermal expansion (NTE) and negative Poisson's ratio (NPR). However, the inverse design of MM exhibiting a wide range of arbitrary target NTEs and NPRs is a challenging task due to the low design flexibility of analytical methods and parametric studies based on numerical simulation. In this study, we propose Bézier curve-based programmable chiral mechanical metamaterials (BPCMs) and a deep autoencoder-based inverse design model (DAIM) for the inverse design of BPCMs. Through iterative transfer learning with data augmentation, DAIM can generate BPCMs with a curved rib shape inaccessible with the Bézier curve, which improves the inverse design performance of the DAIM in the data sparse domain. This approach decreases the mean absolute error of NTE and NPR between the inverse design target and the numerical simulation results of inverse designed BPCMs on the data-sparse domain by 79.25% and 83.33% on average, respectively. A 3D-printed BPCM is validated experimentally and exhibits good coincidence with the target NTE and NPR. Our proposed BPCM and the corresponding inverse design framework enable the inverse design of BPCMs with NTE in the range of -1100 to 0 ppm K-1 and NPR in the range of -0.6 to -0.1. Furthermore, programmable thermal deformation modes with a fixed Poisson's ratio are realized by combining various inverse designed BPCM unit cells. BPCMs and the DAIM for their inverse design are expected to improve the mechanical robustness of high-precision mechanical systems through tunable modulation of thermo-mechanical stimulation.

This work proposes the inverse design of bandstop Frequency Selective Surface using a Graph based Conditional Variational Autoencoder (G-CVAE) integrated with a Physics-Informed Neural Network (PINN). This inverse design involves the prediction of FSS geometry that exhibits ultra-wide stopband characteristics. Initially, the graph convolutional network precisely extracts the topological and spatial relationships within the FSS geometrical design. The features of the graph and simulation results of the FSS dataset are used to train the CVAE, which maps the FSS physical structure and its electromagnetic behavior. The trained CVAE predicts the FSS geometries with desired frequency responses, while the PINN is incorporated to ensure physical feasibility. By monitoring the average relative error values, the simulated and predicted transmission coefficients are brought closer to each other. Also, similar approach is followed to enhance the angular stability and to achieve polarization independence in both TE and TM modes. A G-CVAE-PINN is constructed and trained using various random combinations of graph attributes and simulation outcomes, achieving an average inaccuracy of 3%. Further, one of the best designs from the predicted FSS designs is chosen for experimental validation. This predicted and experimentally validated bandstop FSS exhibits wide band rejection of 20 GHz ranging from 8 GHz to 28 GHz. The fabricated design exhibits polarization independence up to 75°in both normal and oblique angles. Thus, the predicted FSS designs are ideal for radome, EMI shielding, and satellite communications, providing efficient frequency filtering for 5G and beyond 5G networks.

Neural networks have emerged as an effective method for inverse design of metasurfaces. Despite significant progress in inverse design for photonic structures, the inherent complexity from high-dimensional parameter spaces and the nonlinear mapping between structural parameters and optical responses still pose major challenges for the on-demand design of complex photonic systems. In this paper, we propose a multimodal neural network framework for the inverse design of composite periodic microstructures. The proposed framework can generate design results for different modes based on the target spectrum, offering flexibility in meeting design requirements, which solves the inverse design problem efficiently, achieving speeds several orders of magnitude faster than traditional methods. Furthermore, given the critical importance of precise infrared emissivity control in stealth applications, we designed infrared stealth metasurfaces capable of radiative heat dissipation through nonatmospheric windows using the well-trained network. Subsequently, the sample was fabricated for experimental validation. The results demonstrate that, while preserving the low emissivity in the atmospheric window, the average IR emissivity of our prepared samples achieves 0.674 in the 5-8 μm nonatmospheric window. This methodology achieves radiative heat dissipation that is compatible with infrared stealth. This paper gives a novel notion for the inverse design of complicated photonic devices, which has a broad application value.

Simulating soft robots offers a cost-effective approach to exploring their design and control strategies. While current models, such as finite element analysis, are effective in capturing soft robotic dynamics, the field still requires a broadly applicable and efficient numerical simulation method. In this letter, we introduce a discrete differential geometry-based framework for the model-based inverse design of a novel snap-actuated jumping robot. Our findings reveal that the snapping beam actuator exhibits both symmetric and asymmetric dynamic modes, enabling tunable robot trajectories (e.g., horizontal or vertical jumps). Leveraging this bistable beam as a robotic actuator, we propose a physics-data hybrid inverse design strategy to endow the snap-jump robot with a diverse range of jumping capabilities. By utilizing a physical engine to examine the effects of design parameters on jump dynamics, we then use extensive simulation data to establish a data-driven inverse design solution. This approach allows rapid exploration of parameter spaces to achieve targeted jump trajectories, providing a robust foundation for the robot's fabrication. Our methodology offers a powerful framework for advancing the design and control of soft robots through integrated simulation and data-driven techniques.

A comprehensive theoretical framework for the inverse design of correlation induced effects with optical beams is introduced. Correlation induced effects are able to modify the intensity distribution of an optical beam drastically via effects such as correlation induced splitting, focusing, and shifting. The inverse design steps are given analytically, which allows the analysis of several related experiments. Finally, an algorithm for more complex numerical inverse design is overviewed and demonstrated.

We present a machine-learning framework for nano-device inverse design. Using correlated surrogate annealing, our framework generates designs orders of magnitude faster than traditional generative models, offering broad applicability to general inverse design problems.

Locally resonant elastic metamaterials (LREM) can be designed, by optimizing the geometry of the constituent self-repeating unit cells, to potentially damp out vibration in selected frequency ranges, thus yielding desired bandgaps. However, it remains challenging to quickly arrive at unit cell designs that satisfy any requested bandgap specifications within a given global frequency range. This paper develops a computationally efficient framework for (fast) inverse design of LREM, by integrating a new type of machine learning models called invertible neural networks or INN. An INN can be trained to predict the bandgap bounds as a function of the unit cell design, and interestingly at the same time it learns to predict the unit cell design given a bandgap, when executed in reverse. In our case the unit cells are represented in terms of the width's of the outer matrix and middle soft filler layer of the unit cell. Training data on the frequency response of the unit cell is provided by Bloch dispersion analyses. The trained INN is used to instantaneously retrieve feasible (or near feasible) inverse designs given a specified bandgap constraint, which is then used to initialize a forward constrained optimization (based on sequential quadratic programming) to find the bandgap satisfying unit cell with minimum mass. Case studies show favorable performance of this approach, in terms of the bandgap characteristics and minimized mass, when compared to the median scenario over ten randomly initialized optimizations for the same specified bandgaps. Further analysis using FEA verify the bandgap performance of a finite structure comprised of $8\times 8$ arrangement of the unit cells obtained with INN-accelerated inverse design.

Efficiently and precisely designed isotropic auxetic metamaterials present significant challenges due to the inherent uncertainties in their geometric configurations. This study introduces an innovative data-driven structural design strategy that enables accurate prediction of the mechanical properties and inverse design for isotropic auxetic metamaterials. Notably, Kolmogorov-Arnold networks (KANs) are utilized, replacing fixed activation functions with learnable functions, to successfully establish a precise mapping between design parameters and mechanical responses for classical missing rib auxetic metamaterials. The predicted mean square error (MSE) for the stress dataset is as low as 0.81%, only one-fourth of that achieved by multilayer perceptron (MLP) models of equivalent width, while computational efficiency surpasses finite element methods by more than 103 times. Building on this mapping, Model III, optimized using a genetic algorithm, achieves an average MSE of just 0.05%, significantly outperforming the original structure (Model I) and a randomly perturbed structure (Model II) with an average MSE of 2.28% and 1.79%, respectively. Experimental validation and finite element analysis further confirm the accuracy of these results, demonstrating the successful realization of isotropic mechanical response designs. This study presented a data-driven inverse design method as a powerful and efficient tool for the precise design of auxetic metamaterials with isotropic mechanical responses. It holds particular promise for applications in flexible wearable devices and tissue engineering, providing a robust foundation for future innovations in these fields.

Deep learning to catalyze inverse molecular design

In modern communication, radar, and electromagnetic systems, the performance of frequency-selective reflectors (FSRs) is crucial to system performance. However, traditional design methods face numerous limitations when dealing with complex structures and multi-parameter optimization, and simulation-based design approaches also suffer from high computational costs and low efficiency. This paper proposes an inverse design method for FSRs based on a convolutional neural network (CNN). The constructed deep learning inverse design framework includes a parameter constraint network and an inverse design network. The simulation results demonstrate that this method can accurately predict structural parameters. The generated frequency response curves closely match the desired curves. While ensuring high precision, this approach significantly reduces computational costs, providing a new pathway for the efficient and precise design of FSRs.

A multi-foci metalens can realize unprecedented functions (i.e., the large field of view and fully reconfigurable imaging) that are extremely challenging to achieve by conventional lenses. However, a traditional multi-foci metalens shows inhomogeneous/chaotical intensity distributions between multiple focal spots, which is a key challenge in metasurface design and limited for further applications. Herein, an inverse design method is proposed to automatically optimize the in-plane orientation (rather than the shape) of each meta-atom in terahertz multi-foci metalenses that can generate a plethora of focal spots with high-accuracy intensity distributions. The inverse design of multi-foci metalenses for generating circularly polarized and linearly polarized images (rather than holograms) with nearly homogeneous intensity distributions is proposed and experimentally demonstrated. The robust approach for simultaneously and accurately modulating the amplitude, phase, polarization, and intensity distributions of terahertz waves to generate polarization-dependent images with high-accuracy intensity of each focal spot will open an avenue in developing compact imaging, face unlock, and motion sensing.

A shift is occurring from avoiding structural geometric nonlinearities to deliberately exploiting them for new functionalities. Forward design–predicting nonlinear responses from given parameters–is well established, but the inverse problem–identifying parameters that yield a desired nonlinear behaviour–remains a major challenge due to the complexity of the response. Developing an efficient inverse design framework is therefore essential to enable broader application of nonlinear mechanical metamaterials. To address this, we introduce an enhanced conditional generative adversarial network (c-GAN) framework that synergizes three key innovations: (i) surrogate-based physics-informed supervision via a pre-trained simulator network, (ii) residual generator architecture for stable gradient flow, and (iii) structured noise encoding for enhanced diversity and controllability. This c-GAN-Physics-Stochastic architecture generates precise geometric parameters in a single forward pass, bypassing traditional iterative optimization bottlenecks. We demonstrate the framework’s effectiveness through two case studies: mechanical metamaterials designed for recoverable energy dissipation via sequential snap-through instabilities, and auxetic metamaterials maintaining a constant Poisson’s ratio under large deformations. Experimental results validate the physical realisability of the generated designs. Inference with the conditional GAN provides millisecond-level design prediction, while a hybrid c-GAN + genetic algorithm (GA) refinement strategy achieves exceptional agreement with high-fidelity evaluations (up to R 2 > 0.99 ) at increased computational cost. This work demonstrates the potential of data-driven methods, particularly c-GANs, in addressing the inverse design challenge for nonlinear mechanical metamaterials for novel functionalities. By delivering an accessible toolbox, we aim to promote its widespread use and practical implementation by engineers, paving the way for innovative applications.