Inverse Design of Photonic Surfaces via High throughput Femtosecond Laser Processing and Tandem Neural Networks

This work demonstrates a method to design photonic surfaces by combining femtosecond laser processing with the inverse design capabilities of tandem neural networks that directly link laser fabrication parameters to their resulting textured substrate optical properties. High throughput fabrication and characterization platforms are developed that generate a dataset comprising 35280 unique microtextured surfaces on stainless steel with corresponding measured spectral emissivities. The trained model utilizes the nonlinear one-to-many mapping between spectral emissivity and laser parameters. Consequently, it generates predominantly novel designs, which reproduce the full range of spectral emissivities (average root-mean-squared-error < 2.5%) using only a compact region of laser parameter space 25 times smaller than what is represented in the training data. Finally, the inverse design model is experimentally validated on a thermophotovoltaic emitter design application. By synergizing laser-matter interactions with neural network capabilities, the approach offers insights into accelerating the discovery of photonic surfaces, advancing energy harvesting technologies.

Active Learning-Based Guided Synthesis of Engineered Biochar for CO2 Capture

Biomass waste-derived engineered biochar for CO2 capture presents a viable route for climate change mitigation and sustainable waste management. However, optimally synthesizing them for enhanced performance is time- and labor-intensive. To address these issues, we devise an active learning strategy to guide and expedite their synthesis with improved CO2 adsorption capacities. Our framework learns from experimental data and recommends optimal synthesis parameters, aiming to maximize the narrow micropore volume of engineered biochar, which exhibits a linear correlation with its CO2 adsorption capacity. We experimentally validate the active learning predictions, and these data are iteratively leveraged for subsequent model training and revalidation, thereby establishing a closed loop. Over three active learning cycles, we synthesized 16 property-specific engineered biochar samples such that the CO2 uptake nearly doubled by the final round. We demonstrate a data-driven workflow to accelerate the development of high-performance engineered biochar with enhanced CO2 uptake and broader applications as a functional material.

First-Principles High-Throughput Inverse Design of Direct Momentum-Matching Band Alignment van der Waals Heterostructures Utilizing Two-Dimensional Indirect Semiconductors

Two-dimensional (2D) van der Waals (vdW) heterostructures have attracted widespread attention in photocatalysis. Herein, we employ a novel strategy utilizing first-principles high-throughput inverse design of 2D Z-scheme heterojunctions for photocatalysis. This approach is anchored in high-throughput screening conditions, which are fundamentally based on the characteristics of carrier mechanisms influenced significantly by Z-scheme heterojunctions. A pivotal element of our screening process is the integration of the indirect-to-direct bandgap transition with momentum-matching band alignment in k-space, guiding us to combine two 2D indirect bandgap monolayers into direct Z-scheme heterojunctions characterized by pronounced interlayer excitons. Various stacking modes introduce extra and distinct degrees of freedom that can be useful for tuning the properties of heterostructures, encompassing factors such as components, stacking patterns, and sequences. We demonstrate that various stacking modes can facilitate the indirect-to-direct bandgap transition and the emergence of interlayer excitons. These findings provide exciting opportunities for designing Z-scheme heterojunctions in photocatalysis.

Dynamic Hyperspectral Holography Enabled by Inverse-Designed Metasurfaces with Oblique Helicoidal Cholesterics

Metasurfaces are flat arrays of nanostructures that allow exquisite control of phase and amplitude of incident light. Although metasurfaces offer new active element for both fundamental science and applications, the challenge still remains to overcome their low information capacity and passive nature. Here, by integrating an inverse-designed-metasurface with oblique helicoidal cholesteric liquid crystal (ChOH ), simultaneous spatial and spectral tunable metasurfaces with a high information capacity for dynamic hyperspectral holography, are demonstrated. The inverse design facilitates a single-phase map encoding of ten independent holographic images at different wavelengths. ChOH provides precise spectral modulation with narrow bandwidth and wide tunable regime in response to programmed stimuli, thus enabling dynamic switching of the multicolor holography. The results provide simple and generalizable principles for the rational design of interactive metasurfaces that will find numerous applications, including security platform.

Fast Multichannel Inverse Design through Augmented Partial Factorization

Computer-automated design and discovery have led to high-performance nanophotonic devices with diverse functionalities. However, massively multichannel systems such as metasurfaces controlling many incident angles and photonic-circuit components coupling many waveguide modes still present a challenge. Conventional methods require Min forward simulations and Min adjoint simulations-2Min simulations in total-to compute the objective function and its gradient for a design involving the response to Min input channels. Here, we develop a formalism that uses the recently proposed augmented partial factorization method to obtain both the objective function and its gradient for a massively multichannel system in a single or a few simulations, achieving over 2 orders of magnitude speedup and reduced memory usage. We use this method to inverse design a metasurface beam splitter that separates the incident light to the target diffraction orders for all incident angles of interest, a key component of the dot projector for 3D sensing. This formalism enables efficient inverse design for a wide range of multichannel optical systems.

Multi-Dimensional Multiplexed Metasurface Holography by Inverse Design

Multi-dimensional multiplexed metasurface holography extends holographic information capacity and promises revolutionary advancements for vivid imaging, information storage, and encryption. However, achieving multifunctional metasurface holography by forward design method is still difficult because it relies heavily on Jones matrix engineering, which places high demands on physical knowledge and processing technology. To break these limitations and simplify the design process, here, an end-to-end inverse design framework is proposed. By directly linking the metasurface to the reconstructed images and employing a loss function to guide the update of metasurface, the calculation of hologram can be omitted; thus, greatly simplifying the design process. In addition, the requirements on the completeness of meta-library can also be significantly reduced, allowing multi-channel hologram to be achieved using meta-atoms with only two degrees of freedom, which is very friendly to processing. By exploiting the proposed method, metasurface hologram containing up to 12 channels of multi-wavelength, multi-plane, and multi-polarization is designed and experimentally demonstrated, which exhibits the state-of-the-art information multiplexing capacity of the metasurface composed of simple meta-atoms. This method is conducive to promoting the intelligent design of multifunctional meta-devices, and it is expected to eventually accelerate the application of meta-devices in colorful display, imaging, storage and other fields.

More Than 30 000-fold Field Enhancement of Terahertz Nanoresonators Enabled by Rapid Inverse Design

The rapid development of 6G communications using terahertz (THz) electromagnetic waves has created a demand for highly sensitive THz nanoresonators capable of detecting these waves. Among the potential candidates, THz nanogap loop arrays show promising characteristics but require significant computational resources for accurate simulation. This requirement arises because their unit cells are 10 times smaller than millimeter wavelengths, with nanogap regions that are 1 000 000 times smaller. To address this challenge, we propose a rapid inverse design method using physics-informed machine learning, employing double deep Q-learning with an analytical model of the THz nanogap loop array. In ∼39 h on a middle-level personal computer, our approach identifies the optimal structure through 200 000 iterations, achieving an experimental electric field enhancement of 32 000 at 0.2 THz, 300% stronger than prior results. Our analytical model-based approach significantly reduces the amount of computational resources required, offering a practical alternative to numerical simulation-based inverse design for THz nanodevices.

Designing Metasurfaces for Efficient Solar Energy Conversion

Metasurfaces have recently emerged as a promising technological platform, offering unprecedented control over light by structuring materials at the nanoscale using two-dimensional arrays of subwavelength nanoresonators. These metasurfaces possess exceptional optical properties, enabling a wide variety of applications in imaging, sensing, telecommunication, and energy-related fields. One significant advantage of metasurfaces lies in their ability to manipulate the optical spectrum by precisely engineering the geometry and material composition of the nanoresonators' array. Consequently, they hold tremendous potential for efficient solar light harvesting and conversion. In this Review, we delve into the current state-of-the-art in solar energy conversion devices based on metasurfaces. First, we provide an overview of the fundamental processes involved in solar energy conversion, alongside an introduction to the primary classes of metasurfaces, namely, plasmonic and dielectric metasurfaces. Subsequently, we explore the numerical tools used that guide the design of metasurfaces, focusing particularly on inverse design methods that facilitate an optimized optical response. To showcase the practical applications of metasurfaces, we present selected examples across various domains such as photovoltaics, photoelectrochemistry, photocatalysis, solar-thermal and photothermal routes, and radiative cooling. These examples highlight the ways in which metasurfaces can be leveraged to harness solar energy effectively. By tailoring the optical properties of metasurfaces, significant advancements can be expected in solar energy harvesting technologies, offering new practical solutions to support an emerging sustainable society.

Machine Learning Models for Inverse Design of the Electrochemical Oxidation Process for Water Purification

In this study, a machine learning (ML) framework is developed toward target-oriented inverse design of the electrochemical oxidation (EO) process for water purification. The XGBoost model exhibited the best performances for prediction of reaction rate (k) based on training the data set relevant to pollutant characteristics and reaction conditions, indicated by Rext2 of 0.84 and RMSEext of 0.79. Based on 315 data points collected from the literature, the current density, pollutant concentration, and gap energy (Egap) were identified to be the most impactful parameters available for the inverse design of the EO process. In particular, adding reaction conditions as model input features allowed provision of more available information and an increase in the sample size of the data set to improve the model accuracy. The feature importance analysis was performed for revealing the data pattern and feature interpretation by using Shapley additive explanations (SHAP). The ML-based inverse design for the EO process was generalized to a random case for tailoring the optimum conditions with phenol and 2,4-dichlorophenol (2,4-DCP) serving as model pollutants. The resulting predicted k values were close to the experimental k values by experimental verification, accounting for the relative error lower than 5%. This study provides a paradigm shift from conventional trial-and-error mode to data-driven mode for advancing research and development of the EO process by a time-saving, labor-effective, and environmentally friendly target-oriented strategy, which makes electrochemical water purification more efficient, more economic, and more sustainable in the context of global carbon peaking and carbon neutrality.

Application of Inverse Design Approaches to the Discovery of Nonlinear Optical Switches

Molecular switches, in which a stimulus induces a large and reversible change in molecular properties, are of significant interest in the domain of photonics. Due to their commutable redox states with distinct nonlinear optical (NLO) properties, hexaphyrins have emerged as a novel platform for multistate switches in nanoelectronics. In this study, we employ an inverse design algorithm to find functionalized 26R→28R redox switches with maximal βHRS contrast. We focus on the role of core modifications, since a synergistic effect with meso-substitutions was recently found for the 30R-based switch. In contrast to these findings, the inverse design optima and subsequent database analysis of 26R-based switches confirm that core modifications are generally not favored when high NLO contrasts are targeted. Moreover, while push-pull combinations enhance the NLO contrast for both redox switches, they prefer a different arrangement in terms of electron-donating and electron-withdrawing functional groups. Finally, we aim at designing a three-state 26R→28R→ 30R switch with a similar NLO response for both ON states. Even though our best-performing three-state switch follows the design rules of the 30R-based component, our chemical compound space plots show that well-performing three-state switches can be found in regions shared by high-responsive 26R and 30R structures.

A 4D-Printing Inverse Design Strategy for Micromachines with Customized Shape-Morphing

An active heterostructure with smart-response material used as "muscle" and inactive material as "skeleton" can deform over time to respond to external stimuli. 4D printing integrated with two-photon polymerization technology and smart material allows the material or characteristic distribution of active heterostructures to be defined directly at the microscale, providing a huge programmable space. However, the high degree of design freedom and the microscale pose a challenge to the construction of micromachines with customized shape morphing. Here, a reverse design strategy based on multi-material stepwise 4D printing is proposed to guide the structural design of biomimetic micromachines. Inspired by the piecewise constant curvature model of soft robot, a reverse design algorithm based on the Timoshenko model is developed. The algorithm can approximate 2D features to a constant-curvature model and determine an acceptable material distribution within the explored printing range. Three Chinese "Long" (Chinese dragon heralds of good fortune) designed by the strategy can deform to the customized shape. In addition, a microcrawler printed using this method can imitate a real inchworm gait. These results demonstrate that this method can be an efficient tool for the action or shape design of bionic soft microrobots or micromachines with predetermined functions.

An Inverse-Designed Nanophotonic Interface for Excitons in Atomically Thin Materials

Efficient nanophotonic devices are essential for applications in quantum networking, optical information processing, sensing, and nonlinear optics. Extensive research efforts have focused on integrating two-dimensional (2D) materials into photonic structures, but this integration is often limited by size and material quality. Here, we use hexagonal boron nitride (hBN), a benchmark choice for encapsulating atomically thin materials, as a waveguiding layer while simultaneously improving the optical quality of the embedded films. When combined with a photonic inverse design, it becomes a complete nanophotonic platform to interface with optically active 2D materials. Grating couplers and low-loss waveguides provide optical interfacing and routing, tunable cavities provide a large exciton-photon coupling to transition metal dichalcogenide (TMD) monolayers through Purcell enhancement, and metasurfaces enable the efficient detection of TMD dark excitons. This work paves the way for advanced 2D-material nanophotonic structures for classical and quantum nonlinear optics.

Ultra-Compact and Broadband Nano-Integration Optical Phased Array

The on-chip nano-integration of large-scale optical phased arrays (OPAs) is a development trend. However, the current scale of integrated OPAs is not large because of the limitations imposed by the lateral dimensions of beam-splitting structures. Here, we propose an ultra-compact and broadband OPA beam-splitting scheme with a nano-inverse design. We employed a staged design to obtain a T-branch with a wavelength bandwidth of 500 nm (1300-1800 nm) and an insertion loss of -0.2 dB. Owing to the high scalability and width-preserving characteristics, the cascaded T-branch configuration can significantly reduce the lateral dimensions of an OPA, offering a potential solution for the on-chip integration of a large-scale OPA. Based on three-dimensional finite-difference time-domain (3D FDTD) simulations, we demonstrated a 1 × 16 OPA beam-splitter structure composed entirely of inverse-designed elements with a lateral dimension of only 27.3 μm. Additionally, based on the constructed grating couplers, we simulated the range of the diffraction angle θ for the OPA, which varied by 0.6°-41.6° within the wavelength range of 1370-1600 nm.

Inverse design of anisotropic bone scaffold based on machine learning and regenerative genetic algorithm

Introduction: Triply periodic minimal surface (TPMS) is widely used in the design of bone scaffolds due to its structural advantages. However, the current approach to designing bone scaffolds using TPMS structures is limited to a forward process from microstructure to mechanical properties. Developing an inverse bone scaffold design method based on the mechanical properties of bone structures is crucial. Methods: Using the machine learning and genetic algorithm, a new inverse design model was proposed in this research. The anisotropy of bone was matched by changing the number of cells in different directions. The finite element (FE) method was used to calculate the TPMS configuration and generate a back propagation neural network (BPNN) data set. Neural networks were used to establish the relationship between microstructural parameters and the elastic matrix of bone. This relationship was then used with regenerative genetic algorithm (RGA) in inverse design. Results: The accuracy of the BPNN-RGA model was confirmed by comparing the elasticity matrix of the inverse-designed structure with that of the actual bone. The results indicated that the average error was below 3.00% for three mechanical performance parameters as design targets, and approximately 5.00% for six design targets. Discussion: The present study demonstrated the potential of combining machine learning with traditional optimization method to inversely design anisotropic TPMS bone scaffolds with target mechanical properties. The BPNN-RGA model achieves higher design efficiency, compared to traditional optimization methods. The entire design process is easily controlled.

Inverse-Folding Design of Yeast Telomerase RNA Increases Activity In Vitro

Saccharomyces cerevisiae telomerase RNA, TLC1, is an 1157 nt non-coding RNA that functions as both a template for DNA synthesis and a flexible scaffold for telomerase RNP holoenzyme protein subunits. The tractable budding yeast system has provided landmark discoveries about telomere biology in vivo, but yeast telomerase research has been hampered by the fact that the large TLC1 RNA subunit does not support robust telomerase activity in vitro. In contrast, 155-500 nt miniaturized TLC1 alleles comprising the catalytic core domain and lacking the RNA's long arms do reconstitute robust activity. We hypothesized that full-length TLC1 is prone to misfolding in vitro. To create a full-length yeast telomerase RNA, predicted to fold into its biologically relevant structure, we took an inverse RNA-folding approach, changing 59 nucleotides predicted to increase the energetic favorability of folding into the modeled native structure based on the p-num feature of Mfold software. The sequence changes lowered the predicted ∆G of this "determined-arm" allele, DA-TLC1, by 61 kcal/mol (-19%) compared to wild-type. We tested DA-TLC1 for reconstituted activity and found it to be ~5-fold more robust than wild-type TLC1, suggesting that the inverse-folding design indeed improved folding in vitro into a catalytically active conformation. We also tested if DA-TLC1 functions in vivo, discovering that it complements a tlc1∆ strain, allowing cells to avoid senescence and maintain telomeres of nearly wild-type length. However, all inverse-designed RNAs that we tested had reduced abundance in vivo. In particular, inverse-designing nearly all of the Ku arm caused a profound reduction in telomerase RNA abundance in the cell and very short telomeres. Overall, these results show that the inverse design of S. cerevisiae telomerase RNA increases activity in vitro, while reducing abundance in vivo. This study provides a biochemically and biologically tested approach to inverse-design RNAs using Mfold that could be useful for controlling RNA structure in basic research and biomedicine.

Improved Optimization of a Coextrusion Die with a Complex Geometry Using the Coupling Inverse Design Method

The main challenge in a polymer coextrusion process is to have a good die design prior to the process, which can minimize the geometric errors that are caused by extrusion swell and interface motion. For this purpose, a coupling method of optimization and inverse design for a coextrusion die was studied for a medical striped catheter. In the study, the main material was thermoplastic polyurethane (TPU), and the auxiliary material was TPU filled with 30 wt% barium sulfate. An overall optimization design method was used to optimize the geometry of the extrusion die channel for the striped catheter, which had a complex geometry. In the global optimization process, the local inverse design method was used to design the inlet of the auxiliary material. The non-linear programming by quadratic Lagrangian (NLPQL) algorithm was used to obtain the optimal geometric solution of the coextrusion die runner. The experimental verification results showed that the coupling method for coextrusion die design improved the design efficiency of the coextrusion die remarkably. The value of the objective function, which was used to measure the geometric error of the product, was reduced by 72.3% compared with the initial die design.

Learning to learn by using nonequilibrium training protocols for adaptable materials

Evolution in time-varying environments naturally leads to adaptable biological systems that can easily switch functionalities. Advances in the synthesis of environmentally responsive materials therefore open up the possibility of creating a wide range of synthetic materials which can also be trained for adaptability. We consider high-dimensional inverse problems for materials where any particular functionality can be realized by numerous equivalent choices of design parameters. By periodically switching targets in a given design algorithm, we can teach a material to perform incompatible functionalities with minimal changes in design parameters. We exhibit this learning strategy for adaptability in two simulated settings: elastic networks that are designed to switch deformation modes with minimal bond changes and heteropolymers whose folding pathway selections are controlled by a minimal set of monomer affinities. The resulting designs can reveal physical principles, such as nucleation-controlled folding, that enable such adaptability.

Template Design for Complex Block Copolymer Patterns Using a Machine Learning Method

This study represents the first attempt to address the inverse design problem of the guiding template for directed self-assembly (DSA) patterns using solely machine learning methods. By formulating the problem as a multi-label classification task, the study shows that it is possible to predict templates without requiring any forward simulations. A series of neural network (NN) models, ranging from the basic two-layer convolutional neural network (CNN) to the large NN models (32-layer CNN with 8 residual blocks), have been trained using simulated pattern samples generated by thousands of self-consistent field theory (SCFT) calculations; a number of augmentation techniques, especially suitable for predicting morphologies, have been also proposed to enhance the performance of the NN model. The exact match accuracy of the model in predicting the template of simulated patterns was significantly improved from 59.8% for the baseline model to 97.1% for the best model of this study. The best model also demonstrates an excellent generalization ability in predicting the template for human-designed DSA patterns, while the simplest baseline model is ineffective in this task.

Deep Generative Model for Inverse Design of High-Temperature Superconductor Compositions with Predicted Tc > 77 K

Identifying new superconductors with high transition temperatures (T_c > 77 K) is a major goal in modern condensed matter physics. The inverse design of high T_c superconductors relies heavily on an effective representation of the superconductor hyperspace due to the underlying complexity involving many-body physics, doping chemistry and materials, and defect structures. In this study, we propose a deep generative model that combines two widely used machine learning algorithms, namely, the variational auto-encoder (VAE) and the generative adversarial network (GAN), to systematically generate unknown superconductors under the given high T_c condition. After training, we successfully identified the distribution of the representative hyperspace of superconductors with different T_c, in which many superconductor constituent elements were found adjacent to each other with their neighbors in the periodic table. Equipped with the conditional distribution of T_c, our deep generative model predicted hundreds of superconductors with T_c > 77 K, as predicted by the published T_c prediction models in the literature. For the copper-based superconductors, our results reproduced the variation in Tc as a function of the Cu concentration and predicted an optimal T_c = 129.4 K, when the Cu concentration reached 2.41 in Hg_0.37Ba_1.73Ca_1.18Cu_2.41O_6.93Tl_0.69. We expect that such an inverse design model and comprehensive list of potential high Tc superconductors would greatly facilitate future research activities in superconductors.

Inverse Design of Plasmonic Nanoantenna Using Generative Adversarial Network

The local surface plasmon resonance (LSPR) effect has been widely used in various nanophotonic applications. However, because the LSPR effect is highly sensitive to the structure and geometry, it is desirable to efficiently search viable geometries for predefined local field enhancement spectrum. Herein we present a generative adversarial network-based LSPR nanoantenna design scheme. By encoding the antenna structure information into an RGB colour image, the corresponding nanoantenna structure can be inverse-designed to achieve the required enhancement spectrum of the local field. The proposed scheme can accurately offer the multiple geometry layout for the customized specific spectrum in seconds, which could be beneficial for fast design and fabrication of plasmonic nanoantenna.

Environmentally Sustainable and Multifunctional Chrome-like Coatings Having No Chromium Designed with Reinforcement Learning

Decorative chrome plating (DCP) continues to be ubiquitous in creating highly appealing metal finishings and coatings, beating out other organic dye-based finishes. However, the hazardous chrome plating process is fraught with adverse health effects for the workers involved and causes significant environmental damage. In this work, we present a multilayer thin film structure to mimic the chrome appearance. To find a design efficiently, we employ a reinforcement learning (RL) algorithm to perform an automatic inverse design. This results in structures composed of environmentally friendly materials that not only have the chrome color but can also achieve additional functions beyond decoration. As an example, one structure is designed to have high transmission in the radio frequency regime, a property that general metals cannot have, which can broaden the decorative chrome applications to include microwave operating devices. The experimental structures are fabricated by physical vapor deposition to demonstrate the indistinguishable chrome color and validate the effectiveness of the RL inverse design approach.

Coupled Tamm Phonon and Plasmon Polaritons for Designer Planar Multiresonance Absorbers

Wavelength-selective absorbers (WS-absorbers) are of interest for various applications, including chemical sensing and light sources. Lithography-free fabrication of WS-absorbers can be realized via Tamm plasmon polaritons (TPPs) supported by distributed Bragg reflectors (DBRs) on plasmonic materials. While multifrequency and nearly arbitrary spectra can be realized with TPPs via inverse design algorithms, demanding and thick DBRs are required for high quality-factors (Q-factors) and/or multiband TPP-absorbers, increasing the cost and reducing fabrication error tolerance. Here, high Q-factor multiband absorption with limited DBR layers (3 layers) is experimentally demonstrated by Tamm hybrid polaritons (THPs) formed by coupling TPPs and Tamm phonon polaritons when modal frequencies are overlapped. Compared to the TPP component, the Q-factors of THPs are improved twofold, and the angular broadening is also reduced twofold, facilitating applications where narrow-band and nondispersive WS-absorbers are needed. Moreover, an open-source algorithm is developed to inversely design THP-absorbers consisting of anisotropic media and exemplify that the modal frequencies can be assigned to desirable positions. Furthermore, it is demonstrated that inversely designed THP-absorbers can realize same spectral resonances with fewer DBR layers than a TPP-absorber, thus reducing the fabrication complexity and enabling more cost-effective, lithography-free, wafer-scale WS-absorberss for applications such as free-space communications and gas sensing.

Sb2S3-Based Dynamically Tuned Color Filter Array via Genetic Algorithm

Color displays have become increasingly attractive, with dielectric optical nanoantennas demonstrating especially promising applications due to the high refractive index of the material, enabling devices to support geometry-dependent Mie resonance in the visible band. Although many structural color designs based on dielectric nanoantennas employ the method of artificial positive adjustment, the design cycle is too lengthy and the approach is non-intelligent. The commonly used phase change material Ge₂Sb₂Te₅ (GST) is characterized by high absorption and a small contrast to the real part of the refractive index in the visible light band, thereby restricting its application in this range. The Sb₂S₃ phase change material is endowed with a wide band gap of 1.7 to 2 eV, demonstrating two orders of magnitude lower propagation loss compared to GST, when integrated onto a silicon waveguide, and exhibiting a maximum refractive index contrast close to 1 at 614 nm. Thus, Sb₂S₃ is a more suitable phase change material than GST for tuning visible light. In this paper, genetic algorithms and finite-difference time-domain (FDTD) solutions are combined and introduced as Sb₂S₃ phase change material to design nanoantennas. Structural color is generated in the reflection mode through the Mie resonance inside the structure, and the properties of Sb₂S₃ in different phase states are utilized to achieve tunability. Compared to traditional methods, genetic algorithms are superior-optimization algorithms that require low computational effort and a high population performance. Furthermore, Sb₂S₃ material can be laser-induced to switch the transitions of the crystallized and amorphous states, achieving reversible color. The large chromatic aberration ∆E modulation of 64.8, 28.1, and 44.1 was, respectively, achieved by the Sb₂S₃ phase transition in this paper. Moreover, based on the sensitivity of the structure to the incident angle, it can also be used in fields such as angle-sensitive detectors.

Augmented Harris Hawks Optimizer with Gradient-Based-Like Optimization: Inverse Design of All-Dielectric Meta-Gratings

In this paper, we introduce a new hybrid optimization method for the inverse design of metasurfaces, which combines the original Harris hawks optimizer (HHO) with a gradient-based optimization method. The HHO is a population-based algorithm that mimics the hunting process of hawks tracking prey. The hunting strategy is divided into two phases: exploration and exploitation. However, the original HHO algorithm performs poorly in the exploitation phase and may get trapped and stagnate in a basin of local optima. To improve the algorithm, we propose pre-selecting better initial candidates obtained from a gradient-based-like (GBL) optimization method. The main drawback of the GBL optimization method is its strong dependence on initial conditions. However, like any gradient-based method, GBL has the advantage of broadly and efficiently spanning the design space at the cost of computation time. By leveraging the strengths of both methods, namely GBL optimization and HHO, we show that the proposed hybrid approach, denoted as GBL-HHO, is an optimal scenario for efficiently targeting a class of unseen good global optimal solutions. We apply the proposed method to design all-dielectric meta-gratings that deflect incident waves into a given transmission angle. The numerical results demonstrate that our scenario outperforms the original HHO.

New Halide-Based Sodium-Ion Conductors Na3Y2Cl9 Inversely Designed by Building Block Construction

Due to the excellent ionic conductivity and compatibility with high-voltage cathodes, halide-based superionic conductors as promising electrolytes have received widespread attention. A series of halide-based conductors, including Na₃YCl₆, are investigated aiming to find new solid electrolytes for sodium-ion batteries. However, Na₃YCl₆ with high ionic conductivity is meta-stable in thermostability while the stable phase exhibits poor ionic transport properties. In this work, we find that the coplanar formed anionic group (Y₂Cl₉)^3- is the result of a combination of the structural features of the fast ion phase and stable phase of Na₃YCl₆ by systematic analysis of crystal structures. Aiming to find fast sodium-ion conductors, the three-step structure construction method using functional (Y₂Cl₉)^3- groups as building blocks is proposed, and three new crystal structures in the composition of Na₃Y₂Cl₉ with the space group of P6₃, Cc, and R32 are obtained. Na⁺ transport properties, thermostability, and electrochemical window of these structures with various symmetries are investigated by first-principles calculation methods. The results show that the principle to inverse design crystal structures of halides by basic blocks, e.g., anion groups and mobile cations, is proven to be effective and successful. For P6₃-Na₃Y₂Cl₉ with outstanding transport properties, the simulation results indicate that its superionic behavior is attributed to the coherent diffusion connecting two directions. The synchronization of the migration pathways along the ab plane and the migration pathways along the c direction promotes the Na ion conductivity in Na₃Y₂Cl₉. Our research will promote the understanding of the transport mechanism in halide-based electrolytes, and the structure construction method based on functional basic building blocks and special stacking modes will accelerate the inverse design of inorganic crystal structures.

Inverse Design of Whispering-Gallery Nanolasers with Tailored Beam Shape and Polarization

Control over the shape and polarization of the beam emitted by a laser source is important in applications such as optical communications, optical manipulation and high-resolution optical imaging. In this paper, we present the inverse design of monolithic whispering-gallery nanolasers which emit along their axial direction with a tailored laser beam shape and polarization. We design and experimentally verify three types of submicron cavities, each one emitting into a different laser radiation mode: an azimuthally polarized doughnut beam, a radially polarized doughnut beam and a linearly polarized Gaussian-like beam. The measured output laser beams yield a field overlap with respect to the target mode of 92%, 96%, and 85% for the azimuthal, radial, and linearly polarized cases, respectively, thereby demonstrating the generality of the method in the design of ultracompact lasers with tailored beams.

Multicolor and 3D Holography Generated by Inverse-Designed Single-Cell Metasurfaces

Metasurface-generated holography has emerged as a promising route for fully reproducing vivid scenes by manipulating the optical properties of light using ultra-compact devices. However, achieving multiple holographic images using a single metasurface is still difficult due to the capacity limit of a single meta-atom. In this work, an inverse design method based on gradient-descent optimization is presented to encode multiple pieces of holographic information into a single metasurface. The proposed method allows the inverse design of single-cell metasurfaces without the need for complex meta-atom design strategies, facilitating high-throughput fabrication using broadband low-loss materials. By exploiting the proposed design method, both multiplane red-green-blue (RGB) color and three-dimensional (3D) holograms are designed and experimentally demonstrated. Multiplane RGB color holograms with nine distinct holograms are achieved, which demonstrate the state-of-the-art data capacity of a phase-only metasurface. The first experimental demonstration of metasurface-generated 3D holograms with completely independent and distinct images in each plane is also presented. The current research findings provide a viable route for practical metasurface-generated holography by demonstrating the high-density holography produced by a single metasurface. It is expected to ultimately lead to optical storage, display, and full-color imaging applications.

Chiral Metasurface for Near-Field Imaging and Far-Field Holography Based on Deep Learning

Chiral metasurfaces have great influence on the development of holography. Nonetheless, it is still challenging to design chiral metasurface structures on demand. As a machine learning method, deep learning has been applied to design metasurface in recent years. This work uses a deep neural network with a mean absolute error (MAE) of 0.03 to inverse design chiral metasurface. With the help of this approach, a chiral metasurface with circular dichroism (CD) values higher than 0.4 is designed. The static chirality of the metasurface and the hologram with an image distance of 3000 μm are characterized. The imaging results are clearly visible and demonstrate the feasibility of our inverse design approach.

Programming 3D Curves with Discretely Constrained Cylindrical Inflatables

Programming inflatable systems to deform to desired 3D shapes opens up multifarious applications in robotics, morphing architecture, and interventional medicine. This work elicits complex deformations by attaching discrete strain limiters to cylindrical hyperelastic inflatables. Using this system, a method is presented to solve the inverse problem of programming myriad 3D centerline curves upon inflation. The method entails two steps: first, a reduced-order model generates a conceptual solution giving coarse indications of strain limiter placement on the undeformed cylindrical inflatable. This low-fidelity solution then seeds a finite element simulation nested within an optimization loop to further tune strain limiter parameters. We leverage this framework to achieve functionality through a priori programmed deformations of cylindrical inflatables, including 3D curve matching, self-tying knotting, and manipulation. The results hold broad significance for the emerging computational design of inflatable systems.

Designing the Self-Assembly of Arbitrary Shapes Using Minimal Complexity Building Blocks

The design space for self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. We develop a pipeline to explore the design spaces for a set of structures of various sizes and complexities. To understand the implications of the different solutions, we analyze their assembly dynamics using patchy particle simulations and study the influence of the number of distinct building blocks, and the angular and spatial tolerances on their interactions, on the kinetics and yield of the target assembly. We show that the resource-saving solution with a minimum number of distinct blocks can often assemble just as well (or faster) than designs where each building block is unique. We further use our methods to design multifarious structures, where building blocks are shared between different target structures. Finally, we use coarse-grained DNA simulations to investigate the realization of multicomponent shapes using DNA nanostructures as building blocks.

Quasi-Freeform Metasurfaces for Wide-Angle Beam Deflecting and Splitting

Metasurfaces attracted extensive interests due to their outstanding ability to manipulate the wavefront at a subwavelength scale. In this study, we demonstrated quasi-freeform metasurfaces in which the radius, location, and height of the nanocylinder building blocks were set as optimized structure parameters, providing more degrees of freedom compared with traditional gradient metasurfaces. Given a desired wavefront shaping objective, these structure parameters can be collectively optimized utilizing a hybrid optimized algorithm. To demonstrate the versatility and feasibility of our method, we firstly proposed metasurfaces with deflecting efficiencies ranging from 86.2% to 94.8%, where the deflecting angles can vary in the range of 29°-75.6°. With further study, we applied our concept to realize a variety of high-efficiency, wide-angle, equal-power beam splitters. The total splitting efficiencies of all the proposed beam splitters exceeded 89.4%, where a highest efficiency of 97.6%, a maximum splitting angle of 75.6°, and a splitting uniformity of 0.33% were obtained. Considering that various deflecting angles, and various splitting channels with different splitting angles, can be realized by setting the optical response of metasurfaces as the optimization target, we believe that our method will provide an alternative approach for metasurfaces to realize desired wavefront shaping.

Inverse Design of Nanophotonic Devices Using Generative Adversarial Networks with the Sim-NN Model and Self-Attention Mechanism

The inverse design method based on a generative adversarial network (GAN) combined with a simulation neural network (sim-NN) and the self-attention mechanism is proposed in order to improve the efficiency of GAN for designing nanophotonic devices. The sim-NN can guide the model to produce more accurate device designs via the spectrum comparison, whereas the self-attention mechanism can help to extract detailed features of the spectrum by exploring their global interconnections. The nanopatterned power splitter with a 2 μm × 2 μm interference region is designed as an example to obtain the average high transmission (>94%) and low back-reflection (<0.5%) over the broad wavelength range of 1200~1650 nm. As compared to other models, this method can produce larger proportions of high figure-of-merit devices with various desired power-splitting ratios.

Neural-Network-Enabled Design of a Chiral Plasmonic Nanodimer for Target-Specific Chirality Sensing

Quantitative analysis of chiral molecules in various solvents is essential. However, there are still many challenges to enhancing the sensitivity in precisely determining both concentration and chirality. Here, we built an algorithmic methodology to predict and optimally design the chiroptical response of chiral plasmonic sensors for a specific target chiral analyte with the aid of deep learning. Based upon the analytic and intuitive understanding of the Born-Kuhn type plasmonic nanodimer, we designed and trained the neural networks that can successfully predict the chiroptical properties and further inversely design the plasmonic structure to achieve the intended circular dichroism. The developed algorithm could identify the optimum structure exhibiting the maximum sensitivity for the given specific analytes. Surprisingly, we discovered that sensitivity strongly depends on the various conditions of analytes and can be finely tuned with the structural parameters of plasmonic nanodimers. We envision that this study can provide a general platform to develop ultrasensitive chiral plasmonic sensors whose structure and sensitivity have been evolved algorithmically for adoption in specific applications.

Inverse Design of Micro Phononic Beams Incorporating Size Effects via Tandem Neural Network

Phononic crystals of the smaller scale show a promising future in the field of vibration and sound reduction owing to their capability of accurate manipulation of elastic waves arising from size-dependent band gaps. However, manipulating band gaps is still a major challenge for existing design approaches. In order to obtain the microcomposites with desired band gaps, a data drive approach is proposed in this study. A tandem neural network is trained to establish the mapping relation between the flexural wave band gaps and the microphononic beams. The dynamic characteristics of wave motion are described using the modified coupled stress theory, and the transfer matrix method is employed to obtain the band gaps within the size effects. The results show that the proposed network enables feasible generated micro phononic beams and works better than the neural network that outputs design parameters without the help of the forward path. Moreover, even size effects are diminished with increasing unit cell length, the trained model can still generate phononic beams with anticipated band gaps. The present work can definitely pave the way to pursue new breakthroughs in micro phononic crystals and metamaterials research.

Inverse Design of Energy-Absorbing Metamaterials by Topology Optimization

Compared with the forward design method through the control of geometric parameters and material types, the inverse design method based on the target stress-strain curve is helpful for the discovery of new structures. This study proposes an optimization strategy for mechanical metamaterials based on a genetic algorithm and establishes a topology optimization method for energy-absorbing structures with the desired stress-strain curves. A series of structural mutation algorithms and design-domain-independent mesh generation method are developed to improve the efficiency of finite element analysis and optimization iteration. The algorithm realizes the design of ideal energy-absorbing structures, which are verified by additive manufacturing and experimental characterization. The error between the stress-strain curve of the designed structure and the target curve is less than 5%, and the densification strain reaches 0.6. Furthermore, special attention is paid to passive pedestrian protection and occupant protection, and a reasonable solution is given through the design of a multiplatform energy-absorbing structure. The proposed topology optimization framework provides a new solution path for the elastic-plastic large deformation problem that is unable to be resolved by using classical gradient algorithms or genetic algorithms, and simplifies the design process of energy-absorbing mechanical metamaterials.

An Integrated Optical Circuit Architecture for Inverse-Designed Silicon Photonic Components

In this work, we demonstrate a compact toolkit of inverse-designed, topologically optimized silicon photonic devices that are arranged in a "plug-and-play" fashion to realize many different photonic integrated circuits, both passive and active, each with a small footprint. The silicon-on-insulator 1550-nm toolkit contains a 2 × 2 3-dB splitter/combiner, a 2 × 2 waveguide crossover, and a 2 × 2 all-forward add-drop resonator. The resonator can become a 2 × 2 electro-optical crossbar switch by means of the thermo-optical effect, phase-change cladding, or free-carrier injection. For each of the ten circuits demonstrated in this work, the toolkit of photonic devices enables the compact circuit to achieve low insertion loss and low crosstalk. By adopting the sophisticated inverse-design approach, the design structure, shape, and sizing of each individual device can be made more flexible to better suit the architecture of the greater circuit. For a compact architecture, we present a unified, parallel waveguide circuit framework into which the devices are designed to fit seamlessly, thus enabling low-complexity circuit design.

Deep-learning-based inverse design of three-dimensional architected cellular materials with the target porosity and stiffness using voxelized Voronoi lattices

Architected cellular materials are a class of artificial materials with cellular architecture-dependent properties. Typically, designing cellular architectures paves the way to generate architected cellular materials with specific properties. However, most previous studies have primarily focused on a forward design strategy, wherein a geometry is generated using computer-aided design modeling, and its properties are investigated experimentally or via simulations. In this study, we developed an inverse design framework for a disordered architected cellular material (Voronoi lattices) using deep learning. This inverse design framework is a three-dimensional conditional generative adversarial network (3D-CGAN) trained based on supervised learning using a dataset consisting of voxelized Voronoi lattices and their corresponding relative densities and Young's moduli. A well-trained 3D-CGAN adopts variational sampling to generate multiple distinct Voronoi lattices with the target relative density and Young's modulus. Consequently, the mechanical properties of the 3D-CGAN generated Voronoi lattices are validated through uniaxial compression tests and finite element simulations. The inverse design framework demonstrates potential for use in bone implants, where scaffold implants can be automatically generated with the target relative density and Young's modulus.

Multi-Directional Cloak Design by All-Dielectric Unit-Cell Optimized Structure

In this manuscript, we demonstrate the design and experimental proof of an optical cloaking structure that multi-directionally conceals a perfectly electric conductor (PEC) object from an incident plane wave. The dielectric modulation around the highly reflective scattering PEC object is determined by an optimization process for multi-directional cloaking purposes. Additionally, to obtain the multi-directional effect of the cloaking structure, an optimized slice is mirror symmetrized through a radial perimeter. The three-dimensional (3D) finite-difference time-domain method is integrated with genetic optimization to achieve a cloaking design. In order to overcome the technological problems of the corresponding devices in the optical range and to experimentally demonstrate the proposed concept, our experiments were carried out on a scale model in the microwave range. The scaled proof-of-concept of the proposed structure is fabricated by 3D printing of polylactide material, and the brass metallic alloy is used as a perfect electrical conductor for microwave experiments. A good agreement between numerical and experimental results is achieved. The proposed design approach is not restricted only to multi-directional optical cloaking but can also be applied to different cloaking scenarios dealing with electromagnetic waves at nanoscales as well as other types such as acoustic waves. Using nanotechnology, our scale proof-of-concept research will take the next step toward the creation of "optical cloaking" devices.

Fast Topology Optimization for Near-Field Focusing All-Dielectric Metasurfaces Using the Discrete Dipole Approximation

Using an efficient implementation of the discrete dipole approximation and topology optimization, we design all-dielectric metasurfaces capable of focusing light into intense deep subwavelength hotspots. The light focusing of these metasurfaces far outweighs conventional lenses and can provide dramatic enhancements of processes that depend superlinearly on light intensity, such as light-powered membrane distillation and photocatalysis. Our approach can easily be generalized to optimize metasurfaces for other functionalities, such as nonlinear optics or photothermal conversion.

Deep-Learning-Empowered Holographic Metasurface with Simultaneously Customized Phase and Amplitude

Metasurfaces with simultaneously and independently controllable amplitude and phase have provided a higher degree of freedom in manipulating electromagnetic (EM) waves. Compared with phase- or amplitude-only modulation, the capability of simultaneously controlling the phase and amplitude of EM waves can enable holography with a higher resolution. However, this drastically increases the design complexity of holographic metasurfaces, and the design process is usually quite time-consuming. In this paper, we propose an inverse design of meta-atoms that can simultaneously and independently tailor the phase and amplitude of transmitted waves using customized deep ResNet while eliminating the coupling of parameters. To demonstrate the design method, two holographic metasurfaces were designed using the trained network without the need for parameter sweeping, which will significantly enhance design efficiency. Prototypes were fabricated and measured. Both the simulated and measured results show that high-resolution holography is obtained, which sufficiently verifies the reliability of the design method. Our work paves the way for the intelligent design of metasurfaces and can also be applied to the design of other artificial materials or surfaces.

Inverse-Designed Metaphotonics for Hypersensitive Detection

Controlling the flow of broadband electromagnetic energy at the nanoscale remains a critical challenge in optoelectronics. Surface plasmon polaritons (or plasmons) provide subwavelength localization of light but are affected by significant losses. On the contrary, dielectrics lack a sufficiently robust response in the visible to trap photons similar to metallic structures. Overcoming these limitations appears elusive. Here we demonstrate that addressing this problem is possible if we employ a novel approach based on suitably deformed reflective metaphotonic structures. The complex geometrical shape engineered in these reflectors emulates nondispersive index responses, which can be inverse-designed following arbitrary form factors. We discuss the realization of essential components such as resonators with an ultrahigh refractive index of n = 100 in diverse profiles. These structures support the localization of light in the form of bound states in the continuum (BIC), fully localized in air, in a platform in which all refractive index regions are physically accessible. We discuss our approach to sensing applications, designing a class of sensors where the analyte directly contacts areas of ultrahigh refractive index. Leveraging this feature, we report an optical sensor with sensitivity two times higher than the closest competitor with a similar micrometer footprint. Inversely designed reflective metaphotonics offers a flexible technology for controlling broadband light, supporting optoelectronics' integration with large bandwidths in circuitry with miniaturized footprints.

Recent Advances in Tunable Metasurfaces: Materials, Design, and Applications

Metasurfaces, a two-dimensional (2D) form of metamaterials constituted by planar meta-atoms, exhibit exotic abilities to tailor electromagnetic (EM) waves freely. Over the past decade, tremendous efforts have been made to develop various active materials and incorporate them into functional devices for practical applications, pushing the research of tunable metasurfaces to the forefront of nanophotonics. Those active materials include phase change materials (PCMs), semiconductors, transparent conducting oxides (TCOs), ferroelectrics, liquid crystals (LCs), atomically thin material, etc., and enable intriguing performances such as fast switching speed, large modulation depth, ultracompactness, and significant contrast of optical properties under external stimuli. Integration of such materials offers substantial tunability to the conventional passive nanophotonic platforms. Tunable metasurfaces with multifunctionalities triggered by various external stimuli bring in rich degrees of freedom in terms of material choices and device designs to dynamically manipulate and control EM waves on demand. This field has recently flourished with the burgeoning development of physics and design methodologies, particularly those assisted by the emerging machine learning (ML) algorithms. This review outlines recent advances in tunable metasurfaces in terms of the active materials and tuning mechanisms, design methodologies, and practical applications. We conclude this review paper by providing future perspectives in this vibrant and fast-growing research field.

Inverse Design of Valley-Like Edge States of Sound Degenerated Away from the High-Symmetry Points in a Square Lattice

Robust edge states of periodic crystals with Dirac points fixed at the corners or centers of the Brillouin zones have drawn extensive attention. Recently, researchers have observed a special edge state associated with Dirac cones degenerated at the high symmetric boundaries of the first irreducible Brillouin zone. These nodal points, characterized by vortex structures in the momentum space, are attributed to the unavailable band crossing protected by mirror symmetry. By breaking the time reversal symmetry with intuitive rotations, valley-like states can be observed in a pair of inequivalent insulators. In this paper, an improved direct inverse design method is first applied to realize the valley-like states. Compared with the conventional strategy, the preparation of transition structures with degeneracy points is skipped. By introducing the quantitative gauge of mode inversion error, insulator pairs are directly obtained without manually tuning the structure with Dirac cone features.

Compound Meta-Optics for Complete and Loss-Less Field Control

Optical metasurfaces offer a compact platform for manipulation of the amplitude, phase, and polarization state of light. Independent control over these properties, however, is hindered by the symmetric transmission matrix associated with single-layer metasurfaces. Here, we utilize multilayer birefringent meta-optics to realize high-efficiency, independent control over the amplitude, phase, and polarization state of light. High-efficiency control is enabled by redistributing the wavefront between cascaded metasurfaces, while end-to-end inverse design is used to realize independent complex-valued functions for orthogonal polarization states. Based on this platform, we demonstrate spatial mode division multiplexing, optical mode conversion, and universal vectorial holograms, all with diffraction efficiencies over 80%. This meta-optic platform expands the design space of flat optics and could lead to advances in optical communications, quantum entanglement, and information encryption.

Electrically Driven Reprogrammable Vanadium Dioxide Metasurface Using Binary Control for Broadband Beam Steering

Resonant optical phased arrays are a promising way to reach fully reconfigurable metasurfaces in the optical and near-infrared (NIR) regimes with low energy consumption, low footprint, and high reliability. Continuously tunable resonant structures suffer from inherent drawbacks such as low phase range, amplitude-phase correlation, or extreme sensitivity that makes precise control at the individual element level very challenging. We computationally investigate 1-bit (binary) control as a mechanism to bypass these issues. We consider a metasurface for beam steering using a nanoresonator antenna and explore the theoretical capabilities of such phased arrays. A thermally realistic structure based on vanadium dioxide sandwiched in a metal-insulator-metal structure is proposed and optimized using inverse design to enhance its performance at 1550 nm. Continuous beam steering over 90° range is successfully achieved using binary control, with excellent agreement with predictions based on the theoretical first-principles description of phased arrays. Furthermore, a broadband response from 1500 to 1700 nm is achieved. The robustness to the design manufacturing imperfections is also demonstrated. This simplified approach can be implemented to optimize tunable nanophotonic phased array metasurfaces based on other materials or phased shifting mechanisms for various functionalities.

Semi-Supervised Deep Learning Model for Efficient Computation of Optical Properties of Suspended-Core Fibers

Suspended-core fibers (SCFs) are considered the best candidates for enhancing fiber nonlinearity in mid-infrared applications. Accurate modeling and optimization of its structure is a key part of the SCF structure design process. Due to the drawbacks of traditional numerical simulation methods, such as low speed and large errors, the deep learning-based inverse design of SCFs has become mainstream. However, the advantage of deep learning models over traditional optimization methods relies heavily on large-scale a priori datasets to train the models, a common bottleneck of data-driven methods. This paper presents a comprehensive deep learning model for the efficient inverse design of SCFs. A semi-supervised learning strategy is introduced to alleviate the burden of data acquisition. Taking SCF's three key optical properties (effective mode area, nonlinear coefficient, and dispersion) as examples, we demonstrate that satisfactory computational results can be obtained based on small-scale training data. The proposed scheme can provide a new and effective platform for data-limited physical computing tasks.

Data-Enhanced Deep Greedy Optimization Algorithm for the On-Demand Inverse Design of TMDC-Cavity Heterojunctions

A data-enhanced deep greedy optimization (DEDGO) algorithm is proposed to achieve the efficient and on-demand inverse design of multiple transition metal dichalcogenides (TMDC)-photonic cavity-integrated heterojunctions operating in the strong coupling regime. Precisely, five types of photonic cavities with different geometrical parameters are employed to alter the optical properties of monolayer TMDC, aiming at discovering new and intriguing physics associated with the strong coupling effect. Notably, the traditional rigorous coupled wave analysis (RCWA) approach is utilized to generate a relatively small training dataset for the DEDGO algorithm. Importantly, one remarkable feature of DEDGO is the integration the decision theory of reinforcement learning, which remedies the deficiencies of previous research that focused more on modeling over decision making, increasing the success rate of inverse prediction. Specifically, an iterative optimization strategy, namely, deep greedy optimization, is implemented to improve the performance. In addition, a data enhancement method is also employed in DEDGO to address the dependence on a large amount of training data. The accuracy and effectiveness of the DEDGO algorithm are confirmed to be much higher than those of the random forest algorithm and deep neural network, making possible the replacement of the time-consuming conventional scanning optimization method with the DEDGO algorithm. This research thoroughly describes the universality, interpretability, and excellent performance of the DEDGO algorithm in exploring the underlying physics of TMDC-cavity heterojunctions, laying the foundations for the on-demand inverse design of low-dimensional material-based nano-devices.

Predicting Adhesive Free Energies of Polymer-Surface Interactions with Machine Learning

Polymer-surface interactions are crucial to many biological processes and industrial applications. Here we propose a machine learning method to connect a model polymer's sequence with its adhesion to decorated surfaces. We simulate the adhesive free energies of 20000 unique coarse-grained one-dimensional polymer sequences interacting with functionalized surfaces and build support vector regression models that demonstrate inexpensive and reliable prediction of the adhesive free energy as a function of sequence. Our work highlights the promising integration of coarse-grained simulation with data-driven machine learning methods for the design of functional polymers and represents an important step toward linking polymer compositions with polymer-surface interactions.

Machine learning-based inverse design for electrochemically controlled microscopic gradients of O2 and H2O2

In microbiology, extracellular oxygen (O₂) and reactive oxygen species (ROS) are spatiotemporally heterogenous, ubiquitously, at macroscopic level. Such spatiotemporal heterogeneities are critical to microorganisms, yet a well-defined method of studying such heterogenous microenvironments is lacking. This work develops a machine learning–based inverse design strategy that builds an electrochemical platform for achieving spatiotemporal control of O₂ and ROS microenvironments relevant to microbiology. The inverse design strategy not only demonstrates the power of machine learning to design concentration profiles in electrochemistry but also accelerates the development of custom microenvironments for specific microbial systems and allows researchers to better study how microenvironments affect microorganisms in myriads of environmental, biomedical, and sustainability-related applications.

A fundamental understanding of extracellular microenvironments of O₂ and reactive oxygen species (ROS) such as H₂O₂, ubiquitous in microbiology, demands high-throughput methods of mimicking, controlling, and perturbing gradients of O₂ and H₂O₂ at microscopic scale with high spatiotemporal precision. However, there is a paucity of high-throughput strategies of microenvironment design, and it remains challenging to achieve O₂ and H₂O₂ heterogeneities with microbiologically desirable spatiotemporal resolutions. Here, we report the inverse design, based on machine learning (ML), of electrochemically generated microscopic O₂ and H₂O₂ profiles relevant for microbiology. Microwire arrays with suitably designed electrochemical catalysts enable the independent control of O₂ and H₂O₂ profiles with spatial resolution of ∼10¹ μm and temporal resolution of ∼10° s. Neural networks aided by data augmentation inversely design the experimental conditions needed for targeted O₂ and H₂O₂ microenvironments while being two orders of magnitude faster than experimental explorations. Interfacing ML-based inverse design with electrochemically controlled concentration heterogeneity creates a viable fast-response platform toward better understanding the extracellular space with desirable spatiotemporal control.

Inverse-Designed Narrowband THz Radiator for Ultrarelativistic Electrons

THz radiation finds various applications in science and technology. Pump-probe experiments at free-electron lasers typically rely on THz radiation generated by optical rectification of ultrafast laser pulses in electro-optic crystals. A compact and cost-efficient alternative is offered by the Smith-Purcell effect: a charged particle beam passes a periodic structure and generates synchronous radiation. Here, we employ the technique of photonic inverse design to optimize a structure for Smith-Purcell radiation at a single wavelength from ultrarelativistic electrons. The resulting design is highly resonant and emits narrowbandly. Experiments with a 3D-printed model for a wavelength of 900 μm show coherent enhancement. The versatility of inverse design offers a simple adaption of the structure to other electron energies or radiation wavelengths. This approach could advance beam-based THz generation for a wide range of applications.