Optimal Model Structure Research Articles

A mechanics-based data-free Problem Independent Machine Learning (PIML) model for large-scale structural analysis and design optimization

Machine learning (ML) enhanced fast structural analysis and design recently attracted considerable attention. In most related works, however, the generalization ability of the ML model and the massive cost of dataset generation are the two most criticized aspects. This work combines the advantages of the universality of the substructure method and the superior predictive ability of the operator learning architecture. Specifically, using a novel mechanics-based loss function, lightweight neural network mapping from the material distribution inside a substructure and the corresponding continuous multiscale shape function is well-trained without preparing a dataset. In this manner, a problem machine learning model (PIML) that is generally applicable for efficient linear elastic analysis and design optimization of large-scale structures with arbitrary size and various boundary conditions is proposed. Several examples validate the effectiveness of the present work on efficiency improvement and different kinds of optimization problems. This PIML model-based design and optimization framework can be extended to large-scale multiphysics problems.

Cost optimization in structural design for reinforced concrete frames using Jaya algorithm

This study analyzes and optimizes the structural design of three-dimensional (3D) reinforced concrete framestructures to minimize the amount of two main materials, including concrete and steel reinforcement, used inreinforced concrete frames. Jaya algorithm was developed based on evolutionary algorithms to build the structural optimization model. The objective function (minimum material cost) with variables being column andbeam cross-sections was set up. In which, the constraints related to the maximum internal force and displacement being in the structural members satisfy limited strength and serviceability requirements. A subroutine written in Python was used to connect the optimization process to the structural analysis software, ETABS. The 3D reinforced concrete frame of a three-story building was selected for cost and design optimization analysis. In which, the optimization problem was solved in cases of three different maximum numbers of iterations, including 20, 35, and 50. In each iteration level, a setting of five independent runs was performed. The subroutine proved to be fast, robust, and convenient manner for solving optimization problems in designing 3D reinforced concrete frames. In which, the best optimal cost might be obtained after twenty iterations and the better convergence behavior occurred at higher numbers of iterations. The study results showed that, for this reinforced concrete frame, applying optimal design led to a materials cost reduction (success rate) by 33.67% compared to that of the conventional design. This success rate would fluctuate according to different nations’ design codes.

Spatiotemporal modelling of airborne birch and grass pollen concentration across Switzerland: A comparison of statistical, machine learning and ensemble methods

BackgroundStatistical and machine learning models are commonly used to estimate spatial and temporal variability in exposure to environmental stressors, supporting epidemiological studies. We aimed to compare the performances, strengths and limitations of six different algorithms in the retrospective spatiotemporal modeling of daily birch and grass pollen concentrations at a spatial resolution of 1 km across Switzerland. MethodsDaily birch and grass pollen concentrations were available from 14 measurement sites in Switzerland for 2000–2019. To develop the spatiotemporal models, we considered spatiotemporal, spatial and temporal predictors including meteorological factors, land-use, elevation, species distribution and Normalized Difference Vegetation Index (NDVI). We used six statistical and machine learning algorithms: LASSO, Ridge, Elastic net, Random forest, XGBoost and ANNs. We optimized model structures through feature selection and grid search techniques to obtain the best predictive performance. We used train-test split and cross-validation to avoid overfitting and overoptimistic performance indicators. We then combined these six models through multiple linear regression to develop an ensemble hybrid model. ResultsThe 5th-95th percentiles of birch and grass pollen concentrations were 0–151 and 0–105 grains/m3, respectively. The hybrid ensemble model achieved the best RMSE on the test dataset for both birch and grass pollen with 94.4 and 19.7 grains/m3, respectively.Nonlinear models (Random forest, XGBoost and ANNs) achieved lower test RMSE's than linear models (LASSO, Ridge, Elastic net) for both pollen types, with RMSE's ranging from 105.9 to 140.5 grains/m3 for birch and from 20.0 to 25.4 grains/m3 for grass pollen. The Random forest algorithm yielded the best spatial and temporal performance among the six evaluated modelling methods. The ensemble hybrid model outperformed the six linear and nonlinear algorithms. Country-wide pollen concentration, land use, weather, and NDVI were important predictors. ConclusionNonlinear algorithms outperformed linear models and accurately explained complex, nonlinear relationships between environmental factors and measured concentrations.

Optimizing Stand Spatial Structure at Different Development Stages in Mixed Hard Broadleaf Forests

Thinning plays a key role in regulating the stand spatial structure (SpS) to improve the development of stand quality, and the stand has different characteristics of stand structure (SS) at different growth and development stages (DSs), so it is most important to reasonably determine the stage of growth and development of the stand to optimize the stand structure. We applied the TWINSPAN two-way indicator species analysis method to classify the different development stages of mixed hard broadleaf forests. We provided a comprehensive stand spatial structure optimization model for three selected plots at different development stages, respectively, to optimize the SpS. The results demonstrated the classified DS of 29 mixed hard broadleaf plots for three forest stages: the establishment stage, competitive stage, and quality selection stage. We then applied the SpS optimization model to our three plots; the Q(x) increased by 124.04%, 333.74%, and 116.83% when compared with those with no harvest, in which, upon the removal of 10% of the trees from the three plots, the maximum RIP values were all observed. Our results indicated that the SpS optimization model could regulate the SS for different growth stages and DSs.

Research on Optimization of Image Recognition Algorithm Based on Deep Learning

With the rapid development of information technology, image recognition has become increasingly crucial in numerous fields. Deep learning, as a highly potent machine learning approach, has brought about a revolutionary breakthrough in image recognition. This paper delves into the optimization of image recognition algorithms based on deep learning. Firstly, it analyzes the application status of deep learning in image recognition, covering common neural network architectures such as convolutional neural network (CNN). Then, the optimization strategy of the image recognition algorithm is elaborated from multiple aspects, including data augmentation to increase data diversity, model structure optimization for better feature extraction, and hyperparameter adjustment to enhance performance. Through extensive experiments, the effects of different optimization methods are compared meticulously. It is demonstrated that the optimized algorithm shows significant improvements in accuracy, robustness, and efficiency. Finally, the paper looks ahead to the future development trend of image recognition algorithms based on deep learning, envisioning further advancements and broader applications.

Uncovering the Over-Smoothing Challenge in Image Super-Resolution: Entropy-Based Quantification and Contrastive Optimization.

PSNR-oriented models are a critical class of super-resolution models with applications across various fields. However, these models tend to generate over-smoothed images, a problem that has been analyzed previously from the perspectives of models or loss functions, but without taking into account the impact of data properties. In this paper, we present a novel phenomenon that we term the center-oriented optimization (COO) problem, where a model's output converges towards the center point of similar high-resolution images, rather than towards the ground truth. We demonstrate that the strength of this problem is related to the uncertainty of data, which we quantify using entropy. We prove that as the entropy of high-resolution images increases, their center point will move further away from the clean image distribution, and the model will generate over-smoothed images. Implicitly optimizing the COO problem, perceptual-driven approaches such as perceptual loss, model structure optimization, or GAN-based methods can be viewed. We propose an explicit solution to the COO problem, called Detail Enhanced Contrastive Loss (DECLoss). DECLoss utilizes the clustering property of contrastive learning to directly reduce the variance of the potential high-resolution distribution and thereby decrease the entropy. We evaluate DECLoss on multiple super-resolution benchmarks and demonstrate that it improves the perceptual quality of PSNR-oriented models. Moreover, when applied to GAN-based methods, such as RaGAN, DECLoss helps to achieve state-of-the-art performance, such as 0.093 LPIPS with 24.51 PSNR on 4× downsampled Urban100, validating the effectiveness and generalization of our approach.

VO2-Based Spacecraft Smart Radiator with High Emissivity Tunability and Protective Layer.

In the extreme space environment, spacecraft endure dramatic temperature variations that can impair their functionality. A VO2-based smart radiator device (SRD) offers an effective solution by adaptively adjusting its radiative properties. However, current research on VO2-based thermochromic films mainly focuses on optimizing the emissivity tunability (Δε) of single-cycle sandwich structures. Although multi-cycle structures have shown increased Δε compared to single-cycle sandwich structures, there have been few systematic studies to find the optimal cycle structure. This paper theoretically discusses the influence of material properties and cyclic structure on SRD performance using Finite-Difference Time-Domain (FDTD) software, which is a rigorous and powerful tool for modeling nano-scale optical devices. An optimal structural model with maximum emissivity tunability is proposed. The BaF2 obtained through optimization is used as the dielectric material to further optimize the cyclic resonator. The results indicate that the tunability of emissivity can reach as high as 0.7917 when the BaF2/VO2 structure is arranged in three periods. Furthermore, to ensure a longer lifespan for SRD under harsh space conditions, the effects of HfO2 and TiO2 protective layers on the optical performance of composite films are investigated. The results show that when TiO2 is used as the protective layer with a thickness of 0.1 µm, the maximum emissivity tunability reaches 0.7932. Finally, electric field analysis is conducted to prove that the physical mechanism of the smart radiator device is the combination of stacked Fabry-Perot resonance and multiple solar reflections. This work not only validates the effectiveness of the proposed structure in enhancing spacecraft thermal control performance but also provides theoretical guidance for the design and optimization of SRDs for space applications.

Recovery of indium by solvent extraction with crown ether in the presence of KCl and stripping with HCl: A mechanistic study

Hydration of In3+ is the main factor limiting its extraction efficiency from an aqueous solution during a liquid-liquid extraction process. In this study, KCl was introduced into the aqueous solution to facilitate the formation of InCl4− of low charge density, which is expected to possess much weaker hydration compared with In3+, promoting the solvent extraction of indium. The crown ethers (CEs) with varied cavity sizes, benzo-18-crown-6 (B18C6), benzo-15-crown-5 (B15C5), and benzo-12-crown-4 (B12C4), were synthesized. The extraction performance of the CEs toward indium in the presence of sufficient KCl in the aqueous solution was investigated. The liquid-liquid extraction process was analyzed theoretically based on density functional theory (DFT) from the aspects of thermodynamics, geometric structure optimization, electrostatic potential (ESP), and independent gradient model (IGM). The theoretical evaluations agreed well with the experimental results that the hydration of indium could be significantly weakened through the formation of InCl4− and the complexation ability of the CEs toward indium is in the order of B18C6 > B15C5 > B12C4. The complexation mechanism between the CEs and indium during the extraction process was further explored with the assistance of 1H NMR spectrum and SEM-EDS. The results indicate that crown ether coordinates with K+ to form [CE-K]+ at the two-phase interface, which further associates with InCl4− to create the complex of CE-KInCl4, realizing the efficient indium extraction. Moreover, B18C6 showed excellent selectivity toward In3+ over the competing ions such as Fe3+, Al3+, Zn2+, Sn2+ and Ca2+ in a complex system. Indium could be efficiently recovered from the loaded organic phase by using 1 M HCl as the stripping agent with a stripping efficiency of 98.1%.

Comprehensive Production Index Prediction Using Dual-Scale Deep Learning in Mineral Processing.

In mineral processing, the dynamic nature of industrial data poses challenges for decision-makers in accurately assessing current production statuses. To enhance the decision-making process, it is crucial to predict comprehensive production indices (CPIs), which are influenced by both human operators and industrial processes, and demonstrate a strong dual-scale property. To improve the accuracy of CPIs' prediction, we introduce the high-frequency (HF) unit and low-frequency (LF) unit within our proposed dual-scale deep learning (DL) network. This architecture enables the exploration of nonlinear dynamic mapping in dual-scale industrial data. By integrating the Cloud-Edge collaboration mechanism with DL, our training strategy mitigates the dominance of HF data and guides networks to prioritize different frequency information. Through self-tuning training via Cloud-Edge collaboration, the optimal model structure and parameters on the cloud server are adjusted, with the edge model self-updating accordingly. Validated through online industrial experiments, our method significantly enhances CPIs' prediction accuracy compared to the baseline approaches.

Experimental, modeling and optimisation of adipic acid reactive extraction using ionic liquids

Adipic acid (hexanedioic acid, AA) can be utilised as an essential monomer in the production of nylon-6,6 (75 %), but also for urethane foams, fibers, elastomers, tire reinforcements, and synthetic lubricants. Considerable work has been done to develop sustainable biosynthetic processes for its manufacture, especially for adipic acid efficient separation (one of the main challenges for industrialisation). As for scale-up, process optimisation, and thorough engineering mathematical models that describe the system efficiently are required, this study proposes mathematical models for a reactive extraction using ionic liquids as extractants for adipic acid separation to improve the biosynthetic route’s sustainability, efficiency, and environmental performance. Heptane as the solvent and 117.8 g/L [P6,6,6,14][Phos] as the extractant at 2.8 pH of the aqueous phase were the optimum mixture for reactive extraction, resulting in an extraction yield of 97.55 % for adipic acid. The process was modeled using an artificial neural network optimised with a differential evolution algorithm. The optimal model structure had one hidden layer with 20 neurons, and its performance in the testing phase was: explained variance score of 0.974, mean absolute error of 1.917, and coefficient of determination of 0.974.

Quality Enhancement of MIROS Wave Radar Data at Ieodo Ocean Research Station Using ANN

Remote sensing wave observation data are crucial when analyzing ocean waves, the main external force of coastal disasters. Nevertheless, it has limitations in accuracy when used in low-wind environments. Therefore, this study collected the raw data from MIROS Wave and Current Radar (MWR) and wave radar at the Ieodo Ocean Research Station (IORS) and applied the optimal filter by combining filters provided by MIROS software. The data were validated by a comparison with South Jeju ocean buoy data. The results showed it maintained accuracy for significant wave height, but errors were observed in significant wave periods and extreme waves. Hence, this study used an artificial neural network (ANN) to improve these errors. The ANN was generalized by separating the data into training and test datasets through stratified sampling, and the optimal model structure was derived by adjusting the hyperparameters. The application of ANN effectively improved the accuracy in significant wave periods and high wave conditions. Consequently, this study reproduced past wave data by enhancing the reliability of the MWR, contributing to understanding wave generation and propagation in storm conditions, and improving the accuracy of wave prediction. On the other hand, errors persisted under high wave conditions because of wave shadow effects, necessitating more data collection and future research.

Potential of achieving sustainable development through integrated optimization of mariculture species based on the food-energy-water nexus in China

The sustainability of mariculture possesses substantial enormous potential in food security and the mitigation of global warming. Based on the food‑carbon-water nexus, this study assessed the carbon and water footprints of mariculture in China, identified key drivers, and constructed a multi-objective optimization model of mariculture structure. Results showed that the carbon and water footprints of mariculture in China increased continuously from 2008 to 2020, with the intensity of carbon footprint increasing from 0.08 to 0.14 t CO2/t and that of water footprint increasing from 5436.72 to 6169.01 m3/t. Shellfish showed lower intensity of footprints than fish and crustaceans. The carbon footprint intensity of mariculture was high in Tianjin and Hainan but resulted in negative carbon emissions in Shandong and Liaoning. Hainan, Hebei, and Liaoning provinces had the highest average annual water footprint intensity. Provincial population and total mariculture production significantly impacted the carbon and water footprints of mariculture. Optimizing mariculture species structure can reduce carbon and water footprints while increasing protein production. However, a large gap still exists between the current development and optimization scenarios for mariculture structure in China. A targeted increase in the production of mariculture species such as plaice in Tianjin, American redfish in Guangxi, oysters and scallops in Guangdong, wakame in Liaoning, and gracilaria in Fujian, can help promote low carbon and water-saving practices, thus achieving sustainable mariculture development. Therefore, China's mariculture should continuously optimize its structure and enhance carbon sink capacity in the future.

A machine learning and CFD modeling hybrid approach for predicting real-time heat transfer during cokemaking processes

As the development of green energy and smart industries progresses, concerted efforts are being directed towards the transformation of coking industries. Effective management of heat transfer during the coking process is essential to fortify energy consumption management and augment the quality of coke produced. However, the process during cokemaking is a complex thermochemical conversion process where even minor deviations in operating conditions can lead to instability. Additionally, due to the environmental and chemical conditions inside the coke oven, temperature measurements during operation are difficult. As the fields of Industry 4.0 continue to evolve, numerous industries have begun to leverage intelligent strategies to enhance advanced process management. The digital twin (DG) technique stands as a pivotal technology in the realm of industrial transformation, paving the way for a smarter future. However, given the inherent difficulty in real-time data collection for process operations, the challenge of achieving synchronization becomes increasingly prevalent in the development of DG for the smart coking process. As a result, predicting changes in coal temperature during the cokemaking process is crucial. Currently, computer technology allows for the simulation of complex chemical processes. While some numerical models describe the cokemaking process, these models are limited by the time-consuming characteristic and computing resources. To address this issue, this study proposed a Machine Learning (ML) and Computational Fluid Dynamics (CFD) hybrid model for real-time prediction of heat transfer during the cokemaking process. A CFD model was built based on an industrial-scale coke oven, with cokemaking process data generated through CFD simulation serving as input for the ML models. This study used a total of nine ML models, including ensemble and deep learning models. The hyperparameters of each model were optimized by Grey Wolf Optimization (GWO), Particle Swarm Optimization (PSO), and JAYA algorithms to identify the optimal model structure. Both simulation and empirical experimentation using a coke oven, coupled with industrial data verification, have substantiated the superiority of the proposed model. It simulates the heat transfer during the coking process with high accuracy and efficiency, thereby demonstrating its capacity to significantly reduce energy consumption within the coking industry.

Non-Destructive Inspection of Physicochemical Indicators of Lettuce at Rosette Stage Based on Visible/Near-Infrared Spectroscopy.

Lettuce is a globally important cash crop, valued by consumers for its nutritional content and pleasant taste. However, there is limited research on the changes in the growth indicators of lettuce during its growth period in domestic settings. Quality assessment primarily relies on subjective evaluations, resulting in significant variability. This study focused on hydroponically grown lettuce during the rosette stage and investigated the patterns of changes in the indicators and spectral curves over time. By employing spectral preprocessing and selecting characteristic wavelengths, three models were developed to predict the indicators. The results showed that the optimal model structures were S_G-UVE-PLSR (SSC and vitamin C) and Nor-CARS-PLSR (moisture content). The PLSR models achieved prediction set correlation coefficients of 0.8648, 0.8578, and 0.8047, with residual prediction deviations of 1.9685, 1.9568, and 1.6689, respectively. The optimal models were integrated into a portable device, using real-time analysis software written in Matlab2021a, for the prediction of the physicochemical indicators of lettuce during the rosette stage. The results demonstrated prediction set correlation coefficients of 0.8215, 0.8472, and 0.7671, with root mean square errors of prediction of 0.5348, 1.5813, and 2.3347 for a sample size of 180. The small discrepancies between the predicted and actual values indicate that the developed device can meet the requirements for real-time detection.

Modeling and Optimization of the Air-Supported Membrane Coal Shed Structure in Ports

The air-supported membrane coal shed is widely used in bulk cargo terminals. It not only effectively protects goods from adverse weather conditions but also helps reduce coal dust and harmful gas emissions, promoting the green and sustainable development of ports. However, in practical engineering, the design parameters of the coal shed are often based on experience, making it difficult to accurately assess the quality of the structural design. The flexibility of the membrane material also makes the structure susceptible to deformation or tearing. This paper mainly focuses on modeling and solving the optimization design issues of air-supported membrane coal shed structures. According to the evaluation criteria for the form of air-supported membrane coal sheds, a multi-objective structural optimization model is established to minimize the maximum stress on the membrane surface, ensure uniform stress distribution, maximize structural stiffness, and minimize costs. The study utilizes a combined optimization approach using ANSYS 19.0 and MATLAB 2016a, incorporating an improved NSGA-II algorithm program developed in MATLAB into ANSYS for structural form analysis and load calculation. The research results indicate that the optimal solution reduces the maximum stress on the loaded membrane surface by 5.36%, shortens the maximum displacement by 30.3%, and saves on economic costs by 9.85%. Compared to traditional empirical design methods, the joint use of MATLAB and ANSYS for optimization design can provide more superior solutions, helping ports to achieve environmental protection and economic efficiency goals.

A self-organization reconstruction method of ESN reservoir structure based on reinforcement learning

The dynamic reservoir of the randomly generated Echo State Network (ESN) contains numerous redundant neurons, resulting in collinearity in the high-dimensional state space matrix. This collinearity impacts the prediction performance of the network. In order to address this issue, this paper introduces a self-organizing ESN structure optimization model that is based on reinforcement learning, called SR-ESN. The SR-ESN model employs pruning methods to reconstruct the reservoir using contribution and decision mechanisms. To mitigate potential instability caused by high coupling among neurons in a single reservoir, the concept of ensemble learning is applied to create multiple initial reservoir pools, thereby enhancing screening diversity. Simultaneously, the model utilizes reinforcement learning's decision mechanism to identify effective neurons. Neurons with low contribution are pruned, while those with high contribution are retained for self-organizing reconstruction. This optimization of the network structure enhances its prediction performance. Based on both artificial and real datasets, the proposed SR-ESN model demonstrates superior prediction performance with minimal structural complexity compared to other prediction models.

Flexible allocation and optimal configuration of multi-level energy exploitation units for heterogeneous energy systems considering resource distribution

The energy systems are evolving into heterogeneous energy systems (HESs) with complicated integration of sources, networks, loads, and storage towards a decarbonized future of human beings. This paper develops the flexible allocation and optimal configuration of multi-level energy exploitation units (MEEUs) for the HES considering resource distribution including local energy conditions and actual coupled relationship of various energy networks. A bi-level optimal planning model of MEEUs for the HES considering initial investment cost, carbon emission cost, operation cost and line loss is developed to figure out the optimal location, structure, configuration and corresponding operation strategy. To address the non-convex and non-linear model, a novel hybrid solution method considering the mixing characteristics of mixed-integer second-order cone programming (MISOCP) model and quadratic non-convex model is proposed. The solution method adopts MISOCP model for figuring out the optimal location, structure and configuration of MEEUs and quadratic non-convex model for optimal operation strategy of MEEUs, which not only improves the computational efficiency but also ensures the solution accuracy. Finally, the related case studies are conducted to compare the proposed MEEU and distributed energy storage unit (DESU) in terms of energy consumption, renewable energy absorbency, carbon emission and line loss. The results verify the significant improvement of the comprehensive energy efficiency, the investment potentiality and the environmental benefits obtained by the proposed planning model.

Применение байесовского подхода к прогнозированию налоговых поступлений на примере Республики Армения

This paper is devoted to the application of the Bayesian approach to the forecasting of aggregate taxes on the example of the Republic of Armenia. Typically, this approach is used in large-scale BVARs to forecast macroeconomic variables. The objective of this study is to estimate the efficiency of the Bayesian approach to constricting relatively low-scale fiscal VARs. Another objective is to build a specific BVAR model for forecasting tax revenues in the context of actual forecasting rounds. The study is based on seasonally adjusted quarterly aggregate tax data and the corresponding proxy bases. A hierarchical approach to the selection of BVAR’s priors is implemented. It assumes the random nature of variances in the prior values of the coefficients. The hierarchical approach is also characterized by a high level of variability of hyperparameters. To determine the optimal structure of the BVAR model in terms of out-of-sample prediction accuracy, a special algorithm was developed. This algorithm involves a specific procedure for the selection of priors and model parameters, which allows to significantly minimize the prediction error. The Geweke and Gelman-Rubin tests were used/considered to check the convergence of the parameters, and the acceptance rate of the Metropolis-Hastings algorithm was taken into account. It Additional priors, such as the sum-of-coefficients prior and the dummy-initialobservation prior (single-unit-root), are shown to improve the quality of out-of-sample forecasts. These priors allow for the possibility of the existence of a single root and cointegration between variables. The main finding of this study is that the proposed algorithm for selecting parameters in BVAR significantly improves out-of-sample performance compared to traditional frequency VAR.

A fast analysis algorithm for structural vibration modal sensitivity

Vibration modal sensitivity analysis has a wide range of applications in structural optimization design, model correction, fault detection, and reliability analysis. The existing methods for calculating modal sensitivity mainly include modal superposition method, Nelson’s method, and some improved algorithms derived from them. However, the existing algorithms have the drawback of low computational efficiency when applied to modal sensitivity analysis of the large-scale structures. In view of this, the objective of this work is to develop a fast modal sensitivity analysis method that can more efficiently calculate the modal sensitivity of the large structures with thousands of degrees of freedom. This new sensitivity analysis technique integrates Sherman-Morrison-Woodbury formula, subspace iteration and forward-difference to achieve the goal of fast calculation. The innovations of the proposed method mainly include the following aspects. Firstly, the Sherman-Morrison-Woodbury formula is used to quickly calculate the perturbed flexibility matrix due to the minor modification in the structure. Then, the perturbed flexibility matrix is introduced into the subspace iteration method to calculate the perturbed modal parameters. Finally, the forward-difference algorithm is used to calculate the modal sensitivity. Two numerical examples are used to verify the superiority of the proposed modal sensitivity algorithm. Taking the 1952-bar structure as an example, the calculation time of the proposed algorithm is only 8.3 % and 18.2 % of that of the existing approximate modal superposition method and the improved Nelson’s method, respectively. In terms of calculation accuracy, the results obtained by the proposed method are exactly the same as the exact solution when the perturbation scale is set to 10−5. It is found that the proposed method significantly reduces computation time compared to the existing methods on the premise that the calculation accuracy is basically unchanged.

Quantum annealing-aided design of an ultrathin-metamaterial optical diode

Thin-film optical diodes are important elements for miniaturizing photonic systems. However, the design of optical diodes relies on empirical and heuristic approaches. This poses a significant challenge for identifying optimal structural models of optical diodes at given wavelengths. Here, we leverage a quantum annealing-enhanced active learning scheme to automatically identify optimal designs of 130 nm-thick optical diodes. An optical diode is a stratified volume diffractive film discretized into rectangular pixels, where each pixel is assigned to either a metal or dielectric. The proposed scheme identifies the optimal material states of each pixel, maximizing the quality of optical isolation at given wavelengths. Consequently, we successfully identify optimal structures at three specific wavelengths (600, 800, and 1000 nm). In the best-case scenario, when the forward transmissivity is 85%, the backward transmissivity is 0.1%. Electromagnetic field profiles reveal that the designed diode strongly supports surface plasmons coupled across counterintuitive metal–dielectric pixel arrays. Thereby, it yields the transmission of first-order diffracted light with a high amplitude. In contrast, backward transmission has decoupled surface plasmons that redirect Poynting vectors back to the incident medium, resulting in near attenuation of its transmission. In addition, we experimentally verify the optical isolation function of the optical diode.