In recent decades, the issues of global warming and the energy crisis have garnered significant attention due to the extensive combustion of fossil fuels. Energy conservation has emerged as a prominent research area. Currently, 40%–50% of the total global energy consumption comes from building energy consumption, mainly for lighting, ventilation, heating, and air conditioning [1,2]. The energy demand for cooling has surged to approximately 15% of global energy consumption [3,4]. Consequently, thermal management of buildings has garnered attention in scientific literature. Daytime radiative cooling systems that do not require any input power would greatly alleviate the global energy crisis. Daytime radiative cooling technology leverages the atmospheric transparency window, which spans from 8 to 13 μm, to actively dissipate heat from the Earth into the frigid environment of outer space (3 K). Daytime radiative coolers can achieve passive cooling and maintain temperatures lower than the ambient, even in direct sunlight. They have potential applications in cooling solar cells [5] and air conditioning buildings [6], among other possibilities. During the last decade, researchers have investigated various structures of radiative coolers, including micro pyramid structures [7,8], hole structures [9], polymer structures [10], and multilayer thin-film structures [11,12]. The investigation of multi-layer thin film structures has been the subject of extensive research, primarily due to their uncomplicated composition and straightforward manufacturing process. Chen et al. presented a multilayer thin-film radiation cooler made of Si3N4–Si–Al-Substrate to achieve selective thermal radiation in the atmospheric window band. The elimination of parasitic thermal loads is employed to achieve significant reductions in temperature, reaching up to 60 °C below ambient temperature [13]. Kim and colleagues developed a radiative cooler with a multilayer thin-film structure, which operates through an endothermic reaction involving NH4NO3/H2O and driven by water sorption [12]. To optimize the performance of multilayer passive radiative coolers, it is crucial to achieve a broad range of impedance matching within the atmospheric window while simultaneously preventing the absorption of solar radiation within the solar wavelength range. This complex objective requires a thorough strategy that includes conducting extensive experimental studies [14], meticulous optical simulations, and employing classical algorithms to optimize each layer's thickness. Algorithms of this nature often employ a brute-force methodology and are prone to being trapped in local optima. The radiative cooler developed by Wu et al. demonstrates a high level of efficiency in radiative cooling [7]. However, there is potential for further improvement in the radiative cooling efficiency and simplification of the structure through the optimization of the thickness of the multi-layer thin film. The full dielectric quasi-three-dimensional subwavelength structure proposed by He et al. achieves perfect anomalous reflection at optical frequencies through equations and theoretical derivations [15]. However, it is regrettable that further optimization of the structure dimensions to improve device efficiency and simplify the structure was not performed. In the case of other types of two-dimensional optical devices, such as polarization converters [16], beam splitters [17], and metalens [18], the process of calculating the model structure alone can be time-consuming, often requiring several tens of minutes or even hours. Conventional optimization techniques, such as memetic algorithm [19], particle swarm optimization [20], and ant colony optimization [21], are not feasible for optimizing the structural parameters of two-dimensional optical devices.

Recently, the domain of nanophotonics and metamaterial design has experienced integrating deep learning (DL) techniques [22]. This amalgamation has been motivated by the impressive ability of DL to expedite computationally intensive simulation procedures while simultaneously providing flexible design frameworks for a wide array of applications. This approach enables precise engineering of optical properties in various nano photon structures. Researchers have utilized a wide array of well-established neural networks (NN) to advance the boundaries of metamaterial design. These include but are not limited to, multilayer perceptron (MLP), convolutional neural networks (CNNs), recurrent neural networks (RNNs), generative adversarial networks (GANs), radial basis function (RBF), group method of data handling (GMDH) and variational autoencoders. The MLP [23,24], characterized by its simple architecture and ease of implementation, is suitable for handling classification and regression tasks. However, its performance may be limited when dealing with complex data structures such as images and sequential data. CNNs [25] are well-suited for image processing, effectively extracting local features and exhibiting robustness to translations, scalings, and other transformations. Nevertheless, they entail high computational complexity and impose specific requirements on the shape and size of input data. RNNs [26] are adept at handling sequential data, and capturing temporal dependencies, yet they may encounter issues like gradient vanishing or exploding during training. GANs [27] excel in generating highly realistic samples but are susceptible to instability during the training process and prone to mode collapse. RBF networks [28], characterized by their local approximation capability and fast convergence, are sensitive to the selection of centers and widths and are less adept at handling high-dimensional data. GMDH [29] presents a self-organizing approach to model structure construction, suitable for modeling and prediction in complex systems, albeit with relatively low efficiency when dealing with large-scale data. The MLP and CNN are two of the most fundamental and widely applied neural network architectures, and they have also found extensive application in the field of micro-nano optical devices. So et al. introduced a fully connected neural network to predict target spectra accurately. This was achieved by identifying the inherent connection between grating structural parameters and reflectance spectra [30]. Yeung et al. utilized CNN for training to predict the electromagnetic response of metal-dielectric-metal metamaterials, enabling physical discoveries and design optimizations in optics and photonics [31]. Chen et al. designed a neural network based on the Transformer model, which divides the studied spectrum into multiple modules, overcoming the severe overfitting issue of traditional deep learning and enhancing the learning capability [32]. In comparison to traditional numerical methods, these techniques provide a notable decrease in computational demands by directly incorporating the connections between structure and optical response, thereby eliminating the necessity of solving the complex three-dimensional vector Maxwell's equations. The integration of advantages from different networks holds the potential to enhance the learning capability of the network, thereby improving its predictive performance.

Here, we report a method that integrates PE (position encoding) with MLP and CNN to achieve precise prediction of the emission spectrum exhibited by the daytime radiative cooler. Compared to using only MLP or CNN, the hybrid model improves the network's understanding of the complex relationship between structural parameters and optical response. Furthermore, the integration of residual network effectively addresses the problem of overfitting. By integrating PE, the hybrid MLP-CNN with PE model quickly understands the inherent connections between the input and output variables, decreasing the RMSE and MRE. This method, which utilizes PE and integrates MLP and CNN, has demonstrated notable efficacy in optical response. It substantially diminishes simulation duration and circumvents the issue of optimization becoming trapped in local optima. This efficient technique for optimizing structural parameters exhibits promising applicability to various optical devices, including polarization converters, beam splitters, metalens, and other two-dimensional nanostructures.