1. Introduction

Radiative cooling, a novel technology capable of attaining temperatures below the ambient levels without the need for energy consumption, has emerged as a promising solution to combat challenges associated with global warming [1–3]. This cooling mechanism takes advantage of the Earth's atmosphere's transparent electromagnetic window, ranging between 8-13 µm, allowing for effective heat dissipation into the frigid outer space, which harbors temperatures around 3K [4–6]. Capitalizing on these unique characteristics, radiative cooling can serve as an innovative substitute to traditional cooling systems. This can be achieved by integrating it into the external surfaces of buildings, effectively contributing to the reduction of environmental pollution that is typically associated with standard cooling mechanisms. Furthermore, this technology finds relevance in cooling systems for solar cells, as increased temperatures can adversely affect the efficiency of solar energy conversion into electricity.

Radiative coolers (RCs) can be categorized into two main types based on their specific applications: solar-transparent RC (StRC) and solar-opaque RC (SoRC). The StRCs require transparency within the solar spectral region (0.3-2.5 µm) and efficient heat radiation emission within the atmospheric transparent window (8-13 µm) of the long-wave infrared (LWIR) spectrum. On the other hand, The SoRCs necessitate robust sunlight reflection in the solar spectral region, along with strong emission in the LWIR. Numerous photonic structures have been proposed for the effective implementation of these two distinct types of RCs [7–9]. However, many such structures are intricate, leading to escalating fabrication costs and complex assembly procedures.

In an ideal situation, the availability of a simple film with requisite optical constants could obviate the need for implementing complex photonic structures. However, the intricate spectral features demanded by RCs, such as solar transparency/LWIR emission or solar reflection/LWIR emission, create challenges in the discovery of materials with suitable optical constants. From this standpoint, the effective medium theory (EMT) emerges as a viable approach to obtain desired refractive indices. This is because EMT allows for the adjustment of optical constants by modifying the volume ratios of materials when the dimensions of the composite materials are significantly smaller than the wavelength of the incident light [10–12]. Thus, EMT provides the potential to synthesize the necessary optical constants for radiative cooling. Furthermore, Mie scattering describes the scattering of particles whose particle size is comparable to the wavelength of the incoming light, which can explain the reflection of films containing particles with sub-/near-micron diameters in the solar region [13,14].

In this work, we introduce a deep learning method to inversely design both StRC and SoRC, respectively, consisting of a 10 µm-thick polyethylene (PE) film, which is infrared (IR) transparent polymer, and oxide/nitride nanoparticles based on EMT. Deep learning is a non-linear model inspired by the hierarchical architecture of the human brain, transforming data into higher-level abstract representations through multilayers [15,16]. Deep Neural Network (DNN), as a deep learning algorithm, incorporates multiple hidden layers of interconnected nodes, known as neurons, enabling them to learn intricate patterns and representations from input data [17–19]. The most previous studies about inverse design utilizing DNN have used DNN as the former calculation part of inverse design [20–23]. However, we established deep learning model using DNN as an inverse design method directly unlike previous studies. Although the direct application of DNN as an inverse design method usually suffers from non-convergence of neural network, our proposed deep learning model can prevent such degradation by coupling with an accuracy-enhancing calculation process using transfer matrix method (TMM) and EMT, designs high-quality for desired optical results. The application of deep learning in designing structures to obtain desired optical properties enables us to propose novel and diverse structures that have not previously existed [24–26]. The StRCs enhance the performance of solar cells with dropping temperature of 16.4 K reaching high transmittance within the solar spectral region, along with strong emission in the LWIR. The SoRCs exhibit high solar reflectance and strong LWIR emission in the atmospheric transparency window, achieving a temperature drop of 2.06 K.

2. Method

2.1 Maxwell-Garnett effective medium theory

The particle-embedded film, into which various types of particles are injected, can be considered as a homogeneous medium when the particle size is significantly small compared to the wavelength. The effective complex refractive index can be calculated as the complex refractive index between particles and film utilizing Maxwell-Garnett effective medium theory as follows in Eq. (1) [27]:

2.2 Optical simulation

To validate optical properties of inversely designed structure, two optical simulation tools are utilized. A commercial software, DiffractMOD (RSoft Design Group, Synopsys, United States) based on rigorous coupled-wave analysis (RCWA) revealed the total optical efficiencies of the nanoparticle-embedded polyethylene (PE) film. Due to the computational complexity involved, 2D simulations are commonly utilized in many previous studies [28–31] for obtaining the optical properties of complicated 3D photonics structures. To streamline the calculation process, 2D simulation was chosen for all the results. In a previous study [32], the transverse magnetic (TM) mode was employed for calculating the optical properties of particle-embedded structures using RCWA simulation in two dimensions. The sphere entities within the film are considered as circles, an approximation utilized to represent the simplification from a 3D photonic structure to a 2D model. However, in the RCWA 2D simulation, these circular representations are considered as cylindrical structures. In the TM mode, the electric field is parallel to the plane of incidence plane, considering the interaction with the circular components. Therefore, the TM mode was chosen as the suitable approach for determining the optical performance of our structures. The grid size for RCWA simulation was 0.03 × 0.1 µm for each axis (i.e., x and z directions) when the radius of particles is under 2.5 µm, and 0.03 × 0.5 µm for particles with a radius larger than 2.5 µm, respectively. Moreover, complex refractive indices of SiO₂, TiO₂, Si₃N₄, Al₂O₃, HfO₂, and PE were obtained from earlier released results [33–37]. A FullWAVE (RSoft Design Group, Synopsys, United States) was used to investigate electric field profiles of StRC and SoRC. The simulation domain was set to match the width of each structure in the x-direction and 30 µm in the z-direction, with a square grid size of 0.02 µm for FDTD simulation. The boundary conditions were established as periodic in the x-direction and perfectly matched layer (PML) in the z-direction.

2.3 Random particle arrangement within a film

To evaluate optical properties of the inversely designed radiative coolers, structures are needed based on the results of deep learning, which includes the volume ratios of composing materials and particle size distributions. Utilizing a Python, an open-source programming language, nanoparticles are randomly positioned within a PE film without overlapping. The radius of 500 particles is determined based on the inversely designed particle size distribution resulting from deep learning. The thickness of the nanoparticle-embedded PE film is fixed at 10 µm. The width of the structure is calculated by considering the volume ratio of the host material, PE, and the total volume ratio of the 500 particles. The center coordinates of each particle are determined randomly, ensuring no overlap with previous particles. The number of particles for each material is decided based on inversely designed volume ratios out of a total of 500 particles.

3. Results and discussion

3.1 Structure scheme and deep learning process for radiative cooling

The StRCs and SoRCs are filled with nanoparticles composed of five materials that are SiO₂, TiO₂, Si₃N₄, Al₂O₃ and HfO₂, as well as a surrounding binder material, a solar and IR transparent PE film with a thickness of 10 µm (Fig. 1(a)). The sparse distribution of large particles in StRCs diminishes the occurrence of light scattering, while the SoRCs consist of small, closely packed particles, leading to higher degree of scattering in the solar region. The ideal StRCs transmit the incoming sunlight and enable a strong LWIR heat radiation emission through the atmospheric transparent window, whereas the ideal SoRCs completely reflect sunlight and exhibit strong thermal emission in the LWIR (Fig. 1(b)).

 

Fig. 1. (a) Structure of nanoparticles-embedded in the PE film for StRC (left) and for SoRC (right). (b) Desired optical efficiency spectrum of StRC (top) and SoRC (bottom): The StRC emits in the 8-13 µm (blue solid line) and transmits in the solar region (red solid line). The SoRC emits in the 8-13 µm (blue solid line) and reflects in the solar region (pink solid line). Orange area indicates the AM1.5G solar irradiation spectrum and light blue area indicates atmospheric transmission. (c) The overall process involves utilizing three deep learning models, that are the RI model (red area), the VR model (blue area), and the PS model (green area), to obtain the inverse design for StRC and SoRC.

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DNNs suggest the optimal refractive indices of the nanoparticle-embedded PE films and the corresponding volume ratios of five distinct materials to satisfy their desired optical constants for StRCs and SoRCs, respectively. Moreover, the particle size distribution, specifically tailored for each type, is suggested to achieve optimal optical properties for each type within solar region utilizing DNNs algorithm. As shown in Fig. 1(c), three types of deep learning model are used to design RCs in sequence and each model is divided into a training process and an inverse design process. The neural network of refractive index (RI) model has the emissivity spectrum (ε_in) as an input and outputs the optical constants (n_out and k_out) of thin film during training process. In the inverse design process for RI model, the trained neural network of RI model is applied in tandem with TMM in accordance with the calculation of Kirchhoff’s law of thermal radiation (See Section 1 in Supplement 1) [38,39]. By utilizing TMM, emissivity can be calculated based on refractive indices (i.e., n_out and k_out), denoted by ‘ε_cal.’ in Fig. 1(c). The tandem model predicts the inverse designed refractive indices that are expected to satisfy the desired emissivity spectrum that is a unity within atmospheric transparency window (Fig. 1(c); RI model).

In the volume ratio (VR) model, the training process involves a neural network utilizing datasets matched refractive indices (n_in and k_in) to volume ratio (vr_out) of five materials constituting the thin film for radiative cooling. The trained model for volume ratio based on Maxwell-Garnett EMT, which calculates effective refractive indices (n_cal. and k_cal.) from volume ratio (vr_out) of five materials (See “Method” Section for detail), considers desired refractive indices from RI model as input and predicts the optimal volume ratio adjusted to desired refractive indices (Fig. 1(c); VR model). The results of RI model and VR model are designed for achieving high emissivity in the IR region. The inverse designs are based on composing random medium embedded with nanoparticles. Optical simulations based on rigorous-coupled wave-analysis (RCWA) method investigate the optical efficiencies of generated random media reflecting the results of two models from ultra-violet (UV) to IR regions (0.28 -15 µm) (See “Method” Section for detail). The calculated reflectance spectra serve as the datasets for third model (i.e., particle size model). The particle size (PS) model consists of two neural networks: the inverse network considers reflectance (R_in) as an input and outputs particle size distribution (PSD_out) while the forward network predicts reflectance (R_cal.) based on PSD_out. The PS model with two neural networks provides the optimal particle size distribution corresponding to desired reflections (Fig. 1(c); PS model).

3.2 Datasets and deep learning for high emissivity in the LWIR region

Datasets for three types of deep learning models based on supervised learning are labeled as input and output for each model. The volume ratio of PE, the host medium, is set at 50% and the combined fill rates of the remaining materials, which include SiO₂, TiO₂, Si₃N₄, Al₂O₃, and HfO₂ amounts to 50%. The effective refractive index, which matches volume ratios of thin films composed of various combinations, is calculated using Maxwell-Garnett EMT method and the emissivity obtained using the TMM. The refractive indices and emissivity spectra consist of 1000 spectral points in a wavelength rage from 4 to 15 µm which can be applied EMT. The total datasets for each model are divided into training (80%), validation (10%) and test (10%) datasets and these subsets are utilized according to their purpose during the training process.

In contrast to the conventional methods that rely on optical structures to compute optical properties, the neural network in the deep learning model, known as the inverse network, designs optical structures as outputs when provided with optical characteristics as inputs. As shown in Fig. 2(a), in the RI model, the input is the emissivity spectrum (ε_in). The model predicts the optical constants (n_out and k_out) of the thin film leveraging the weights and biases within the inverse network. The inverse network of the RI model is a fully connected network with seven hidden layers, denoted as ‘N₁ Layers’ in Fig. 2(a), and each layer contains 500 neurons. ‘Rectified linear unit (ReLU)’ activation function is utilized at the end of each layer [40,41]. The training process is divided into three wavelength ranges as follows: Emissivity is 1 at 8-13 µm and 0 at 4-8 µm and 13-15 µm, respectively, for selective emission. For this, the loss function is also defined as the weighted average losses for three wavelength ranges such as l_{(4-8 µm)}, l_{(8-13 µm)} and l_{(13-15 µm)}, as given in Eq. (4).

 

Fig. 2. (a) Schematics of the RI model (red box) and VR model (blue box). (b) Training and validation loss over epochs of the RI model (top) and the VR model (bottom). (c) Comparing of actual refractive index spectrum (‘n’ is represented by a black solid line and ‘k’ is depicted as a red solid line) and predicted responses (‘n’ is represented by a green solid line and ‘k’ is depicted as a blue solid line) obtained from the RI model. (d) Comparing of actual volume ratios to the predicted volume ratios for each material: SiO₂, TiO₂, Si₃N₄, Al₂O₃, and HfO₂.

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The RI model and the VR model are trained using each training datasets with 500 epochs, and the validation datasets are used to evaluate the trained network on every 10 epochs. After 500 epochs, the trained network is evaluated by the test datasets that have never been used in previous training or validation steps. Once training is complete, weights and biases are saved and used for the next training. The training error and validation error of the first iteration of RI model and VR model are plotted (Fig. 2(b)). Error of the RI model decreases rapidly up to 50 epochs, but then reduces slowly and error of validation process also decreases. In the VR model, the error diminishes swiftly within the first 100 epochs, at a slower rate compared to the RI model. As two models repeat training, new weights and biases are saved each training iteration. The final weights and biases are obtained after 12 iterations for RI model and 5 iterations for VR model.

As shown in Fig. 2(c), comparing spectrum of the RI model describes that the difference of actual value and predicted response of refractive indices that is one of the smallest loss. The calculated overall loss between the actual value and the predicted response is 0.00662 and the predicted response exhibits a shape similar to the actual value. Comparisons between actual volume ratios and predicted volume ratios are based on the volume ratio of the nanoparticle materials, excluding the ratio of the host material, the total of which amounts to 100%. The differences between actual and predicted volume ratios in the case of the smallest loss are remarkably subtle, and the overall calculated error is 0.000891 (Fig. 2(d)).

3.3 Inverse design model

Inverse design model enhances design quality by integrating a calculation process with the pre-trained network, where the RI model connects the TMM calculation process, and the VR model integrates the EMT calculation process. In the inverse design process, the RI model predicts the inversely designed refractive indices when the model considers the desired emissivity spectrum as an input. The result of the RI model serves as the targeted refractive indices working as the input of the VR model. The VR model suggests an optimum volume ratio to obtain the targeted refractive indices. Through this continuous inverse design process, the inversely designed volume ratio is proposed for radiative cooling. The detailed inverse design process of RI model and VR model is described in the Section 2 of Supplement 1.

Furthermore, the use of a model that integrates the RI model and VR model can be utilized more easily when designing inversely, as shown in Fig. 3(a). The integrated model can be implemented by providing the refractive indices denoted as ‘n_out.’ and ‘k_out.’ in Fig. 3(a), which is the output of the RI model, as the input of the VR model. The integrated model is trained based on the datasets used to train the existing RI model and VR model. In inverse design process, the integrated model is connected with EMT and TMM calculation process, sequentially. The integrated model considers the desired emissivity spectrum (ε_in), which has a unity emission in the spectral range from 8 to 13 µm and zero at other IR regions, as an input. The VR model within the integrated model predicts the inversely designed volume ratios (vr_out.). Continuously, the refractive indices (n_cal. and k_cal.) are obtained from the EMT calculation based on the volume ratios (vr_out.), the output of VR model. The emissivity spectrum (ε_cal.) can be calculated through the TMM process based on the refractive indices (n_cal. and k_cal.). The integrated model can suggest inversely designed volume ratios by comparing between the desired emissivity spectrum (ε_in) with the calculated spectrum (ε_cal.). This also determines the difference between the predicted refractive indices (n_out. and k_out.) from the RI model and those calculated through TMM calculation (n_cal. and k_cal.).

 

Fig. 3. (a) Schematics of integrating the RI model with the VR model, including the training process and inverse design process. In inverse design process, the RI model, the VR model, EMT calculation, and TMM calculation process are combining sequentially. (b) Results obtained by utilizing the RI model and VR model individual. (i) Spectra of desired emissivity (black solid line), calculated emissivity based on volume ratio (blue solid line) and emissivity of inverse design obtained from the RI model (red solid line). (ii) Spectra of refractive indices obtained from the RI model (‘n’ is represented by a black solid line and ‘k’ is depicted as a red solid line) and refractive indices based on VR model (‘n’ is represented by a green solid line and ‘k’ is depicted as a blue solid line). (iii) The bar graph represents the inverse designed results of VR model. The volume ratio of PE is established at 50% and the combined volume ratios of the remaining materials amounts to 50%. (c) Results obtained by combining the RI model and VR model. (i) Spectra of desired emissivity (black solid line) and calculated emissivity obtained from the integrated model (red solid line). (ii) Spectra of refractive indices calculated using the EMT process in the integrated model (‘n’ is represented by a black solid line and ‘k’ is depicted as a red solid line) and refractive indices obtained from the RI model of the integrated model ‘n’ is represented by a green solid line and ‘k’ is depicted as a blue solid line). (iii) The inversely designed volume ratios obtained from the integrated model are represented.

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Within DNNs algorithm, adjusting the hyperparameters such as the depth of hidden layers, the number of neurons, learning rate, and weights in the loss function during the inverse design process leads to diverse outcomes. The results of inverse design for each set of hyperparameters in the RI model and the integrated model are summarized in the Section 2 of Supplement 1. One of the results from the RI model and the integrated model is represented in Fig. 3(b) and Fig. 3(c), respectively. Information about the hyperparameters of the models used can be found in Table S1 of Supplement 1. Figure 3(b)(i) exhibits the desired emissivity (i.e., black solid line), the calculated emissivity (i.e., red solid line) derived from TMM based on inversely designed refractive indices in the RI model, and the emissivity (i.e., blue solid line) determined based on inverse-designed volume ratio in the VR model. Figure 3(b)(ii) depicts a comparison between the targeted refractive indices (i.e., black and red solid line) derived from RI model, and the calculated refractive indices (i.e., green and blue solid line) derived from EMT based on inverse-designed volume ratios from VR model. Figure 3(b)(iii) represents the volume ratio obtained from the VR model, with each result targeting the refractive indices generated through the RI model. For results from the integrated model, Fig. 3(c)(i) illustrates the comparison between the desired emissivity spectrum (i.e., black solid line) and calculated emissivity (i.e., red solid line) results from TMM process. Comparison between the optical constants (i.e., blue and green solid line) from the RI model and those (i.e., black and red solid line) from the EMT calculation is depicted in Fig. 3(c)(ii). The inversely designed volume ratio from the integrated model can be observed in Fig. 3(c)(iii). The integrated model offers the advantage of enhanced usability compared to the existing separate models. However, upon comparing the results, the integrated model does not significantly differ from those obtained using the existing models.

3.4 StRCs and SoRCs particle size distributions and performances

As shown in Fig. 4(a), the particle size model (PS model) consists of two neural networks: inverse network and forward network. The inverse network aims to estimate particle size distribution (PSD_out) of films from reflectance (R_in) in the solar spectral region. The forward network predicts reflectance (R_cal.) from the particle size distribution (PSD_out). Each network is a fully connected network featuring four hidden layers, labeled as ‘N₅ Layers’ for the inverse network and ‘N₆ Layers’ for the forward network, with 100 neurons per layer. The forward network replaces calculation processes such as TMM calculation in the RI model and EMT calculation in the VR model, improving design quality during the inverse design process. This substitution is necessary as optical efficiencies cannot be accurately calculated through EMT calculation below the wavelength of 4 µm, which includes solar spectral region. This limitation primarily arises from the fact that the medium cannot be considered homogeneous, as the particle size is comparable to the wavelength. In the Section 3 of Supplement 1, a detailed explanation for applicability of EMT calculation is provided. To generate datasets for the PS model, RCWA simulation is utilized to obtain the optical efficiencies of particle-embedded films. The particles within the structure are randomly positioned following particle size distributions derived from Gaussian distributions. The detailed explanation of generating random structure can be found in the Method section. The particles composing the structure adhere to the volume ratios obtained through the RI and VR inverse design model. The datasets consist of labeled PSD and reflectance calculated using RCWA simulation with randomly generated structures. The two networks are trained using the datasets, and after the training is complete, the forward network remains fixed while being used in the inverse design process along with the inverse network. During the inverse design process, the PS model predicts PSDs that satisfy low reflectance for StRCs and high reflectance for SoRCs in the solar spectral region. The detailed performance of PS model is described in the Section 4 in Supplement 1. In Fig. 4(b), which is the results of PS model, a noticeable contrast is illustrated in the inversely designed distribution of particles composing StRCs and SoRCs. The PSD of StRCs consists of larger particles, leading to a sparser structure that results light transmission. In contrast, the PSD of SoRCs comprises smaller particles, contributing to increased Mie scattering in the solar region.

 

Fig. 4. (a) Schematics of the PS model, consisting of two networks: the inverse network (orange dashed box) and the forward network (purple dashed box). (b) Particle size distribution of two types of RCs obtained from PS model. (c) Electric field intensity profiles for StRC and SoRC at 500 nm. The comparison of transmitted electric field power and volume ratios of StRC and SoRC. (d) Optical efficiency spectrum, including reflectance (red dashed line), absorption (blue dashed line), and transmittance (black dashed line) of StRC, is plotted in the top side. Reflectance (red solid line), absorption (blue solid line), and transmittance (black solid line) of SoRC is plotted in the bottom side, with additional reflectance (green solid line) when the thickness of the SoRC is 100 µm. (e) Net power of StRC with a silicon solar cell and net power of SoRC for each non-radiative heat transfer coefficients.

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To validate optical properties of inversely designed structure, optical simulations are utilized. The detailed information about optical simulations is described in the Method section. For optical simulations, nanoparticles are randomly positioned in the StRC and the SoRC, according to inversely designed volume ratios and particle size distributions for each type, with 500 particles. As shown in Fig. 4(c) the electric field distributions is calculated through the finite-difference time-domain (FDTD) simulation. The comparison of electric field intensity profiles reveals wave propagation at 500 nm (i.e., intense spectral regime in solar spectrum) in Fig. 4(c). In the StRC, the wave propagates through the structure, whereas the SoRC exhibits high reflectance, resulting in a 58% reduction in transmitted electric field power (i.e., 0.3779 a.u. to 0.1584 a.u.) despite maintaining identical volume ratios. This result is explained by smaller particles in SoRC than those of StRC, which are proper to cause multiple Mie scattering in solar spectrum.

The RCWA simulations verify the features of SoRC and StRC, respectively, as shown in Fig. 4(d). Within the solar spectral region, particularly from 400 nm onwards, StRC demonstrates high transmittance, while SoRC exhibits higher reflectance than transmittance. Simultaneously, both structures reveal a strong thermal emission in the atmospheric transparent window region. For SoRC structure, higher reflection is observed as the thickness increases, which is 100 µm (i.e., green solid line). As the thickness of film increases, scattering enhances due to an extension in the optical path, resulting in higher reflection. When the thickness is 100 µm, which is 10 times thicker than the existing film, additional inverse designs are obtained for each radiative cooler. The detailed results of inverse designs for a higher thickness of 100 µm are explained in the Section 5 in Supplement 1. In Fig. 4(d), the optical efficiencies of the SoRC suggest a thicker SoRC and higher solar reflectance as thicker SoRC can offer more opportunities that causes Mie scattering by particles.

To evaluate the thermal performance of StRCs and SoRCs, the net power is calculated, differently for each, as depicted in Fig. 4(e). In the case of StRCs, the net power is determined when StRC is positioned on top of a silicon solar cell. The net power is determined by the energy balance equation, given by [44] in Eq. (5):

For SoRCs, the net power is determined by excluding the P_out(T_s) term in the equation. As shown in Fig. 4(e), the net power of the StRCs with solar cell is 85.53, 181.83, and 356.28 Wm⁻² with the non-radiative heat transfer coefficient of 5, 7, and 10 Wm⁻²K⁻¹, respectively, at solar cell operating temperature of 75°C. Moreover, the StRCs integrated with a solar cell enable reducing the temperature by 16.4 K during solar cell operation when the non-radiative heat transfer coefficient is 10 Wm⁻²K⁻¹. For the SoRCs, the calculated temperature drop is 3.22, 2.61, and 2.06 K with the non-radiative heat transfer coefficient of 5, 7, and 10 Wm⁻²K⁻¹, respectively. The detailed calculation process for net power and temperature drop is described in the Section 6 and 7 in Supplement 1.

4. Conclusion

Our deep learning algorithms recommend specific variables for the design of radiative coolers tailored to the situations. These variables include the refractive indices, the volume ratio of corresponding materials, and the size distributions of particles. The suggested variables encompass variations in radiative cooler structures, such as those optimized for solar transparency or opacity, depending on the specific requirements of the situation. Our deep learning models are categorized into three types for each design variable. In the inverse design process, to enhance design quality, the RI and VR models connect calculation processes individually, while the PS model consists of two networks. These deep learning models can overcome the issues of non-uniqueness and non-convergence, allowing for diverse designs for desired spectra using DNN directly as an inverse design method. Furthermore, our study suggests integrating the RI and VR models, which demonstrates improved usability compared to separate models. Employing our algorithms during the design phase accelerates the process and enhances cost-effectiveness in achieving the desired optical characteristics for the structure. The inversely designed radiative coolers consist of particles such as SiO₂, TiO₂, Si₃N₄, Al₂O₃ and HfO₂ embedded within the PE film. Notably, the StRCs exhibit a sparsely distributed particle size, whereas the SoRCs possess a closely packed structure. The StRCs demonstrate remarkable performance characteristics, boasting a high emissivity of up to 93.2% in the LWIR region and a substantial transmittance of up to 93.3% in the solar region. Furthermore, the StRCs integrated with a solar cell enhance the efficiency and longevity of the solar cell by reducing the temperature by 16.4 K during solar cell operation when the non-radiative heat transfer coefficient is 10 Wm⁻²K⁻¹. The SoRCs exhibit notable characteristics, with a high emissivity of up to 94.9% in the AW region and, when the film thickness is 100 µm, a high reflectance of up to 90.4% in the solar region. In addition, the SoRCs demonstrate a cooling effect, capable of reducing the temperature by approximately 2.06 K when the non-radiative heat transfer coefficient is 10 Wm⁻²K⁻¹. Our proposed two types of RCs offer tailored solutions for diverse applications. In summary, our inversely designed StRC is suitable for the situation requiring cooling with solar transparency such as cooling solar cells and vehicles windows, while the inversely designed SoRC is particularly effective in energy-efficient building envelopes and sustainable agricultural structures.