An ANN–CNN Hybrid Surrogate Model for Fast Prediction of 3D Temperature Fields in Large Datacenter Rooms

Abstract

The increasing energy consumption of large datacenters, with cooling systems constituting a significant portion, calls for efficient thermal management strategies. Conventional computational fluid dynamics (CFD) methods, although accurate, are time-consuming for supporting real-time tasks in dynamic datacenter environments. Machine learning (ML)-based methods, particularly artificial neural network (ANN)-based surrogate models, have emerged as potential alternatives, but they struggle with generalization across diverse working conditions. Meanwhile, ML models’ performance in large datacenters still remains unclear. This research introduces a hybrid surrogate model combining ANNs and CNNs for the precise and rapid prediction of 3D temperature distributions in large datacenters. The proposed method incorporates an ANN for feature processing and a CNN for decoding spatial features, leveraging both to capture complex airflow patterns and temperature distributions under varying conditions. A dataset of 500 CFD-simulated temperature fields based on a real datacenter is established for model training and validation. The CFD method is evaluated by comparing the simulation results with experimental data. Results of the ML models’ performance indicate that the proposed hybrid surrogate model outperforms the conventional ANN model, reducing mean absolute error (MAE) by 87.44%. Additionally, the model is 300,000 times faster than CFD simulations, offering an efficient solution for further supporting real-time thermal management.

1. Introduction

With the rapid development of the information society and the surge in demand for computing and storage resources, the energy consumption of datacenters has significantly increased in recent years, making it a crucial component of global energy consumption [1]. Nowadays, datacenters consume approximately 1% of the world’s total electricity [2], which might rise significantly in the coming decades as computing power demands continue to escalate [3]. Thus, it is crucial to improve the operational energy efficiency and achieve the energy conservation of datacenters.

Commonly, the energy consumption of datacenters is primarily driven by IT equipment, the cooling system, and auxiliary systems such as power distribution system and lighting system [4]. Among them, nearly 50% of the energy is used by the cooling system to provide airflow for cooling IT equipment [5]. Therefore, the cooling system has significant potential for energy savings. Developing effective cooling system control strategies (i.e., thermal management) to maintain energy efficiency while ensuring the safety of IT equipment is a key element in reducing energy consumption and carbon emissions for datacenters [6].

For achieving effective thermal management in datacenters, computational fluid dynamics (CFD) is widely regarded as the most powerful tool [7,8]. CFD methods aim to solve the governing equations of fluid mechanics numerically on computers, thereby enabling accurate prediction of airflow distributions in datacenter rooms, providing adequate and effective information for thermal management [9]. For example, Zhou et al. [10] optimized the thermal management system of a small datacenter by employing a validated CFD model (prediction accuracy within 2 °C of experimental results) to simulate airflow and heat transfer, thereby enhancing cooling efficiency and improving the uniformity of the temperature distribution. Cao et al. [11] used CFD simulations to optimize server inlet areas in a data center, achieving a reduction in the bottom server temperature from 309.2 K to 299.9 K without additional cooling infrastructure, thus enhancing thermal management and potential energy savings. However, the CFD process is inherently complex, as it requires the discretization of differential equations over a large number of mesh nodes [12]. This makes CFD simulations highly time-consuming, particularly in a datacenter scenario, where high-resolution modeling or complex geometries must be considered. Consequently, CFD methods are often limited to the design and optimization stage [13] and are generally unsuitable for real-time energy-saving control applications, which demand rapid computation of airflow patterns [14].

With the rapid development of artificial intelligence (AI), machine learning (ML) models, especially neural network (NN)-based surrogate models [15], have demonstrated significant potential and are expected to serve as a promising alternative to time-consuming CFD methods in real-time energy-saving operations [16]. This approach involves the development of predictive models using existing experimental or simulation datasets of airflow. It skips complex physical solving processes, as a well-trained model can provide accurate predictions in a very short time [17], fully meeting the computational speed requirements for real-time control. For instance, Wang et al. [18] used an artificial neural network (ANN) to predict the thermal effects of workloads on datacenter temperatures, achieving a reduction of 6.67 °C in the maximum temperature, which translates to a 13.34% reduction in cooling system power consumption. Athavale et al. [19] employed an ANN to predict rack inlet air temperatures in datacenters. The ANN demonstrated good accuracy in predicting rack inlet air temperatures, with an average absolute error of 0.7 °C, corresponding to a relative error of 3.2%. Fang et al. [20] proposed an improved deep neural network (DNN) combined with an attention mechanism to predict server temperatures in a datacenter, achieving a significant reduction in prediction error, with the mean absolute error (MAE) dropping from 3.51 °C for the standard DNN model to 0.65 °C, an improvement of 81.48%. Meanwhile, the surrogate model only required 0.47 s for prediction.

However, in real-world scenarios, the operating conditions of datacenter environments are highly variable, resulting in significantly different airflow patterns. For instance, the temperature of the incoming airflow fluctuates as the cooling system operates. [21]. The power of different server cabinets is variant depending on users’ demand [22]. The existing NN-based methods are usually proposed for a specific scene. Most of them suffer from poor generalization ability because they are trained and utilized in the same working conditions [23]. Their precision and reliability would be doubtful when they are applied in new working conditions which are outside of the training data. Meanwhile, existing studies have primarily been conducted on smaller datacenters. In comparison, large datacenters serve as the main energy consumers in the datacenter industry [24]. These larger facilities exhibit more diverse operating conditions, resulting in more complex and variant airflow fields [25]. Therefore, a question arises about how to utilize ML-based methods in effectively predicting airflow distributions of large datacenter rooms under various working conditions, as these ML-based methods are trained on the CFD database, with limited working conditions. In essence, the scientific problem is the generalization ability of ML-based models, which is the ability to predict airflow distributions in large datacenters under diverse and fluctuating operational conditions, in order to provide high-quality data support for real-time thermal management applications in datacenters, thereby further enhancing the effectiveness of thermal management.

For conventional ANN-based methods, there are two main challenges for directly utilizing them to handle the aforementioned situation. Firstly, the fully connected structure in conventional ANN-based methods assumes that the output units are independent of each other [26], which does not align with the spatial correlations inherent in airflow patterns. In scenarios where airflow distribution varies across diverse operating conditions, the spatial dependencies between different regions of the flow field are more crucial, making fully connected structures inadequate for accurately capturing and predicting these variations. Secondly, due to the dense connectivity of fully connected structures, conventional ANN-based methods require an enormous number of parameters when handling high-dimensional inputs and outputs [27]. In the context of large data centers, the dimensions of the input features (i.e., working conditions) are relatively higher, while the outputs (i.e., airflow fields) are characterized by intricate spatial structures and high resolution. This not only results in substantial memory consumption for conventional ANN-based methods, but also leads to prohibitively high computational costs and extended training times. In summary, there still lacks an appropriate method that can effectively learn the relationship between complex input condition vectors and the spatial distribution of output airflow patterns, while efficiently generating detailed spatial airflow distributions in large datacenter rooms.

In the artificial intelligence community, the convolutional neural network (CNN) is one of the most crucial concepts. It is inspired by the visual perception of humans, who can focus on key portions of a large object that needs to be analyzed. Instead of a fixed sequence for conventional ML-based methods, it takes a 2D/3D tensor as input/output and introduces convolutional operators to process spatial features [28]. The CNN has found extensive applications in the domain of computer vision, including tasks such as image recognition [29], space semantic segmentation [30] and video comprehension [31], etc. Results indicate its powerful capacity in uncovering hidden knowledge in spatial data, learning the complex relationships between input features and output space. Hence, combined with the processing ability for complex features of ANN, the CNN has great potential to overcome the challenge of fast and accurate airflow predictions under different working conditions in large datacenter rooms. However, to the best of the authors’ knowledge, the feasibility and effectiveness of CNN-based methods in the domain of large datacenter room environment analysis are still unclear. There still lacks a framework to merge CNN with conventional ANN-based methods to analyze airflow in large datacenter rooms.

To address this issue, this paper proposes an ANN–CNN hybrid method to rapidly predict the temperature distributions of large datacenter rooms under variant working conditions. This study makes three main contributions. Firstly, an ANN–CNN hybrid framework is proposed. The role of the ANN component is to transform the input operating conditions into feature vectors that can be processed by the CNN. The CNN is responsible for efficiently decoding these latent feature vectors to reconstruct the target temperature fields. Secondly, a simulated dataset containing 500 3D temperature fields with different working conditions is established and validated based on a real large datacenter in Hubei, China. The simulation is processed by 6 Sigma 15 software [32]. Thirdly, comprehensive evaluations on different airflow regions are made to evaluate the performance of the proposed method across different operating conditions.

2. Method

The structure of the proposed method is illustrated in Figure 1, comprising three steps, i.e., data preprocessing, label transformation, and airflow prediction based on the ANN–CNN framework. The data preprocessing part aims to obtain high-quality data from raw CFD data. There are two steps, i.e., feature selection and data normalization. Based on the preprocessed data, the purpose of label transformation is to construct suitable labels for the surrogate model, which represent the spatial relationships and temperature patterns of airflow in datacenter rooms properly. The ANN–CNN-based airflow prediction part aims to predict target airflow distributions under variant working conditions. It consists of two main components, i.e., the ANN feature processor and the CNN decoder.

2.1. Data Preprocessing

2.1.1. Feature Selection

Feature selection ensures that the surrogate model learns from the most relevant and impactful features, thereby enhancing its ability to make accurate and reliable predictions. In this study, we select four types of features from raw CFD data. Firstly, airflow distributions are selected since it they are the target feature, representing the output we seek to predict. Secondly, environmental conditions such as inlet temperature, which are considered relevant to HVAC system and have a great impact on global airflow patterns, are selected as one part of the input features. Thirdly, server cabinet conditions, including heat source, which directly impacts airflow patterns, are selected as another part of the input features. Lastly, for more efficient training and faster prediction, the 3D labeled data is decomposed into 2D slices through height dimension (see Section 2.2). Thus, the target plane height is also selected as the input feature. By segmenting these features into the above-mentioned parts, we aim to ensure that the surrogate model can process data efficiently and learn both the environmental cooling factors within the HVAC system and the heat source within the server system.

2.1.2. Data Normalization

To improve convergence speed, prevent gradient issues, and enhance the training stability of the surrogate model, the min-max normalization [33] is applied in this study to scale numerical variables (i.e., airflow distributions and working conditions) to a fixed range of [0, 1], as shown in Equation (1).

$$x_{norm}={\displaystyle \frac{x-min\left(x\right)}{max\left(x\right)-min\left(x\right)}}$$

(1)

where x is the original value of the variable, min(x) is the minimum value of the variable in the dataset, max(x) is the maximum value of the variable in the dataset.

2.2. Label Transformation

Convolutional-based models, such as the CNN, exhibit strong capabilities in processing spatial features. However, they encounter challenges when handling irregular geometric representations due to their mathematical foundations. To overcome this limitation, a label transformation method is proposed to convert the target airflow distributions into suitable outputs for surrogate models. Initially, the datacenter room space is discretized into a Cartesian grid [34] with an appropriate spatial resolution. Subsequently, target airflow fields are resampled to the corresponding resolution and assigned to each grid cell. The resampling airflow fields serves as labels, which become the outputs for the surrogate model. To ensure that the output labels of surrogate models preserve enough spatial details of the target physical field while remaining computationally feasible, the resolution of output airflow fields is selected to balance the accuracy with the computational efficiency. Finally, considering that 3D convolutions typically require much more parameters and higher memory usage, making them more computationally expensive, the processed 3D data is further decomposed into several 2D slices through height dimension. In practice, the proposed surrogate model is trained to predicted these 2D slices individually, then compose them into the target 3D airflow distributions.

2.3. ANN–CNN Hybrid Surrogate Model for Airflow Prediction

An ANN–CNN framework is developed to predict airflow distributions under diverse working conditions in large datacenters. Figure 2 shows the architecture of the proposed ANN–CNN model, there are two main components, i.e., the ANN-based feature processor and the CNN-based decoder.

2.3.1. ANN-Based Feature Processor

ANN is the main component of many neural networks. It can represent a highly non-linear relationship between inputs and outputs. In this study, the ANN-based feature processor receives a 1D vector with n variables as input features representing working conditions. Several fully connected layers are incorporated, in order to merge different features effectively, which are defined by Equation (2).

$${\mathit{x}}_{i+1}=\sigma ({\mathit{W}}_i{\mathit{x}}_i+{\mathit{b}}_i)$$

(2)

where ${\mathit{x}}_i$ denotes the input vector for the i-th layer. $\mathit{W}$ and $\mathit{b}$ are the weight matrix and bias vector to be learned, respectively. $\sigma$ denotes the ReLU function [35].

2.3.2. CNN-Based Decoder

The CNN-based decoder receives the merged feature vector of the datacenter environment from the ANN-based feature processor and aims to gradually generate the target airflow distribution. It is composed of an input layer and several convolutional modules. The input layer reshapes the merged feature vector produced by the ANN into features in 2D array form sequentially, allowing merged features to be transmitted to the convolutional modules. Each convolutional module consists of an up-sampling layer followed by a convolutional layer. Equation (3) defines the convolutional layer, applying a series of 2D convolutional kernels to generate hidden features for the subsequent layer.

$${\mathit{X}}_i^{out}=\sigma ({\mathit{W}}_i\ast {\mathit{X}}_i^{in}+{\mathit{b}}_i)$$

(3)

where ${\mathit{X}}_i^{in}$ is the input feature of the i-th convolutional layer and $\mathit{W}$ and $\mathit{b}$ are weight matrix and bias vector to be learned, respectively. $\sigma$ denotes the ReLU function, * is the convolutional kernel [29], and ${\mathit{X}}_i^{out}$ is the output feature of the i-th convolutional layer.

The upsampling layer is employed to increase the spatial resolution of features, aligning them with the resolution of the target airflow field. In this study, the nearest neighbor upsampling with 2 × 2 resolution is chosen, as defined in Equation (4).

$${\mathit{Y}}_{i,j}={\mathit{X}}_{⌊{\displaystyle \frac{i}{2}}⌋,⌊{\displaystyle \frac{j}{2}}⌋}$$

(4)

where $\mathit{X}$ is the input feature in 2D array form, $\mathit{Y}$ is the output feature in 2D array form, i and j correspond to the grid positions of $\mathit{Y}$, $⌊i⌋$ and is the largest integer less than or equal to i.

2.3.3. Model Training

After defining the ANN–CNN hybrid structure, the surrogate model is trained using the mean square error (MSE) loss function, as expressed in Equation (5). The training process aims to minimize this loss function to optimize the model.

$${Loss}_{mse}={\displaystyle \frac{1}{m}}{\sum }_1^m({\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{(y_i-\widehat{y_i})}^2)$$

(5)

where $y_i$ is the predicted value of the i-th grid cell, $\widehat{y_i}$ is the true value of the i-th grid cell, n is the number of grid cells in one sample, and m is the number of samples in the training set.

3. Dataset Description

3.1. CFD Model of Datacenter Room

A real large datacenter in Hubei, China is selected to verify the proposed method. Figure 3 presents a schematic representation of the datacenter room; there are 10 micro-modules in a room. Each micro-module contains 27–28 server cabinets, each server cabinet is designed with a power limitation of 6kW, resulting in a total IT equipment max power of 168 kW per micro-module and a total IT equipment max power of 1656 kW per room. The cooling system of the IT rooms utilizes air-wall Air Handling Units (AHUs) for horizontal, diffused air supply, with hot aisles enclosed at the sides of the server cabinets. Cold air is dispersed from the AHU sides into the cold aisle (the room’s cooling zone), eliminating the need for a raised floor. After absorbing the heat from the server cabinets, the cooled air is returned from the rear of the cabinets into the closed hot aisle, and then through a hot return air duct (located in the ceiling) to the return air intake of the air handling units. The cooling system is designed with a dual-side air supply configuration. Each side of the air-wall AHUs follows a 5 configuration, and the entire room is equipped with a total of 10 air-wall AHUs. The room is 28.8 m long, 27.6 m wide, and 5.5 m high. The CFD simulations are run using 6 Sigma software. The detailed CFD settings are shown in

Table 1. CFD simulation settings.

Mesh information
Mesh number	468,4670
Maximum element size (m)	0.250
Minimum element size (m)	0.017
Maximum element growth rate	8.0
Solver conditions
Numerical model	RANS k-ε
Air assumption	Constant physical properties, incompressible
Residual	10−3

.

After establishing the CFD model of the datacenter room, the CFD simulation method is validated by utilizing the same setting from a real operation condition; the airflow inlet temperature of each AHU and the power of each server cabinet are shown in Figure 4. Then, the simulation results are compared with experimental measurements. For the server cabinets, six typical cabinets are selected, for each cabinet, the inlet and outlet temperature at two different heights are measured; the results are shown in

Table 2. Comparison between actual measured values and simulated values of selected cabinets.

Cabinet	Position	Height (m)	Measurement (°C)	Simulation (°C)	Error (°C)
102	Inlet	0.8	24.4	24.2	0.2
		1.5	24.5	24.2	0.3
	Outlet	0.8	29.1	29.9	−0.8
		1.5	28.6	27.6	1
110	Inlet	0.95	24.8	24.2	0.6
		1.5	24.8	24.2	0.6
	Outlet	0.95	31.8	31.0	0.8
		1.5	30.9	30.4	0.5
202	Inlet	0.65	22.8	23.7	−0.9
		1.2	23.4	23.7	−0.3
	Outlet	0.65	29.2	28.7	0.5
		1.2	31.7	31.2	0.5
605	Inlet	0.8	24.4	24.0	0.4
		1.5	24.4	24.0	0.4
	Outlet	0.8	32.2	31.5	0.7
		1.5	31.9	31.6	0.3
609	Inlet	0.8	23.8	23.6	0.2
		1.5	24.2	23.9	0.3
	Outlet	0.8	32.0	31.3	0.7
		1.5	32.0	31.4	0.6
613	Inlet	0.8	24	23.9	0.1
		1.5	24.2	23.9	0.3
	Outlet	0.8	31.7	31.2	0.5
		1.5	33.0	32.8	0.6

. For the AHUs, each running ACU’s airflow supply temperature is measured; the results are shown in

Table 3. Comparison between actual measured values and simulated values of ACUs.

ACU	Measurement (°C)	Simulation (°C)	Error (°C)
01	24.8	24.2	0.6
04	18.8	19.7	−0.9
06	23.6	23.9	−0.3
07	21.9	22.2	−0.3
08	24.4	23.7	0.7
09	22.8	22.6	0.2
10	21.0	20.8	0.2

. The results demonstrate a strong correlation between the CFD simulation data and the measured data. Consequently, the CFD simulation dataset produced using this CFD model can be considered reliable.

3.2. Dataset Generation

After establishing a reliable CFD simulation method for the datacenter room, 500 CFD cases with different airflow conditions are further generated by randomly changing the airflow inlet temperature of each AHU and the power of each server cabinet. The inlet airflow temperature is a low spatially dependent variable, which affects the global temperature intensity. The power of each server cabinet is a local spatial variable, which has significant influence on the distribution of the heat source. The ranges of the airflow inlet temperature of each AHU and the power of each server cabinet are listed in

Table 4. Ranges of key items varied in this study.

Factor	Range
Airflow inlet temperature (°C)	[18, 30]
Server cabinet’s power (kW)	[0, 6]

according to actual operational data. The selection is based on covering a broad spectrum of realistic working conditions for the target large datacenter, ensuring that both low and high extremes of inlet temperature and server power were included. The purpose was to generate a diverse range of airflow patterns and thermal conditions, representing various possible operational states of the datacenter. Figure 5 demonstrates the variation in airflow distribution within the same sample at different heights in the CFD dataset, showcasing the diverse patterns and behaviors of temperature flow across different slices. The temperature distributions reveal how airflow structures change within the space, with some areas exhibiting higher concentrations of heat while others maintain lower temperatures. This indicates the complexity of airflow organization in a large datacenter room, emphasizing how various factors, such as spatial location and environmental conditions, influence the distribution of heat within the sample. Figure 6 and Figure 7 further showcase significant variations in airflow patterns and thermal conditions across different samples in the dataset. Each sample, due to its distinct operational parameters, demonstrates unique airflow organization and temperature distribution. Figure 6 illustrates the distribution of various operational conditions within the dataset, demonstrating that the values are fairly uniform and cover a comprehensive range of operating conditions. The cabinet power values and ACU temperature set points are evenly distributed, indicating a well-rounded representation of different operational states. This balanced coverage allows the surrogate model to perform a more accurate assessment of airflow behavior across the full spectrum of operational scenarios, providing a foundation for the surrogate model to understand how different conditions impact the internal airflow organization and temperature distribution. In Figure 7, the differences in temperature distributions across various ACUs highlight how distinct operational environments lead to highly dissimilar airflow structures. These variations are reflected in the corresponding frequency histograms for cabinet power and the recorded temperature values, which fluctuate significantly depending on the specific operating conditions of each sample. The complex and dynamic nature of airflow within the dataset demonstrates how internal conditions, such as power usage and temperature set points, dramatically influence the airflow organization within the system.

4. Evaluation

4.1. Accuracy Metrics

Three common accuracy metrics are utilized to evaluate the ANN–CNN hybrid surrogate model, i.e., mean absolute error (MAE), mean absolute percentage error (MAPE), and coefficient of determination (R²). The definition of these accuracy metrics is shown in Equations (6)–(8).

$$MAE={\displaystyle \frac{1}{m}}{\sum }_1^m({\displaystyle \frac{1}{n}}{\sum }_{i=1}^n|y_i-\widehat{y_i}|)$$

(6)

$$MAPE={\displaystyle \frac{1}{m}}{\sum }_1^m({\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{\displaystyle \frac{|y_i-\widehat{y_i}|}{\widehat{y_i}}})$$

(7)

$$R^2={\displaystyle \frac{1}{m}}{\sum }_1^m({\displaystyle \frac{1}{n}}{\sum }_{i=1}^n(1-{\displaystyle \frac{{(y_i-\widehat{y_i})}^2}{{(\overline{y}-\widehat{y_i})}^2}}))$$

(8)

where $y_i$ is the predicted value of the i-th grid cell, $\widehat{y_i}$ is the true value of the i-th grid cell, n is the number of grid cells in one sample, and m is the number of samples in the training set.

4.2. Performance of the Proposed Method

For evaluating the capability of the proposed method, the ANN-based surrogate is selected for comparison since it has been widely used in predicting temperature fields in small datacenters under specific working conditions. U-Net [36], a variant of the CNN architecture, is also considered for comparison by replacing the CNN part in the proposed ANN–CNN structure. This aims to validate the role of convolutional-based neural networks more comprehensively. The dataset is partitioned randomly, with 90% allocated to the training set (450 samples) and 10% to the testing set (50 samples). In this scenario, the data in the testing set exhibit substantial differences from the training set, as the input features (i.e., working conditions) are assigned randomly, leading to completely distinct airflow patterns for each sample. This split ensures that the surrogate model can be trained on a diverse set of conditions while being evaluated on unseen data to test its generalization ability, which aims to verify the generalization ability of surrogate models under limited CFD data. The exact splitting procedure is randomized to minimize any bias that could arise from the order of the cases. The ANN baseline model, the ANN–CNN hybrid model and the ANN–U-Net hybrid model are all trained in the training set, then verified in the testing set. All surrogate models are implemented using PyTorch 2.9.0 [37], an opensource python library for machine learning. Training hyperparameters are configured according to standard recommended values. In detail, the batch size is set as 50, the number of epochs is set as 100, loss function is set as the mean square error (MSE) defined by Equation (5), and the optimization method used during training process is set as Adam [38].

To identify the best combination that maximizes all surrogate models’ performances, we use a grid search to systematically explore a predefined set of hyperparameters. Firstly, the hyperparameters that need to be tuned are selected, and their search ranges are defined. Secondly, every possible combination of hyperparameter values within the defined range is evaluated. Finally, the combination that yields the best performance according to the evaluation metrics is selected. The selected crucial hyperparameters and their ranges, as well as the optimal values of surrogate models, are listed in

Table 5. Optimal hyperparameters of the surrogate model.

Model	Hyperparameter	Search Space	Optimal Value
ANN	Number of hidden layers	[1, 2, 3, 4, 5, 6]	5
	Number of neurons in each hidden layer	[128, 256, 512, 1024, 2048]	1024
ANN–CNN	Number of convolutional layers	[1, 2, 3, 4]	2
	Number of filters in each convolution layer	[16, 32, 64, 128, 256]	64 for the first layer, 32 for the second layer
	Number of fully connected layers in the fully connected module	[1, 2, 3, 4, 5]	3
	Number of neurons in each fully connected layer	[128, 256, 512, 1024, 2048]	1024
	Size of convolutional kernel	[3 × 3, 5 × 5, 7 × 7, 9 × 9]	[3 × 3]
ANN–U-Net	Number of convolutional layers	[1, 2, 3, 4]	3
	Number of filters in each convolution layer	[16, 32, 64, 128, 256]	64
	Number of fully connected layers in the fully connected module	[1, 2, 3, 4, 5]	3
	Number of neurons in each fully connected layer	[128, 256, 512, 1024, 2048]	1024
	Size of convolutional kernel	[3 × 3, 5 × 5, 7 × 7, 9 × 9]	[3 × 3]

. Parameters related to the kernel size, such as stride and padding, are determined based on the optimized kernel size to maintain the spatial dimensions of the output feature map. Specifically, the optimal kernel size is 3 × 3 in this work; thus, stride and padding are both set as 1. The loss curves of the training process of the three surrogate models under the selected hyperparameters are shown in Figure 8.

Table 6. Accuracy comparison of the surrogate models.

Model	MAE (°C)	MAPE	R2
ANN	4.147	23.27%	0.299
ANN–CNN	0.521	1.96%	0.930
ANN–U-Net	0.575	2.18%	0.912

presents the prediction accuracy of the three models in the test set.

From the training loss curves, the baseline ANN model demonstrates relatively slower convergence and higher loss fluctuations during training, suggesting less stable gradient updates and limited capacity to capture the spatial complexity of the temperature field. In contrast, both the ANN–CNN and ANN–U-Net hybrid surrogate models achieve much faster and smoother convergence, with the loss rapidly dropping to a stable plateau within the first 20 epochs. This improvement can be attributed to the CNN-based parts, which enable more efficient spatial-feature extraction and enhance the models’ ability to learn local and global thermal patterns simultaneously. Between the two hybrid architectures, the ANN–U-Net model shows slightly smoother convergence behavior, reflecting its skip-connection structure that facilitates stable information propagation across different network depths. The addition of a CNN-based decoder enhances the model’s learning ability, making the model training process more effective. Accuracy comparisons indicate that the ANN–CNN hybrid model and the ANN–U-Net hybrid model both significantly outperform the ANN baseline model in predicting the temperature field in large datacenter rooms when facing unseen working conditions. Specifically, the ANN–CNN hybrid model’s MAE represents an 87.44% and a 9.39% reduction compared to the baseline ANN model and the ANN–U-Net model, respectively. The ANN–CNN hybrid model’s MAPE represents a 91.57% and a 10.09% decrease relative to that of the ANN baseline model and the ANN–U-Net model, respectively. The ANN–CNN hybrid model’s R² represents a 210.37% and a 1.94% improvement over that of the ANN baseline model and the ANN–U-Net model, respectively.

4.2.1. Model Performance in Different Positions

To visually assess the models’ performance in predicting airflow temperature fields under different spatial position, a case from the testing set is randomly selected. Figure 9 visualizes temperature fields simulated from the CFD method and temperature fields predicted by the ANN–CNN hybrid surrogate model and the ANN–U-Net hybrid surrogate model, which allows for a more intuitive understanding. The visualized results from the testing set demonstrate the performance of the trained model in predicting the temperature field within the datacenter room at various positions. Results show a clear alignment in the overall temperature distribution patterns across different height planes. Both models successfully capture general thermal structures, reflecting similar trends in both the true and predicted temperature fields. However, both models exhibit higher prediction errors at the cabinet locations, particularly in non-rack planes, such as the plane at 0.0 m (Figure 9a), where discrepancies between the predicted and true temperature fields are more pronounced. These errors are particularly noticeable in regions without racks, where the cooling dynamics are different, and airflow distribution is less consistent compared to areas with cabinets. While both the ANN–CNN and ANN–U-Net models show strong performance in predicting the overall temperature pattern, the ANN–U-Net model tends to produce smoother and more continuous representations of the airflow temperature fields, whereas the ANN–CNN model yields sharper and more spatially distinct thermal patterns, especially in the higher plane heights (such as 4.0 m and 5.0 m).

4.2.2. Model Performance in Different Samples

Four cases from the testing set are randomly selected to visualize the models’ performance in predicting airflow temperature fields under working conditions. This enables an intuitive understanding of the errors produced by the surrogate model. Figure 10 visualizes temperature fields simulated from the method and temperature fields predicted by the ANN–CNN hybrid surrogate model and the ANN–U-Net hybrid surrogate model in columns. The results demonstrate the ability of the models to accurately predict the temperature fields at the same height across different samples with varying operating conditions. Both surrogate models demonstrate a strong ability to reproduce the general temperature distribution patterns observed in the CFD simulations, effectively capturing the major thermal structures across all cases. The temperature fields predicted by the ANN–CNN model exhibit sharper and more distinct thermal boundaries, while the ANN–U-Net model tends to generate smoother and more continuous flow structures. This difference suggests that the ANN–CNN model emphasizes local thermal gradients, whereas the ANN–U-Net model achieves better spatial coherence and continuity in the predicted fields. Across all four cases, the predicted results closely align with the true temperature fields, with only minor deviations near the cabinet regions and airflow outlets. The mean absolute error for each case remains low, indicating that both models maintain high predictive accuracy even under varying operational conditions. The consistency of predictions across different scenarios highlights the robustness and adaptability of the hybrid surrogate models in large datacenter environments.

4.2.3. Model Performance Under Unseen Extreme Condition

To further evaluate robustness and potential overfitting of surrogate models, an additional extreme condition is designed beyond the range of the training dataset. In this case, all server cabinets operate at maximum capacity, with each cabinet power set to 7 kW, exceeding the dataset’s upper limit of 6 kW. Moreover, the supply air temperatures of AHUs are reduced to 17 °C, below the dataset’s lower bound of 18 °C, to simulate a scenario requiring additional cooling capacity. This configuration pushes the models beyond their learned operational domain, providing insights into their generalization ability and stability under unseen, high-stress conditions. Figure 11 presents the temperature fields predicted by the ANN–CNN and ANN–U-Net hybrid surrogate models at various height planes under this extreme scenario. Results show that both models successfully reproduce the general flow structures and large-scale temperature distribution patterns, maintaining a consistent representation of the cold and hot aisle arrangements. However, their prediction accuracy decreases compared with the results under normal operating conditions, particularly in regions exhibiting strong thermal gradients and non-linear airflow interactions near the rack outlets and return zones. The ANN–CNN model demonstrates relatively better resilience, preserving clearer thermal boundaries and retaining sharper representations of localized hot spots. It continues to reflect the overall stratification trend within the datacenter environment, albeit with minor deviations near high-temperature zones. In contrast, the ANN–U-Net model tends to produce smoother and more homogenized predictions. This leads to greater blurring and loss of detail in scenarios characterized by steep temperature gradients. Consequently, the U-Net architecture shows a higher degree of performance degradation under extreme operating stress, indicating a potential sensitivity to over-smoothing when facing abrupt temperature transitions.

5. Discussion

5.1. Discussion on Model Generalization Ability

Comparative analysis of the models and visualized results demonstrate that the ANN–CNN hybrid model can accurately predict temperature distributions of large datacenter rooms under variant working conditions. The ANN-based feature processor enhances the model’s ability to efficiently handle complex input parameters, while the CNN-based decoder restores detailed airflow patterns. The depth and hierarchical nature of convolutional filters in the CNN-based models allow them to progressively capture more abstract spatial features, leading to superior accuracy in predicting airflow distributions. The sequential processor–decoder structure of the proposed method thus combines the advantages of feature extraction and spatial correlation learning, achieving high predictive accuracy of airflow distributions when applied to unseen operational scenarios in large datacenter rooms.

Compared with conventional ANN-based approaches reported in previous studies [18,19,20], which primarily rely on fully connected structures and treat output nodes as independent, both hybrid models achieve markedly higher predictive accuracy, while the output temperature distributions are more detailed with higher spatial resolution. This improvement arises from the CNN-based components’ capacity to capture spatial correlations and hierarchical features within the airflow field—an ability absent in purely ANN-based architectures.

However, certain deviations between predicted and simulated temperature fields remain. These errors primarily occur near localized high-power-density regions and air inlets, where abrupt thermal gradients lead to more complex heat transfer phenomena that are challenging for data-driven models to capture accurately. Moreover, small discrepancies may arise from the training dataset, which constrains the model’s exposure to extreme operating conditions.

5.2. Discussion on Model Efficiency

Another critical aspect to consider is the computational efficiency of the surrogate models, specifically, the prediction time required for each working condition, because the primary objective of this study is to construct a fast simulation framework as an alternative to the conventional CFD approach, which is time-consuming. The average prediction time per working condition for surrogate models and the corresponding simulation time using the CFD method are listed in

Table 7. Time costs of surrogate models and the CFD method.

	ANN	ANN–CNN	ANN–U-Net	CFD
Average running time (s)	0.02	0.04	0.07	12643.52

. The results indicate that the prediction speed of the proposed model is comparable to that of a conventional ANN-based model, while being approximately 300,000 times faster than CFD simulations. Compared with other convolutional-based frameworks such as U-Net, the ANN–CNN model demonstrates comparable spatial reconstruction quality while maintaining greater computational efficiency, owing to its more compact feature-processing design. This enhancement in computational efficiency demonstrates the model’s potential for supporting various thermal management applications, for example, the real-time control of large data center environments.

6. Conclusions

In this study, an ANN–CNN hybrid surrogate model is developed for the rapid and precise prediction of airflow temperature fields in large datacenter rooms under variant working conditions. A CFD simulation dataset is generated based on a real large datacenter located in Hubei, China. This dataset consists of 500 distinct working conditions, each corresponding to a three-dimensional temperature field within the datacenter room. The reliability of the CFD model is validated through a comparison between the simulation results and actual measurement data. Then, a domain customized ANN–CNN framework is developed to process input working condition more effectively and predict airflow distribution with high-fidelity spatial details. The generalization ability of the proposed method is evaluated on a testing set with working conditions and temperature fields that are completely distinct from those in the training set.

Results of the comparison between the CFD simulation data and actual measured data demonstrate a high level of consistency. The errors between the measured and simulated temperatures are generally small, with most discrepancies falling within a range of less than 1 °C and percentage errors typically under 5%. This result demonstrates that the CFD simulation model is reliable and capable of generating datasets for further training surrogate models. The validation results of surrogate models indicate that the proposed ANN–CNN hybrid surrogate model and its variant, the ANN–U-Net hybrid surrogate model, are both capable of accurately predicting the temperature field of large datacenter rooms under operating conditions that are not encountered during the training process. Compared to the conventional ANN surrogate model, the ANN–CNN hybrid surrogate model achieved a reduction of 87.44% in MAE and 91.57% in MAPE, while its R² increased by 210.37%. The conventional ANN surrogate model exhibits significant errors in this task, with a MAE greater than 4 °C, making it difficult to provide effective predictions. Compared to the ANN–U-Net hybrid surrogate model, the ANN–CNN hybrid surrogate model achieved a reduction of 9.39% in MAE and 10.09% in MAPE, while its R² increased by 1.94%. Results show that convolutional-based decoders, i.e., CNN or U-Net, allow surrogate models to progressively capture more abstract spatial features, leading to superior accuracy in predicting airflow distributions under variant working conditions.

This study addresses the challenge of rapidly predicting the temperature field of large datacenter rooms under varying working conditions, providing a powerful tool for real-time, efficient thermal management of large datacenters. However, there are still areas for improvement. For example, the model occasionally struggles with local regions where airflow patterns are highly complex. Incorporating physical constraints into the model might be useful for enhancing its accuracy and reliability. In addition, the proposed method is now utilized in predicting temperature fields under certain spatial configuration. Further studies are necessary to extend this work to include diverse spatial conditions, achieving a more robust generalization capability, encompassing both the generalization across operating conditions and the generalization across spatial dimensions.