## 2 IDC Prototype Details and Fast Thermal Reconstruction Method
### Real-Time Thermal Environment Reconstruction Method  
Considering the large time consumption to obtain a large quantity of data through testing, an experiment-validated CFD model provides a fast and accurate way to simulate the temperature, velocity, and pressure of flow in the data center. 6 SigmaDCX R15 is used to generate datasets for real-time temperature prediction training. The controlled variables are the cabinet power and the setting temperature of the air conditioner. The real-time prediction method is an autoencoder-based U-Net neural network model, which can predict temperature fields of DC in real time. Based on the existing work of [PERSON] et al. [10], we modified their architecture to predict flow temperature of a two-dimensional plane. The architecture of the overall network is shown in Figure 3. The proposed network takes the current power of servers, CRAC temperature, and temperature sensor data as inputs and outputs a two-dimensional array as the predicted temperature field.  
This model works as a surrogate model during DQN training, providing high accurate temperature distribution. After optimizing hyperparameters during ablation studies, we prepared a test set of five simulations, which are new to the model, to evaluate the accuracy and robustness of predictions using mean absolute error (MAE) and mean absolute percentage error (MAPE).  
The results show that predictive MAE reduces to 2.27 \({}^{\circ}\)C, and MAPE reduces to 9.21%, providing accurate and reliable predictions, as listed in Table 1. For instance, Figure 4 shows an example of the predicted two-dimensional temperature field in the test set, together with the ground truth temperature field and the prediction error. The testing results proves  
Figure 2: Temperature measurement of six servers using thermocouples during the heating and cooling process. The cooling action starts from the time marked at the read dash-line.  
modeled as a Markov Decisional Process (MDP). The architecture structure of the DQN decision-making agent is illustrated in Figure 5.  
The training process employs a dual-network architecture comprising an evaluation network for action generation and a target network for value estimation. Both networks have three hidden layers with widths of 24-48-24, and are initialized with identical parameters. Since the cooling process is modeled as an MDP for decision-making, critical components (\(S\), \(A\), \(E\), \(R\), \(P\)) are setting, where \(S\) is state, \(A\) is action space, \(R\) is reward, \(E\) is dynamic environment changing with \(A\) and \(P\) stands for state-transition function. \(A\) replay memory buffer, termed as the experience pool, stores state transitions (\(S_{t}\), \(A_{t}\), \(R_{t+1}\), \(S_{t+1}\)), while an initial state \(S_{0}\) is randomly sampled from the state space \(S\). As illustrated in Figure 5, the iterative training cycle starts with the evaluation network generating action \(A_{t}\) for the current state \(S_{t}\). The fast thermal reconstruction module computes the real-time temperature distribution, from which the multi-objective reward \(R_{t+1}\) is derived via reward functions. Subsequent state \(S_{t+1}\) is determined based on the simulated data, with episodes terminating when rewards fall below a minimum threshold.  
Parameter optimization occurs through periodic sampling of batched experiences from the replay memory. The target network periodically synchronizes with the primary network parameters to stabilize training. This architecture decouples policy evaluation from improvement while experience replay mitigates temporal correlations, collectively enhancing convergence robustness. The learning rate is initialized at 0.1 for preliminary exploration, with systematic hyperparameter optimization conducted in subsequent phases.