## 3 Theory and Methods
### Convolutional LSTM Networks  
LSTMs, a variant of RNNs introduced by [PERSON] et al. (2016), differ from the traditional form by incorporating gates that enhance control over the gradient flow. These gates consist of the forget gate (F), which determines which components of the cell state can be discarded; the input gate (I), which regulates the addition or modification of components in the cell state; and the output gate (O), which determines the portion of the cell state to be output. The following equations and Figure 2 depict the three LSTM network modules:  
\[f_{t}=\sigma\Big{(}W_{f}\times[h_{t-1},x_{t}]+b_{f}\Big{)} \tag{6}\]  
\[i_{t}=\sigma(W_{i}\times[h_{t-1},x_{t}]+b_{i}) \tag{7}\]  
\[o_{t}=\sigma(W_{o}\times[h_{t-1},x_{t}]+b_{o}) \tag{8}\]  
\[\hat{C_{t}}=tanh(W_{c}\times[h_{t-1},x_{t}]+b_{c}) \tag{9}\]  
\[C_{t}=f_{t}\times C_{t-1}+i_{t}\times\hat{C_{t}}) \tag{10}\]  
\[h_{t}=o_{t}\times tanh(C_{t}) \tag{11}\]  
These gates enable LSTMs to overcome the issue of vanishing gradients and maintain longer-term memory. In traditional RNNs, the gradient often diminishes significantly over long sequences, rendering the learning process ineffective. The LSTM method for multivariate tuning comprises three stages: data conversion, LSTM modeling, and tuning. The data conversion module converts time-series data into supervised learning sequences and identifies the variable sets with the highest regression coefficients for the predictive value Y. The LSTM modeling module connects multiple LSTM perceptrons to construct an LSTM network. The tuning module iteratively adjusts the parameters based on root-mean-square deviations (RMSE) and updates the data for further training. The data conversion module tackles the challenge of multivariate problems with high dimensions by leveraging the periodicity of the data and reducing rows of data to a single row; it involves two processes: data preparation and data conversion. The second data conversion operation aims to combine multiple rows into one by transforming time-series data into supervised learning sequences based on the data's periodicity. Consequently, the operation defines the problem as finding a positive integer number. In the statistical downscaling problem, we consider the transfer function between high-resolution observations and coarse-resolution outputs using a spatiotemporal sequence of state variables as input. To address this, we propose an end-to-end trainable model called ConvLSTM SR (Convolutional LSTM Statistical Downscaling) by integrating fully connected LSTMs with convolutions. This model combines convolutional LSTMs with a super-resolution block. The LSTM model used in our study, along with a simplified block diagram, is depicted in Figure 2. The LSTM model is constructed using the function: \(C_{t}=f\ (X)\), where \(h_{t}\) represents the variable value, \(C\) denotes the climate state, \(O_{t}\) represents the set of predictor variables on the \(t_{\text{th}}\) day, and \(C_{t-1}\) represents the variable value on the \((t-1)\)th day. RMSD Technique Based on Multivariate Classification for Road Maintenance Systems and Climate Change  
Road maintenance systems (RMS) are critical for guaranteeing the safety and efficiency of nations' road networks. Concerns have been made about the negative consequences of climate change on road maintenance systems, which make road networks more vulnerable to weather events and consequent damage. To solve this issue, we offer RMSDC (Road Maintenance Systems Using Deep Learning and Climate Adaptation), a new strategy that uses Convolutional Long Short-Term Memory (ConvLSTM) techniques with climate change forecasts to improve road maintenance systems. We use a multivariate dataset in this study that includes road surface condition measurements (S1-S11), friction, temperature (Ta), moisture content (S7), road surface temperature (Tsurf), water content, vehicle speed, direction, geographical coordinates (latitude and longitude), elevation (height), and other relevant parameters.