Algorithm 2: Deep Learning-based Traffic Flow Estimation

Input: Network structure G(N, A), Set of links with sensors (L_sensors), Reference demand matrix (T0), Stochastic User Equilibrium (SUE) assignment model, Number of auto-encoder layers (L), Hidden units per layer (H) Step 1: Data Preparation Generate synthetic training data: For i = 1 to sample_size (n):    Ti ← Randomly perturb T0 using a defined statistical distribution    Vi ← Assign Ti to network using SUE model to get full link flows EndFor Step 2: SAE Model Pre-Training (Unsupervised) X ← Measured flows from L_sensors for all Vi For each layer l in SAEs (bottom-up):    Initialize sparse auto-encoder AE_l    AE_l ← Train auto-encoder on X to minimize reconstruction error with sparsity constraint    X ← Encode X to hidden representation of AE_l for next layer EndFor Step 3: Fully Connected Layer Pre-Training (Supervised) Input_Features ← Output of final auto-encoder layer Fully_Connected ← Initialize fully connected layer Fully_Connected ← Train layer on Input_Features to predict full link flows Vi using supervised learning (Backpropagation) Step 4: Fine-Tuning (Supervised) For epochs = 1 to max_epochs:    Forward propagate Input_Features through SAE and Fully_Connected layer    Calculate prediction error between estimated and actual link flows Vi    Update all weights and biases through Backpropagation to minimize prediction error EndFor Output: Trained Deep Learning Model capable of estimating entire network flows from partial sensor measurements