This work presents a systematic comparative assessment of four machine learning methods for compressing Flamelet Generated Manifold (FGM) libraries in methane combustion simulations: Multi-Layer Perceptron (MLP), Random Forest (RF), Linear Regression (LR), and Support Vector Machine (SVR). Scalar dissipation rate and mixture fraction are used jointly as continuous input features, enabling each model to learn the full thermochemical response across the operating space. Models are trained on seven FlameMaster libraries and evaluated on fifteen unseen scalar dissipation rate conditions to assess genuine generalization capability. Hyperparameter optimization via cross-validated grid search identifies the optimal MLP configuration: four hidden layers (10-15-20-15 neurons), Tanh activation, and Adam solver. This model achieves a mean R² of 0.9747 across all species on the unseen test set (Temperature R²=0.9959, OH R²=0.9647). Random Forest achieves mean R²=0.9159, while Linear Regression performs poorly (mean R²=0.42), confirming the necessity of nonlinear methods for this thermochemical regression task. The results demonstrate that MLP-based FGM compression can achieve high accuracy with substantially reduced memory requirements compared to full look-up table storage.