Comparative Evaluation of Machine Learning and Deep Learning Models for Nonlinear Regression under Increasing Input Uncertainty: A Synthetic Benchmark Study

Machine learning models are increasingly deployed in high-stakes domains, yet their reliability under imperfect input data remains poorly understood. This study presents a comprehensive benchmark of nine machine learning and deep learning models for nonlinear regression under increasing input measurement uncertainty. Using a synthetic data framework, we evaluate model performance across two distinct experimental settings: sequential prediction with temporal dependencies and static function approximation across four nonlinear tasks. Models were assessed on predictive accuracy (RMSE), uncertainty calibration (95\% interval coverage), and computational efficiency. Our results reveal a critical dependence on data structure: deep learning models (GRU, BNN) are superior for sequential tasks, while tree-based ensembles (Random Forest, XGBoost) are significantly more robust for static, high-dimensional tasks. Standard and Noisy Input Gaussian Processes exhibited catastrophic performance degradation under severe noise in complex static functions. LightGBM emerged as the most efficient model, balancing competitive accuracy with unmatched speed. These findings provide a clear guide for model selection, highlighting that no single architecture is universally optimal and that robustness to input uncertainty is highly task-dependent.