A Hybrid Mathematical Optimization and Deep Learning Framework for Intelligent Engineering Systems

Abstract

This paper suggests a Hybrid Mathematical Optimization-Deep Learning to intelligent engineering systems to improve predictive accuracy, convergence stability, and computational efficiency. The model combines Alex iterative neural network frameworks with deterministic optimization methods with a single objective function and parameter tuning mechanism. The model was tested with the help of a structured engineering dataset consisting of both operational and environmental variables as compared to single-use artificial neural network (ANN) and optimization-based methods. The experimental findings show that the proposed hybrid model has better performance with 96.8 percent accuracy and a substantially lower mean squared error (0.012), faster convergence and superior robustness in response to variation in input noise. The reliability and the ability to generalise the framework is confirmed by cross-validation and statistical significance testing. The fact of case study validation in smart manufacturing, energy load forecasting, and predictive maintenance also confirms scalability and realistic applicability. The suggested solution provides a well-developed, effective, and flexible system of next-generation intelligent engineering.