Statistical Modelling and Numerical Analysis for Predicting Nonlinear System Behavior

Nonlinear systems are prevalent in engineering, physics, and data-driven sciences, where small variations in input parameters can produce complex and unpredictable outputs. This paper presents an integrated approach that combines statistical modeling techniques with numerical analysis to predict and interpret the behavior of nonlinear systems. The methodology employs regression-based models, correlation analysis, and residual diagnostics to identify system trends and interdependencies. Complementary numerical methods, such as finite difference approximation and iterative solvers, are used to enhance the precision of predictive models. Simulation results demonstrate that hybrid statistical–numerical techniques provide improved accuracy and stability over purely analytical approaches. The study highlights the potential of data-assisted mathematical modeling in optimizing performance, reducing uncertainty, and supporting real-time decision-making in dynamic environments.