Optimizing Artificial Intelligence Performance through Mathematical Modelling and Statistical Evaluation
DOI:
https://doi.org/10.31305/trjtm2025.v05.n01.010Keywords:
Artificial Intelligence Optimization, Mathematical Modelling, Statistical Evaluation, Performance Analysis, Algorithm EfficiencyAbstract
The improved accuracy of artificial intelligence (AI) has intensified the need for robust theoretical frameworks that ensure reliability, efficiency, and scalability of intelligent systems. While empirical success has driven much of modern AI development, sustained performance optimization increasingly depends on sound mathematical modeling and rigorous statistical evaluation. This paper examines how mathematical structures and statistical methodologies contribute to optimizing AI system performance across learning, inference, and decision-making processes. Core mathematical tools such as linear algebra, calculus, optimization theory, and dynamical systems are analyzed for their roles in model formulation, parameter estimation, and convergence behavior. Complementarily, statistical techniques including probabilistic modeling, statistical learning theory, uncertainty quantification, and hypothesis testing are explored as mechanisms for evaluating model robustness and generalization. The study adopts a systematic analytical approach grounded in established theoretical literature and representative case-based evidence, highlighting how mathematical and statistical principles guide model design choices and performance assessment. Emphasis is placed on understanding trade offs between model complexity, computational efficiency, and predictive accuracy. The paper further discusses how statistical evaluation metrics and validation strategies support objective performance comparison and reliability assessment in complex AI systems. By integrating mathematical modeling with statistical evaluation, the paper provides a unified perspective on performance optimization, offering insights relevant to next generation AI applications in data intensive and safety critical domains. The findings underscore that mathematically and statistically grounded methodologies are essential for developing AI systems that are not only powerful but also interpretable, stable, and trustworthy.
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