ARTIFICIAL INTELLIGENCE TECHNOLOGIES IN MATHEMATICAL MODELING

Mathematical modeling plays a fundamental role in the development, analysis, and practical implementation of artificial intelligence (AI) systems. It provides a rigorous formal framework for representing real-world processes, learning mechanisms, and decision-making strategies. This paper examines the significance of mathematical models in artificial intelligence with particular emphasis on machine learning, neural networks, optimization algorithms, and probabilistic reasoning. The study demonstrates how mathematical formalization improves accuracy, robustness, interpretability, and scalability of AI systems. In addition, existing challenges and prospective research directions in mathematical modeling for artificial intelligence are discussed.

数学建模在人工智能（AI）系统的开发、分析与实际实现中发挥着基础性作用。其可为现实世界过程、学习机制与决策策略的形式化表征提供严谨的理论框架。本文探讨了数学模型在人工智能领域的重要意义，并着重围绕机器学习、神经网络、优化算法及概率推理展开论述。本研究阐明了数学形式化如何提升AI系统的准确性、鲁棒性、可解释性与可扩展性。此外，本文还讨论了人工智能领域数学建模现存的挑战与未来研究方向。