Mathematical Models in AI: Theory and Applications

Mathematical models are the foundation of artificial intelligence (AI), allowing for the description, analysis, and prediction of complex systems and behaviors. Complex systems are mathematically modeled by evaluating their structure and behavior in order to acquire insights into interactions and unpredictable effects. Common approaches include system dynamics, network theory, and algebraic methods. Furthermore, artificial intelligence technologies such as machine learning (ML) and deep learning(DL) are used for prediction, classification, anomaly detection, optimization, and decision-making. These models fill the gap between theoretical ideas and real AI applications, providing the necessary framework for algorithms to learn from data, make judgments, and maximize performance. Complex systems are mathematically modeled by evaluating their structure and behavior in order to acquire insights into interactions and unpredictable effects. Common approaches include system dynamics, network theory, and algebraic methods. Furthermore, AI technologies such as machine learning and deep learning are used for prediction, classification, anomaly detection, optimization, and decision-making. This paper investigates the importance of mathematical models in artificial intelligence, concentrating on their theoretical basis and broad applications across multiple fields.