Artificial Intelligence-Based Mathematical Modeling: Recent Advances, Challenges and Future Directions

Mohammad Sayeed, Umesh Chandra Gupta, Nitin Bharti

Abstract: Artificial Intelligence (AI) is becoming an important tool for improving mathematical modeling and solving complex real-world problems. Traditional mathematical models have been widely used in science and engineering, but they often require more time, high computational effort, and may not perform well for complex and uncertain situations. AI techniques, especially Machine Learning and Deep Learning, can learn from data, identify hidden patterns, and make faster and more accurate predictions. As a result, AI-based mathematical modeling is now being used in many fields such as engineering, healthcare, finance, environmental science, transportation, and manufacturing. This review paper presents the recent advances in AI-based mathematical modeling and explains how AI is helping to improve the performance of mathematical models. It also discusses the main challenges, including data quality, model reliability, lack of transparency, and high computational requirements. In addition, the paper highlights future research directions, such as explainable AI, hybrid AI–mathematical models, physics-informed AI, and intelligent decision-support systems. Overall, the review shows that combining Artificial Intelligence with mathematical modeling can provide faster, more accurate, and more reliable solutions for solving complex scientific and engineering problems. This review will be useful for researchers, academicians, and professionals who want to understand the current progress, challenges, and future opportunities in AI-based mathematical modeling. Keywords: Artificial Intelligence; Mathematical Modeling; Machine Learning; Deep Learning; Optimization.