ADVANCING COMPUTATIONAL MATHEMATICAL MODELING: INTEGRATING QUANTUM COMPUTING AND AI-DRIVEN OPTIMIZATION FOR COMPLEX SYSTEM SIMULATIONS
Keywords:
Computational mathematical modeling, numerical methods, artificial intelligence, optimization algorithms, differential equations, probability theory, quantum computing, predictive modeling, interdisciplinary applications, high-performance computingAbstract
Computational mathematical modeling has become essential across scientific fields, leveraging numerical methods, AI, and optimization techniques. This research explores core methodologies, including finite element analysis, differential equation solvers, and machine-learning prediction models, underpinned by probability theory, statistical modeling, and differential equations to represent complex systems. Applications span physics, engineering, biology, medicine, finance, and environmental science, addressing structural analysis, disease modeling, risk assessment, and climate simulation. Despite advancements, challenges like computational inefficiency, accuracy limits, and scalability remain. Emerging technologies—AI, quantum computing, and hybrid models—offer promising solutions to enhance efficiency and predictive power. Future research should focus on adaptive algorithms, interdisciplinary approaches, and high-performance computing to drive more realistic simulations and data-driven decision-making. These innovations will propel scientific progress and expand the potential of computational modeling in science, engineering, and applied mathematics.
