Systems and methods for solving problems

Abstract

This chapter addresses the challenges of performing calculations and obtaining solutions to complex problems through the application of artificial intelligence. Initially, methods employing algorithms optimized for execution on graphics processing units (GPUs) are examined, demonstrating their efficiency in solving tasks where the evolution of processes and outcomes is explicitly defined, particularly for integrated problems characterized by a unique solution. Furthermore, symbolic approaches based on formal logic are analyzed, with emphasis on their role in the development of expert and recommender systems. The concept of computational graphs grounded in mathematical logic is also explored as a means of problem representation and reasoning. Special attention is devoted to connectionist models, including advanced neural architectures such as deep learning networks and Kolmogorov–Arnold networks, highlighting their potential in addressing high-dimensional and nonlinear tasks. The chapter concludes with illustrative examples that showcase the practical applicability and effectiveness of these models in solving real-world problems.