An Introduction to Artificial Neural Networks in Ordinary Differential Equations: A Harrod-Domar Growth-Based Approach

In many scientific and engineering fields, ordinary differential equations (ODEs) are essential for modeling a broad variety of phenomena. Even if they work well, traditional numerical techniques for solving ODEs can be computationally demanding and may not work well for complex or high-dimensional situations. This study highlights the crucial role that ODEs play in influencing modern developments by creating a link between theoretical underpinnings and practical applications. ODEs have revolutionized deep neural network training methodologies. Even if they work well, traditional numerical techniques for solving ODEs can be computationally demanding and may not work well for complex or high-dimensional situations. Because of its capacity to imitate intricate patterns and functions, Artificial Neural Networks (ANNs) have recently surfaced as a viable substitute for solving ODEs. They make it possible for dynamic topologies, in which the behavior of the network changes continually over time, enhancing its capacity to recognize intricate patterns and adjust to shifting data. The mathematics behind these applications is examined in this essay, with a focus on ODE critical contributions to the development of artificial intelligence as well as their importance in influencing the current scientific and economic environment. This article's goal is to give scholars and students interested in this significant subject a clear and succinct guide.