Exploring physics-informed neural networks to compute definite integrals through differential equations

Document Type : Regular Articles

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Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt

Abstract

This research focuses on the application of physics-informed neural networks (PINNs) in the field of definite integral evaluation. PINNs is the name assigned to artificial neural networks. They are different from standard neural networks in that they include loss terms that explain the physics of the issue. This work investigates the effectiveness of physics-informed neural networks in accurately computing definite integrals, a critical process in many scientific and engineering fields. The study aims to assess the precision and effectiveness of PINNs in evaluating definite integrals in contrast to traditional integration techniques or numerical integral methods. Discover how mathematical analysis computing methods, particularly those involving definite integral computations, may be transformed by neural networks. This study adds to the developing field of artificial intelligence (AI) in mathematical computations by utilizing the built-in characteristics of PINNs, such as their capacity to learn from data and integrate existing knowledge. The results of this study offer a solid basis for upcoming advancements in neural network-based techniques for mathematical modeling, numerical analysis, and other scientific fields.

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