Study of Artificial Intelligence-Assisted Methods for Solving Differential Equations and Applications in Engineering

• Grant number: 25/19437-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: November 01, 2025
• End date: October 31, 2026
• Field of knowledge: Engineering - Electrical Engineering - Telecommunications
• Principal Investigator: Guilherme Simon da Rosa
• Grantee: Ícaro Hideki Otino de Almeida
• Host Institution: Faculdade de Engenharia. Universidade Estadual Paulista (UNESP). Campus São João da Boa Vista. São João da Boa Vista , SP, Brazil

Abstract

This undergraduate research project proposes the study and development of methodologies based on artificial intelligence (AI), particularly physics-informed neural networks (PINNs), for solving ordinary and partial differential equations applied to problems in electromagnetic engineering. The proposal is aligned with the current advances in AI applied to the modeling of microwave devices, antennas, and wave propagation in complex media, addressing challenges inherent to the nonlinear nature and high computational cost of traditional approaches. Using Python programming language and libraries such as PyTorch and SciPy, the student will develop algorithms capable of predicting solutions to problems governed by the vector Helmholtz equation, with the potential to provide analytical interpretations and a deeper physical understanding of the modeled phenomena. The project is part of ongoing research initiatives coordinated by the faculty advisor within the research group at Unesp, São João da Boa Vista campus, supported by adequate infrastructure and contributions from graduate students and postdoctoral fellows.