Physics-Informed Neural Networks

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Mirzaei, Nazanin | 2024

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 58035 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Safdari, Mohammad; Rohban, Mohammad Hossein
Abstract:
This research focuses on physics-informed neural networks, which are trained to solve supervised machine learning tasks while adhering to physical laws described by general nonlinear partial differential equations. Previous studies utilized Gaussian process regression to develop functional representations designed for a given linear operator. However, despite the flexibility of Gaussian processes, solving nonlinear problems presents two major limitations: first, authors had to linearize each nonlinear term over time, and second, the Bayesian nature of Gaussian process regression requires specific assumptions that may limit the model’s representational capacity. For these reasons, data-driven algorithms are employed to infer solutions to nonlinear partial differential equations and construct efficient physics-based surrogate models. This research aims to examine these challenges and enhance the accuracy of existing methods in these domains
Keywords:
Machine Learning ; Neural Network ; Nonlinear Partial Differential Equation ; Physics Informed Neural Network