Robust deep learning on graphs using neural PDEs

• Main Author: Gui, Pengzhe
• Other Authors: Tay Wee Peng
• Format: Thesis-Master by Coursework
• Language: English
• Published: Nanyang Technological University 2023
• Subjects: Engineering::Electrical and electronic engineering::Computer hardware, software and systems
• Online Access: https://hdl.handle.net/10356/172761
• Institution: Nanyang Technological University

Neural Partial Differential Equations(Neural PDEs) offer a data-driven method for modeling and solving high-dimensional PDE problems by combining the robust representation capabilities of deep learning with the traditional framework of partial differential equations (PDEs). This approach combines the strengths of machine learning, mathematical modelling, and numerical methods in order to gain a deeper understanding of the underlying processes and make accurate predictions. In this dissertation, we delve into the intricacies of neural networks, with a keen focus on Beltrami flows, examining their foundational equations and integration in graph neural networks. Our analysis primarily addresses their dispersion and continuity within graph structures. Furthermore, we explore a range of prevalent neural network attacks, detailing their mechanisms and impacts. Central to our study is the assessment of the resilience of graph neural PDEs against these adversarial attacks, especially examining the effects of poisoning attacks. Through targeted experiments, we establish a framework for evaluating the vulnerability of these PDEs to such attacks. The results of our experimental analysis not only shed light on the robustness of graph neural PDEs but also lay the groundwork for future research in this evolving area of study.