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Minisymposium Presentation
Towards Neural Green's Operators for Magnetic Fusion
Presenter
I am currently an assistant professor in the Department of Mechanical Engineering at Eindhoven University of Technology. After receiving my PhD from the Department of Mechanical Engineering at Eindhoven University of Technology, I became a postdoctoral fellow at the Oden Institute of the University of Texas at Austin. My research interests are two-fold, on the one hand I work on computational models and methods for kinetic theory (e.g. rarefied gases, radiative transport, plasma, etc), and on the other hand I work on operator learning for partial differential equations.
Description
Operator networks have emerged as promising machine learning tools for reduced order modeling of a wide range of physical systems described by partial differential equations (PDEs). This work describes a new architecture for operator networks that approximates the Green's operator to a linear PDE. Such a ‘Neural Green’s Operator’ (NGO) acts as a surrogate for the PDE solution operator: it maps the PDE’s input functions (e.g. forcings, boundary conditions, material parameters) to its solution. We apply NGOs to relevant canonical PDEs and ask the question whether the NGO architecture would lead to significant computational benefits and conclude the discussion with numerical examples.