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This talk from the DDPS (Data-Driven Physical Simulation) series features Youngjoon Hong from Seoul National University presenting innovative research on operator networks for solving parametric partial differential equations (PDEs). Learn about a novel approach that combines deep learning with traditional numerical techniques like finite element and spectral element methods to tackle complex PDEs without requiring paired input-output training data. The presentation covers applications ranging from singularly perturbed convection-diffusion equations to the Navier-Stokes equations, demonstrating the method's versatility in accuracy, generalization, and computational efficiency. Discover how this framework can be applied to modeling complex domains with diverse boundary conditions and singular behavior, supported by rigorous theoretical convergence analysis grounded in numerical analysis. Youngjoon Hong, an Associate Professor at Seoul National University, specializes in the mathematics of machine learning and its applications in scientific computing, bringing expertise developed through his Ph.D. work with Professor Roger Temam and postdoctoral research on electromagnetic and water waves.
