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AARMS Scientific Machine Learning Seminar: Scott MacLachlan (Memorial)
March 29, 2022 @ 11:00 am - 12:00 pm
Optimization and Learning in the Design of Preconditioners
Computer simulation algorithms are a major tool in many areas of science and industry, particularly in areas where the behaviour of fluids or complex materials governs the physical processes of interest. A typical core of these tools is the numerical approximation of the solution to coupled nonlinear systems of partial differential equations, relying on nonlinear and linear solvers, such as Newton’s method and preconditioned Krylov iterations. Among the most effective preconditioners for these systems are multigrid and domain decomposition methods, which use multiscale representations of the systems to be solved to achieve linear-scaling complexity for the solution of these linear systems. These preconditioners typically rely on heuristics in their construction, to approximate solutions to underlying combinatorial (and other) optimization problems that specify parameters and other components of the preconditioners, based on the discrete problem to which they are being applied. In this talk, I will discuss the use of advanced optimization and machine learning techniques to approximately solve these optimization problems and the impact these techniques can have on advanced preconditioner design.