Mathematics Colloquia and Seminars

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I will discuss two recent results from my lab related to the application of machine learning techniques to the simulation of computational solid and fluid mechanics. First, I will discuss a data-driven preconditioner for discrete Poisson equations that arise in the simulation of the incompressible Euler equations. These Poisson systems are defined over regular grids with irregular voxelized internal boundaries (e.g. at water free surface and at solid boundaries). This irregularity complicates the use of fast solvers like multigrid etc. We show that a data-driven model can be used to learn an approximate inverse capable of accelerating Krylov methods beyond the performance possible with a state-of-the-art algebraic multigrid preconditioner. Second, I will discuss the use of machine learning techniques in estimating elastic equilibria. This type of technique is used to improve the realism of animated characters in visual effects applications. I will briefly discuss the application of this in the computational biomechanics of musculoskeletal driven locomotion.