ICES Seminar, Mohamed Ebeida, Sandia National Laboratories, "Exploring high-dimensional spaces using Well-spaced Random Points and Hyperplane Sampling with application to Graphics, Meshes, Global Optimization, Uncertainty and Robotics"
Talk Audience: UTCS Faculty, Grads, Undergrads, Other Interested Parties
Host: Chandra Bajaj
Talk Abstract: Well-spaced random points are useful for a host of applications, including sampling for texture synthesis in computer graphics finite element simplicial and Voronoi meshes for fracture mechanics sample points for exploring abstract spaces in optimization and uncertainty quantification over scientific simulations and collision free path planning for robots.
These disciplines differ in terms of the dimensions of the space and how the boundaries are handled, but a unifying theme is that since the problems are too large and complex to solve analytically, we must explore the space at specific points, and make informed guesses as to what happens between.
Designing point sets with the right properties is essential to get good quality solutions, in a reasonable amount of time. Two recurring and valued properties are "well-spaced," no two sample points are too close together, yet no domain point is too far from a sample and "random," so that no deterministic patterns spoil the prediction or integration.
Speaker Bio: FN Senior Member of Technical Staff at Sandia National Laboratories.
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