active manifolds a non linear analogue to active subspaces
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Active Manifolds: A non-linear analogue to Active Subspaces Robert - PowerPoint PPT Presentation

Jun 11, 2023 •503 likes •600 views

Active Manifolds: A non-linear analogue to Active Subspaces Robert A. Bridges PhD, Oak Ridge National Laboratory bridgesra@ornl.gov Anthony Gruber, PhD, TTU Christopher Felder, MS, WUSTL Miki Verma, BS, ORNL Chelsey Hoff, BS ORNL is managed

  1. Active Manifolds: A non-linear analogue to Active Subspaces Robert A. Bridges PhD, Oak Ridge National Laboratory bridgesra@ornl.gov Anthony Gruber, PhD, TTU Christopher Felder, MS, WUSTL Miki Verma, BS, ORNL Chelsey Hoff, BS ORNL is managed by UT-Battelle, LLC for the US Department of Energy

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f Regression Algorithm Idea: • Use gradient ascent/descent to walk up/down hill and record values f ( x, y ) = x 3 + y 3 + 0 . 2 x + 0 . 6 y of —an active manifold. f Level sets (orange) and gradient vector field (blue) f ( x 0 ) • To approximate walk along a tangent to an active level set to the active manifold. manifold at every point. Robert A. Bridges 3

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