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SUMMARY:Joseph Bakarji (University of Washington)
DTSTART:20220714T160000Z
DTEND:20220714T170000Z
DTSTAMP:20260423T003244Z
UID:MPML/83
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MPML/83/">Di
 mensionally Consistent Learning with Buckingham Pi</a>\nby Joseph Bakarji 
 (University of Washington) as part of Mathematics\, Physics and Machine Le
 arning (IST\, Lisbon)\n\n\nAbstract\nDimensional analysis is a robust tech
 nique for extracting insights and finding symmetries in physical systems\,
  especially when the governing equations are not known. The Buckingham Pi 
 theorem provides a procedure for finding a set of dimensionless groups fro
 m given measurements\, although this set is not unique. We propose an auto
 mated approach using the symmetric and self-similar structure of available
  measurement data to discover the dimensionless groups that best collapse 
 this data to a lower dimensional space according to an optimal fit. We dev
 elop three data-driven techniques that use the Buckingham Pi theorem as a 
 constraint: (i) a constrained optimization problem with a nonparametric fu
 nction\, (ii) a deep learning algorithm (BuckiNet) that projects the input
  parameter space to a lower dimension in the first layer\, and (iii) a spa
 rse identification of nonlinear dynamics (SINDy) to discover dimensionless
  equations whose coefficients parameterize the dynamics. I discuss the acc
 uracy and robustness of these methods when applied to known nonlinear syst
 ems.\n
LOCATION:https://researchseminars.org/talk/MPML/83/
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