Dimensionally Consistent Learning with Buckingham Pi
Joseph Bakarji (University of Washington)
Abstract: Dimensional analysis is a robust technique 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 from given measurements, although this set is not unique. We propose an automated 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 develop three data-driven techniques that use the Buckingham Pi theorem as a constraint: (i) a constrained optimization problem with a nonparametric function, (ii) a deep learning algorithm (BuckiNet) that projects the input parameter space to a lower dimension in the first layer, and (iii) a sparse identification of nonlinear dynamics (SINDy) to discover dimensionless equations whose coefficients parameterize the dynamics. I discuss the accuracy and robustness of these methods when applied to known nonlinear systems.
data structures and algorithmsmachine learningmathematical physicsinformation theoryoptimization and controldata analysis, statistics and probability
Audience: researchers in the topic
Mathematics, Physics and Machine Learning (IST, Lisbon)
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Zoom link: videoconf-colibri.zoom.us/j/91599759679
Organizers: | Mário Figueiredo, Tiago Domingos, Francisco Melo, Jose Mourao*, Cláudia Nunes, Yasser Omar, Pedro Alexandre Santos, João Seixas, Cláudia Soares, João Xavier |
*contact for this listing |