Dear all,
The next speaker in our seminar on Uncertainty Quantification and Machine Learning in scientific computing is Joseph Bakarji, working at the University of Washington with Steven Brunton and Nathan Kutz (https://www.josephbakarji.com/). The topic of his talk will be the use of sparse identification and machine learning for discovering dimensionless groups, see abstract below. The (online) talk will take place on October 13th at 16h CET.
Best regards,
Wouter Edeling
Join Zoom Meeting https://cwi-nl.zoom.us/j/83204615411?pwd=VmNLelBwWVZLaEU4QWFYYXNZYS9qZz09
Meeting ID: 832 0461 5411 Passcode: 669720
13 October 2022 16h00 CET: Joseph Bakarji (University of Washington) : Discovering dimensionless groups from data using constrained sparse identification and deep learning methods
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 parameters and variables. However, this set is often non-unique which makes dimensional analysis an art that requires experience with the problem at hand. In this talk, I'll propose a data-driven approach that takes advantage of the symmetric and self-similar structure of available measurement data to discover dimensionless groups that best collapse the data to a lower dimensional space according to an optimal fit. We develop three machine learning methods 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 differential equations method to discover differential equations with dimensionless coefficients that parameterize the dynamics. I discuss the accuracy and robustness of these methods when applied to known nonlinear systems where dimensionless groups are known, and propose a few avenues for future research.