Dimensionally Consistent Learning with Buckingham Pi

In the absence of governing equations, dimensional analysis is a robust technique for extracting insights and finding symmetries in physical systems. Given measurement variables and parameters, the Buckingham Pi theorem provides a procedure for finding a set of dimensionless groups that spans the solution space, 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 non-parametric input-output fitting function, (ii) a deep learning algorithm (BuckiNet) that projects the input parameter space to a lower dimension in the first layer, and (iii) a technique based on sparse identification of nonlinear dynamics (SINDy) to discover dimensionless equations whose coefficients parameterize the dynamics. We explore the accuracy, robustness and computational complexity of these methods as applied to three example problems: a bead on a rotating hoop, a laminar boundary layer, and Rayleigh-Bénard convection.

[fateenahmed]

The volume is very low. Please correct if possible or add subtitles if you can.

[straightedgesoldierx]

have you thought about combining this dimensionless SINDy method with the autoencoder coordinate discovery. it would be interesting to see if you could not only find the right coordinates to build your model, but also the correct scaling of that model. it would also be interesting to see if you could combine this approach with E-SINDy to get ranges the parameters of your dimensionless model. Very fascinating stuff!

[lahoucineouhsaine]

Thank you, it's really very interesting approach, I'm just excited to know what can be found for heat transfer problem as a scale parameter? I use a physical appraoch then i find just 2 parameters