Learning Equations from Data

[pablo]

Space to read and discuss strategies for using data to help learn reduced equations for building reduced order models

A straightforward way of obtaining reduced equations is by performing a Galerkin projection (check this, or this, or this, and here is also a video). Nevertheless, in many situations (non-affine and non-linear systems, experimental set ups, exotic reduced coordinates) it can be problematic to rely on Galerkin projections.

The Model Order Reduction community has been active in the past decades on finding various workarounds for such issues. We can use this space for reading and discussing literature on these topics. As a starter, some interesting papers that might have insights in this direction:

• Calibrated reduced-order POD-Galerkin system for fluid flow modelling (2005)

• A tutorial on data-driven eigenvalue identification: Prony analysis, matrix pencil, and eigensystem realization algorithm (2020)

• Data-Driven Extraction of Uniformly Stable and Passive Parameterized Macromodels (2021)

• From Data to Reduced-Order Models via Generalized Balanced Truncation (2023)

• Symbolic Regression Of Implicit Equations (2009)

• An Introduction to Implicit Regression: Extending Standard Regression to
  Rotational Analysis and Non-Response Analysis (2016)

Lets compile more and make a good map of what is out there and what we can immediately use for our research