A framework for optimally weighted invariant subspace discovery.

by Jonas Katona (University of Yale)

Monday 25 May 2026, 15:30 → 17:30 Europe/Stockholm

Albano 3: 6228 - Mega (22 seats) (Albano Building 3)

Many datasets in the physical sciences lie on low-dimensional manifolds defined by conserved quantities or other implicit constraints among variables. Recovering these invariants from noisy observations is central to scientific machine learning, system identification, and reduced-order modeling, yet classical regression frameworks assume explicit input-output relationships and are poorly suited for discovering such implicit structure.

We develop a framework for invariant subspace discovery by expanding candidate invariants in a function basis, yielding a data matrix whose null space corresponds to conserved quantities satisfied by the observations. Using matrix perturbation theory, we derive plug-and-play error bounds for the recovered invariant subspace and determine optimal weights that minimize worst-case reconstruction error under different noise structures. The resulting estimator is given by the bottom eigenvectors of a weighted covariance matrix with inverse-variance–type weights, providing a robust and computationally practical method that performs accurately across varying noise regimes. This approach enables reliable, robust recovery of conserved quantities from noisy data and connects invariant discovery with classical statistical estimators such as generalized least squares and weighted PCA.

 

zoom : https://stockholmuniversity.zoom.us/j/622224375