3 papers
cs.LG2026
A Dirac-Frenkel-Onsager principle: Instantaneous residual minimization with gauge momentum for nonlinear parametrizations of PDE solutions
Matteo Raviola, Benjamin Peherstorfer
Dirac-Frenkel instantaneous residual minimization evolves nonlinear parametrizations of PDE solutions in time, but ill-conditioning can render the parameter dynamics non-unique. We…
math.NA2026
Nonlinear model reduction for transport-dominated problems
Jan S. Hesthaven, Benjamin Peherstorfer, Benjamin Unger
This article surveys nonlinear model reduction methods that remain effective in regimes where linear reduced-space approximations are intrinsically inefficient, such as transport-d…
math.NA2025
Filtered Neural Galerkin model reduction schemes for efficient propagation of initial condition uncertainties in digital twins
Zhiyang Ning, Benjamin Peherstorfer
Uncertainty quantification in digital twins is critical to enable reliable and credible predictions beyond available data. A key challenge is that ensemble-based approaches can bec…