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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
Prediction error certification for PINNs: Theory, computation, and application to Stokes flow
Birgit Hillebrecht, Benjamin Unger
Rigorous error estimation is a fundamental topic in numerical analysis. With the increasing use of physics-informed neural networks (PINNs) for solving partial differential equatio…