11 citations · 20 across the 7 of their papers we have counts for
7 papers
L2-L2-gain bounds for quadratic output systems
Birgit Hillebrecht
We derive an explicit bound for the L2-L2-gain of linear time-invariant systems whose output is a quadratic function of the state and the input. Such systems appear naturally in ma…
Estimation of the input-to-state stability gain functions from finite-dimensional approximations
Birgit Hillebrecht, Benjamin Unger
Since the concept of input-to-state stability (ISS) was introduced, it has been extensively investigated for finite-dimensional control systems and has recently received attention…
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…
model order reduction for quadratic output systems
Birgit Hillebrecht, Benjamin Unger
Linear time-invariant quadratic output (LTIQO) systems generalize linear time-invariant systems to nonlinear regimes. Problems of this class occur in multiple applications naturall…
Certified machine learning: Rigorous a posteriori error bounds for PDE defined PINNs
Birgit Hillebrecht, Benjamin Unger
Prediction error quantification in machine learning has been left out of most methodological investigations of neural networks, for both purely data-driven and physics-informed app…
Certified machine learning: A posteriori error estimation for physics-informed neural networks
Birgit Hillebrecht, Benjamin Unger
Physics-informed neural networks (PINNs) are one popular approach to incorporate a priori knowledge about physical systems into the learning framework. PINNs are known to be robust…
Continuum limit of lattice quasielectron wavefunctions
Aniket Patra, Birgit Hillebrecht, Anne E. B. Nielsen
Trial states describing anyonic quasiholes in the Laughlin state were found early on, and it is therefore natural to expect that one should also be able to create anyonic quasielec…