9 papers
Wavelet compression for sampling deep Gaussian processes
Oskar Broukal, Michael Feischl, Conor Osborne
Deep Gaussian processes (DGPs) use iterative sampling to create non-stationary random fields. This is notoriously expensive because the covariance at each non-initial layer depends…
High Probability Derivative Bounds for Random tanh Neural Networks on a Hypercube
Josef Dick, Michael Feischl, Fabian Zehetgruber
We establish high-probability bounds for mixed input derivatives of wide random neural networks whose activation derivatives satisfy a factorial growth bound. Our main result speci…
BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: a-priori error estimates
Michele Aldé, Dirk Praetorius, Michael Feischl
We consider the Landau-Lifshitz-Gilbert equation (LLG), which models time-dependent micromagnetic phenomena. We analyze a fully discrete scheme that combines first-order finite ele…
Optimal Time-Adaptivity for Parabolic Problems
Michael Feischl, Fernando Henríquez, David Niederkofler
Since the first optimality proofs for adaptive mesh refinement algorithms in the early 2000s, the theory of optimal mesh refinement for PDEs was inherently limited to stationary pr…
A Reduced Basis Method for the Stochastic Landau-Lifshitz-Gilbert Equation
Andrea Scaglioni, Michael Feischl, Fernando Henríquez
In this work, we consider the construction of efficient surrogates for the stochastic version of the Landau-Lifshitz-Gilbert (LLG) equation using model order reduction techniques,…
Optimal adaptive implicit time stepping
Michael Feischl, David Niederkofler
We revisit adaptive time stepping, one of the classical topics of numerical analysis and computational engineering. While widely used in application and subject of many theoretical…
Computational Math with Neural Networks is Hard
Michael Feischl, Fabian Zehetgruber, Benedikt Grässle
We establish asymptotic complexity barriers for three basic numerical tasks with neural-network data: integration of a network realization, solution of a Poisson problem with a neu…
Well-Posedness of Discretizations for Fractional Elasto-Plasticity
Michael Feischl, David Niederkofler, Barbara Wohlmuth
We consider a fractional plasticity model based on linear isotropic and kinematic hardening as well as a standard von-Mises yield function, where the flow rule is replaced by a Rie…
Regularized dynamical parametric approximation
Michael Feischl, Caroline Lasser, Christian Lubich +1
This paper studies the numerical approximation of evolution equations by nonlinear parametrizations $u(t)=Φ(\param(t))$ with time-dependent parameters $\param(t)$, which are to be…