Michael Innerberger

Michael Innerberger
Howard Hughes Medical Institute | HHMI · Janelia Farm Research Campus

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30
Publications
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152
Citations

Publications

Publications (30)
Preprint
This report presents a comprehensive data release exploring the tissue microarchitecture of P7 aged mice using Focused Ion Beam Scanning Electron Microscopy (FIB-SEM) combined with machine learning-based segmentations of nuclei. The study includes high-resolution 3D volumes and nucleus segmentations for seven vital tissues - pancreas, liver, kidney...
Preprint
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Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show that graph neural networks can be designed to jointly learn the interaction rules and the structure of the heterogeneity from data alone. The learned latent structure and dynamics can be used to virtuall...
Article
Full-text available
Unfortunately, there is a flaw in the numerical analysis of the published version [IMA J. Numer. Anal., DOI:10.1093/imanum/drad039], which is corrected here. Neither the algorithm nor the results are affected, but constants have to be adjusted.
Article
Full-text available
In this work, we formulate and analyze a geometric multigrid method for the iterative solution of the discrete systems arising from the finite element discretization of symmetric second-order linear elliptic diffusion problems. We show that the iterative solver contracts the algebraic error robustly with respect to the polynomial degree $p \ge 1$ a...
Article
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We consider a general nonsymmetric second-order linear elliptic partial differential equation in the framework of the Lax–Milgram lemma. We formulate and analyze an adaptive finite element algorithm with arbitrary polynomial degree that steers the adaptive meshrefinement and the inexact iterative solution of the arising linear systems. More precise...
Article
Full-text available
We consider scalar semilinear elliptic PDEs where the nonlinearity is strongly monotone, but only locally Lipschitz continuous. We formulate an adaptive iterative linearized finite element method (AILFEM) which steers the local mesh refinement as well as the iterative linearization of the arising nonlinear discrete equations. To this end, we employ...
Article
We present an easily accessible, object oriented code (written exclusively in Matlab) for adaptive finite element simulations in 2D. It features various refinement routines for triangular meshes as well as fully vectorized FEM ansatz spaces of arbitrary polynomial order and allows for problems with very general coefficients. In particular, our code...
Preprint
Full-text available
We consider a general nonsymmetric second-order linear elliptic PDE in the framework of the Lax-Milgram lemma. We formulate and analyze an adaptive finite element algorithm with arbitrary polynomial degree that steers the adaptive mesh-refinement and the inexact iterative solution of the arising linear systems. More precisely, the iterative solver...
Article
Full-text available
We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising linear systems by means of a contractive iterative solver like the optimally preconditioned conjugate gradien...
Preprint
Full-text available
We consider scalar semilinear elliptic PDEs where the nonlinearity is strongly monotone, but only locally Lipschitz continuous. We formulate an adaptive iterative linearized finite element method (AILFEM) which steers the local mesh refinement as well as the iterative linearization of the arising nonlinear discrete equations. To this end, we employ...
Preprint
Full-text available
In this work, a fully adaptive finite element algorithm for symmetric second-order elliptic diffusion problems with inexact solver is developed. The discrete systems are treated by a local higher-order geometric multigrid method extending the approach of [Mira\c{c}i, Pape\v{z}, Vohral\'{i}k, SIAM J. Sci. Comput. (2021)]. We show that the iterative...
Preprint
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We discuss goal-oriented adaptivity in the frame of conforming finite element methods and plain convergence of the related a posteriori error estimator for different general marking strategies. We present an abstract analysis for two different settings. First, we consider problems where a local discrete efficiency estimate holds. Second, we show pl...
Article
Full-text available
We formulate and analyze a goal-oriented adaptive finite element method for a semilinear elliptic PDE and a linear goal functional. The discretization is based on finite elements of arbitrary (but fixed) polynomial degree and involves a linearized dual problem. The linearization is part of the proposed algorithm, which employs a marking strategy di...
Preprint
Full-text available
We present an easily accessible, object oriented code (written exclusively in Matlab) for finite element simulations in 2D. The object oriented programming paradigm allows for fast implementation of higher-order FEM on triangular meshes for problems with very general coefficients. In particular, our code can handle problems typically arising from i...
Preprint
We formulate and analyze a goal-oriented adaptive finite element method (GOAFEM) for a semilinear elliptic PDE and a linear goal functional. The strategy involves the finite element solution of a linearized dual problem, where the linearization is part of the adaptive strategy. Linear convergence and optimal algebraic convergence rates are shown.
Preprint
We consider an elliptic linear-quadratic parameter estimation problem with a finite number of parameters. An adaptive finite element method driven by an a posteriori error estimator for the error in the parameters is presented. Unlike prior results in the literature, our estimator, which is composed of standard energy error residual estimators for...
Preprint
Full-text available
We consider a linear symmetric and elliptic PDE and a linear goal functional. We design a goal-oriented adaptive finite element method (GOAFEM), which steers the adaptive mesh-refinement as well as the approximate solution of the arising linear systems by means of a contractive iterative solver like the optimally preconditioned conjugate gradient m...
Article
We perform time-resolved exact diagonalization of the Hubbard model with time-dependent hoppings on small clusters of up to 12 sites. Here, the time dependence originates from a classic electromagnetic pulse, which mimics the impact of a photon. We investigate the behavior of the double occupation and spectral function after the pulse for different...
Article
Full-text available
We present a straightforward implementation scheme for solving the time-dependent Schrödinger equation for systems described by the Hubbard Hamiltonian with time-dependent hoppings. The computations can be performed for clusters of up to 14 sites with, in principle, general geometry. For the time evolution, we use the exponential midpoint rule, whe...
Article
Full-text available
We consider a linear elliptic PDE and a quadratic goal functional. The goal-oriented adaptive FEM algorithm (GOAFEM) solves the primal as well as a dual problem, where the goal functional is always linearized around the discrete primal solution at hand. We show that the marking strategy proposed in [M. Feischl, D. Praetorius and K. G. van der Zee,...
Article
We consider the time-dependent Landau–Lifshitz–Gilbert equation. We prove that each weak solution coincides with the (unique) strong solution, as long as the latter exists in time. Unlike available results in the literature, our analysis also includes the physically relevant lower-order terms like Zeeman contribution, anisotropy, stray field, and t...
Preprint
We perform time-resolved exact diagonalization of the Hubbard model with time dependent hoppings on small clusters of up to $12$ sites. Here, the time dependence originates from a classic electromagnetic pulse, which mimics the impact of a photon. We investigate the behavior of the double occupation and spectral function after the pulse for differe...
Preprint
We present a straightforward implementation scheme for solving the time dependent Schr\"odinger equation for systems described by the Hubbard Hamiltonian with time dependent hoppings. The computations can be performed for clusters of up to 14 sites with in principle general geometry. For the time evolution, we use the exponential midpoint rule, whe...
Preprint
Full-text available
We consider a linear elliptic PDE and a quadratic goal functional. The goal-oriented adaptive FEM algorithm (GOAFEM) solves the primal as well as a dual problem, where the goal functional is always linearized around the discrete primal solution at hand. We show that the marking strategy proposed in [Feischl et al, SIAM J. Numer. Anal., 54 (2016)] f...
Article
We consider an adaptive finite element method with arbitrary but fixed polynomial degree {p\geq 1} , where adaptivity is driven by an edge-based residual error estimator. Based on the modified maximum criterion from [L. Diening, C. Kreuzer and R. Stevenson, Instance optimality of the adaptive maximum strategy, Found. Comput. Math. 16 2016, 1, 33–68...
Preprint
Full-text available
We consider the time-dependent Landau-Lifshitz-Gilbert equation. We prove that each weak solution coincides with the (unique) strong solution, as long as the latter exists in time. Unlike available results in the literature, our analysis also includes the physically relevant lower-order terms like Zeeman contribution, anisotropy, stray field, and t...
Preprint
Full-text available
We consider an adaptive finite element method with arbitrary but fixed polynomial degree p ≥ 1, where adaptivity is driven by an edge-based residual error estimator. Based on the modified maximum criterion from [Diening et al, Found. Com-put. Math. 16, 2016], we propose a goal-oriented adaptive algorithm and prove that it is instance optimal. Numer...
Preprint
Full-text available
We consider an adaptive finite element method with arbitrary but fixed polynomial degree $p \ge 1$, where adaptivity is driven by an edge-based residual error estimator. Based on the modified maximum criterion from [Diening et al, Found. Comput. Math. 16, 2016], we propose a goal-oriented adaptive algorithm and prove that it is instance optimal. Mo...

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