The research group Applied Mathematics and Machine Learning at the IDea_Lab of the University of Graz works at the interface of data science, machine learning, inverse problems and image processing. Within these fields, our research is characterized by a close connection of the development and analysis of mathematical models in function space with concrete, interdisciplinary applications.
IDea_Lab - The Interdisciplinary Digital Lab at the University of Graz
Leechgasse 34
A-8010 Graz
Austria
| phone (Secretary): | +43 316 380 - 1177 |
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| phone (Head): | +43 316 380 - 1645 |
| mail (Secretary): | tanja.weiss(at)uni-graz.at |
| mail (Head): | martin.holler(at)uni-graz.at |
| 2026 | 05. October | 14:30 | SR 127.11, IDea_Lab | Babak Maboudi: Adjoint-Based Uncertainty Quantification for PDE-constrained Inverse ProblemsAbstract: Inverse problems constrained by nonlinear PDEs arise throughout science and engineering, where optimization provides powerful tools for reconstructing unknown parameters from indirect and noisy observations. Yet a single optimal reconstruction tells only part of the story: in ill-posed problems, understanding uncertainty, parameter correlations, and non-identifiability can be just as important as finding a minimizer. In this talk, I will introduce a Bayesian perspective on uncertainty quantification (UQ) for PDE-constrained inverse problems, using the reconstruction of doping profiles in semiconductor devices as a motivating example. Particular attention will be given to parameters with sharp interfaces, where conventional smooth prior models can be inadequate. I will discuss how structured pushforward priors can encode nearly piecewise-constant fields while retaining differentiability, making them compatible with adjoint-based gradients and modern sampling methods such as Hamiltonian Monte Carlo. Numerical examples will illustrate how this approach can recover interfaces, quantify spatial uncertainty, and expose structural non-identifiability when geometry and material parameters are inferred simultaneously. More broadly, the talk will highlight connections between optimization and Bayesian inference, and how tools familiar from PDE-constrained optimization can be leveraged to make uncertainty quantification computationally practical. |
| 2026 | 01. October | SR 127.11, IDea_Lab | Laurenz Kogler: Three discretizations of the Radon transform and their convergence rates | |
| 2026 | 07. September | 14:30 | SR 127.11, IDea_Lab | Luca Calatroni (University of Genoa): Learning spatially adaptive regularisation for computational imaging problemsAbstract: Modern computational imaging increasingly calls for methods that combine physical models of image formation with the flexibility of data-driven learning. In this talk, I will present an overview of my research at this interface, focusing on hybrid reconstruction methods that retain the mathematical structure and interpretability of variational models while learning problem-dependent components.I will take as an example the spatially adaptive Total Variation (TV) and Total Generalised Variation (TGV) regularisation models, in which regularisation strength varies across the image to better preserve edges, smooth regions, and fine details. I will discuss different strategies for estimating these parameter maps, ranging from statistical principles to bilevel optimisation and neural networks embedded within unrolled reconstruction algorithms. Applications to image denoising and accelerated MRI will illustrate how physics-aware learning can produce flexible and interpretable reconstruction methods, even when reference images or large training datasets are unavailable. |
| 2026 | 02. November | The paper Systematic analysis of penalty-optimised illumination design for tomographic volumetric additive manufacturing via the extendable framework TVAM AID using the Core Imaging Library, authored by Richard Huber in cooperation with his colleagues Nicole Pellizzon, Jon Spangenberg and Jakob Sauer Jorgensen from the Technical University of Denmark (DTU), was published in Additive Manufacturing. |
| 2026 | 30. October | The paper Finite-sample Calibration Guarantees for Binary Segmentation, authored by Bruno Viti and Martin Holler, was published in Transactions on Machine Learning Research. |
| 2026 | 22. October | The paper Kernel methods in the deep Ritz framework: theory and practice, co-authored by Hendrik Kleikamp, was published in the Springer Journal Computational Science and Engineering. |
| 2026 | 19. October |
Martin Holler organized a workshop on Generative AI within the Special Semester on AI in Scientific Computing at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) in Linz. Matthias Höfler and Hendrik Kleikamp had the chance to participate in the workshop as well and learn about recent development in the area of generative models. |
| 2026 | 15. October | From 5 to 9 October, Richard Huber visited the FACTAS team at Inria Centre at Université Côte d'Azur (Sophia Antipolis, France), and from 12 to 15 October his former colleagues at the Laboratoire TIMC in Grenoble, France. Topics discussed included inverse magnetization problems, computed tomography and magnetic resonance imaging. |
