arXiv subjects

Martin Brückmann

Publications and source records attributed to Martin Brückmann.

3 recordsLinked to original sources

arXiv2026

Model discovery for dynamical systems with complex-valued product units

Discovering the governing equations of a dynamical system from observed trajectories provides deeper insight into its structure than mere prediction of future states. We present a data-driven approach to model discovery based on complex-valued product-unit networks, in which each unit represents a complex monomial and the network output is a sparse linear combination of such monomials. In contrast to established library-based methods such as SINDy, our approach does not require a predefined set of candidate functions: the relevant monomials, including those with fractional or negative exponents, are learned directly from data. Across four chaotic benchmark systems (Lorenz63, Lorenz84, the Four-Wing attractor, and a fractional variant of Lorenz63), we recover the exact governing equations in 90% of trials for the first three systems, and in 70-90% of trials for the fractional case, using at least 3000 training points. Applied to real-world human-gait accelerometer signals, the model produced stable trajectories with bounded prediction errors, corresponding to an RMSE of approximately 12-14% of the signal amplitude range over a test horizon three times longer than the training interval, demonstrating its potential for high-dimensional systems in which analytic equations are unavailable.

cs.CV↗

arXiv2026

Anatomy-Informed Deep Learning for Abdominal Aortic Aneurysm Segmentation

In CT angiography, the accurate segmentation of abdominal aortic aneurysms (AAAs) is difficult due to large anatomical variability, low-contrast vessel boundaries, and the close proximity of organs whose intensities resemble vascular structures, often leading to false positives. To address these challenges, we propose an anatomy-aware segmentation framework that integrates organ exclusion masks derived from TotalSegmentator into the training process. These masks encode explicit anatomical priors by identifying non-vascular organsand penalizing aneurysm predictions within these regions, thereby guiding the U-Net to focus on the aorta and its pathological dilation while suppressing anatomically implausible predictions. Despite being trained on a relatively small dataset, the anatomy-aware model achieves high accuracy, substantially reduces false positives, and improves boundary consistency compared to a standard U-Net baseline. The results demonstrate that incorporating anatomical knowledge through exclusion masks provides an efficient mechanism to enhance robustness and generalization, enabling reliable AAA segmentation even with limited training data.

cs.CV↗

arXiv2024

Simple Grid Polygon Online Exploration Revisited

Due to some significantly contradicting research results, we reconsider the problem of the online exploration of a simple grid cell environment. In this model an agent attains local information about the direct four-neigbourship of a current grid cell and can also successively build a map of all detected cells. Beginning from a starting cell at the boundary of the environment, the agent has to visit any cell of the grid environment and finally has to return to its starting position. The performance of an online strategy is given by competitive analysis. We compare the number of overall cell visits (number of steps) of an online strategy to the number of such visits in the optimal offline solution under full information of the environment in advance. The corresponding worst-case ratio gives the competitive ratio. The aforementioned contradiction among two publications turns out to be as follows: There is a journal publication that claims to present an optimal competitive strategy with ratio 7/6 and a former conference paper that presents a lower bound of 20/17. In this note we extract the flaw in the upper bound and also present a new slightly improved and (as we think) simplified general lower bound of 13/11.

cs.CG↗