Martin Brückmann

Martin Brückmann, Babette Dellen, Uwe Jaekel

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.

Osamah Sufyan, Martin Brückmann, Ralph Wickenhöfer et al.

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.