Dominik Geng

Martin Uray, Dominik Geng, Florian Graf et al.

Multivariate time series anomaly detection (MTSAD) is critical for a wide range of application areas, such as industrial monitoring, cybersecurity, or healthcare. Real-world data is often sparse, irregularly sampled or partially observed, yet existing methods assume uniformly sampled time series. We propose a generative approach based on Latent SDEs that projects the observed time series on a continuous-time stochastic dynamical system, directly being able to handle missing observations and irregular sampling, while also naturally capturing possible cyclic behavior that many real-world use cases inherently possess. Experiments on six anomaly benchmark datasets show that our proposed method ranks first among state-of-the-art baselines. We further demonstrate that our method remains robust under severe data sparsity, while performance significantly degrades for the tested baseline methods. These results highlight latent SDEs as a natural inductive bias for anomaly detection in multivariate time series, especially in presence of real-world irregularities.

Dominik Geng, Florian Graf, Martin Uray et al.

Molecular dynamics (MD) simulations generate trajectories in a high-dimensional configuration space whose analysis critically depends on molecular descriptors, typically handcrafted observables or learned kinetic embeddings. Designing descriptors that are both expressive and broadly applicable, however, remains challenging. We study persistent homology (PH) as a general-purpose representation for MD and introduce the masked Flood complex, a protein-tailored modification of a recently introduced simplicial complex construction that emphasizes inter-residue structure at low computational cost. Vectorized persistence diagrams then provide information-rich, geometry-aware summaries of protein conformations, which we evaluate on protein class prediction, frame-level observable regression, and Markov state model (MSM) estimation from learned low-dimensional coordinates in a single shared representation space. Results on the mdCATH dataset show that PH-based descriptors are competitive across tasks, with masked Flood PH yielding the most consistent overall performance. Further, when using topologically-informed MSMs as a drop-in replacement within the recent MarS-FM framework for generative modeling of protein conformations, we obtain consistently better ensemble statistics than MSMs based on physical observables. Finally, we explore the transferability of the generative model to qualitatively different, fast folding, proteins.

Roman Remme, Tobias Kaczun, Tim Ebert et al.

Hohenberg and Kohn have proven that the electronic energy and the one-particle electron density can, in principle, be obtained by minimizing an energy functional with respect to the density. While decades of theoretical work have produced increasingly faithful approximations to this elusive exact energy functional, their accuracy is still insufficient for many applications, making it reasonable to try and learn it empirically. Using rotationally equivariant atomistic machine learning, we obtain for the first time a density functional that, when applied to the organic molecules in QM9, yields energies with chemical accuracy relative to the Kohn-Sham reference while also converging to meaningful electron densities. Augmenting the training data with densities obtained from perturbed potentials proved key to these advances. This work demonstrates that machine learning can play a crucial role in narrowing the gap between theory and the practical realization of Hohenberg and Kohn's vision, paving the way for more efficient calculations in large molecular systems.