News

All things have to come to an end at some point.

Our former group member and Alexander von Humboldt PostDoc Yu Xing leaves the group to start a faculty position in China.

Congrats Yu, and all the best for your future endeavours.

Josef Hoppe will present the paper Robustness of Reinforcement Learning-Based Congestion Management in Low-Voltage Grids at SEST 2026 in September. It is already available as a preprint on arxiv.

The paper is a result of a cooperation between Computational Network Science, the Institute for High Voltage Equipment and Grids, Digitalization and Energy Economics (IAEW), and E.ON. We investigated the robustness of a previously-developed reinforcement learning approach to different uncertainties and modified it further to improve its performance.

We are happy to announce that three contributions from our group have been accepted for presentation at the 2026 Asilomar Conference on Signals, Systems, and Computers, taking place from October 25-28, 2026:

• Dhiraj Patel and Michael Schaub: “Random multi-layer sampling on simplicial complexes”
• Jana Hauer, Vincent Grande and Michael Schaub: “Improving Noise Robustness in Frame-Potential-Based Graph Signal Sampling”
• Vincent Grande and Michael Schaub: “Multiscale Localised Hodge Energy Signatures: Quantifying Topology and Geometry in Networks and Point Clouds”

The full papers will be published after the conference.

We look forward to presenting our work at Asilomar 2026!

We have a new paper in Nature Communicatons entitled “Phase locking and multistability in the topological Kuramoto model on cell complexes”. The authors are Iva Bačić (FZ Jülich), Michael Schaub, Jürgen Kurths (PIK Potsdam) & Dirk Witthaut (FZ Jülich). The paper introduces topological nonlinear Kirchhoff conditions to characterize all phase-locked states of the topological Kuramoto model. Our results show how the topology and boundary structure of cell complexes influence phase locking and multistability.

Damin Kühn recently led a workshop on machine learning for omics data, organized in collaboration with the CCLS. To help bridge the two disciplines, the session began with introductory primers for both computational genomics and machine learning researchers. Working directly in Jupyter notebooks, participants then learned how to handle scRNA-seq data in the AnnData format and use it to build PyTorch dataloaders, implement models, and train them.

The goal of the workshop was twofold: helping genomics researchers move beyond standard toolboxes like Scanpy to build their own deep learning models, and introducing ML researchers to complex single-cell datasets to evaluate novel methods. The event concluded by demonstrating how to write custom dataloader classes and loss functions, using Supervised Optimal Transport as an advanced practical example of a method that conceptually links microscopic single cells to macroscopic patient conditions. All hands-on materials and tutorials are freely available online and can be run directly in the browser.

Vincent Grande has a new preprint on selecting interpretable circular coordinates from data on arxiv: Circular coordinates obtained from persistent cohomology reveal loop structure in data, but they usually remain abstract: A detected circle does not tell us which measured angle, phase, torsion, or decoder explains it. In the preprint, we propose a method for selecting interpretable circle-valued coordinates from a user-supplied dictionary of scientifically meaningful candidates explaining the detected cohomology.

Michael Schaub gave a talk on “Vectorial representations of topological features: a spectral perspective” at the ICERM workshop Applied and Computational Discrete Algorithms in AI and Data Science.

In the talk, Michael discussed how Hodge-Laplacian eigenvectors and eigenvalues can provide vectorial representations of topological information and how these ideas can be used in applications such as clustering and the signal processing of flows on discrete spaces.

There will be three talks from our group at the Discrete Laplacians Workshop at the Max Planck Institute of Molecular Cell Biology and Genetics (MPI CBG) in Dresden, Germany, on 22-25 June 2026. First, Michael will talk talk on Random Abstract Cell Complexes and Applications, then Vincent will present “Point-Level Topological Representation Learning at the Intersection of Topology and Geometry using the Hodge Laplacian”, and finally Bastian will talk on Graph Neural Networks Do Not Always Oversmooth.

Yu Xing coauthored the preprint “Embodied Opinion Dynamics for Safety-Critical Motion Control in Dynamic Environments” which is now available on arXiv.

The paper proposes an adaptive control framework that embeds nonlinear opinion dynamics into the sensorimotor layers of an automated vehicle. The framework enables adaptive decision-making and safe motion control under interaction uncertainty with non-cooperative neighboring agents.

The preprint is available here.

Josef Hoppe gave a talk at the Graph Signal Processing Workshop 2026 in Madrid.

His talk, “Don’t be Afraid of Cell Complexes! An Introduction to Cell Complexes and Topological Signal Processing from an Applied Perspective”, based on work with Vincent Grande and Michael Schaub, gives an applied introduction to cell complexes and topological signal processing.

The preprint is available on arXiv.

On 28 June 2026, Vincent Grande will give a talk on Local Uncertainty, Global Information: Topology and Geometry in Complex Data at the final UnRAVeL symposium. UnRAVeL is the Research Training Group that has accompanied him throughout his PhD for the last four years.

We are happy to announce that Jana Hauer has won the Berthold Voecking award for her excellent Master thesis in Computer Science. The award, which is highest honor of the Computer Science department for excellent Master thesis, is named after the late Berthold Vöcking, a former Professor in Computer Science at RWTH who passed away tragically early.

Congratulations, Jana!

Alexandre Rene has submitted the final version of his PhD thesis “Learning Interpretable Theories for Complex Neural Systems” at the University of Ottawa.

In his thesis, Alex develops methods for learning interpretable, mechanistic models for complex neural systems.

The thesis is available through the uOttawa repository.

Congratulations, Alex!

Bastian Epping and Michael Schaub coauthored the preprint “RAwR: Role-Aware Rewiring via Approximate Equitable Partition” which is now available on arXiv.

In this paper, the authors propose a graph rewiring framework based on approximate equitable partitions. The approach augments an input graph with a quotient graph that improves information flow between nodes with similar structural roles.

The preprint is available on arXiv.

Dhiraj Patel coauthored the paper “Constructive approximation in mixed-norm spaces” which has been published in Analysis and Mathematical Physics.

The paper studies constructive approximation in mixed-norm spaces, including mixed-norm Lebesgue and Orlicz spaces.

The preprint is available on arXiv.

In the upcoming winter term 2026/27, we will be offering the

• Dynamical Processes on Networks (Lecture, Bachelor+Master)

Furthermore, there will be the following network-science related seminars:

• (Advanced) Topics in Network Science (Seminar, Bachelor/Master)
• Milestones in Network Science (Proseminar, Bachelor)

Additionally, we will offer the following practical lab:

• Network Analytics (Practical Lab, Master)
• Network Science in Biology (Practical Lab, Biology)

For more information on each course, please visit the respective links or wait until we release further information.

Hoping to see you there!

Alexandre Rene coauthored the paper “Characterizing Neural Manifolds’ Properties and Curvatures using Normalizing Flows” which has been published in PRX Life.

The paper introduces a normalizing-flow based approach to characterize the statistical properties and geometry of neural manifolds.

Yu Xing and Michael Schaub coauthored the preprint “Approximate Simulation-Based Verification of Compatibility of the Friedkin-Johnsen Model with Binary Observations” which is now available on arXiv.

The paper considers how one can verify whether a Friedkin-Johnsen opinion dynamics model is compatible with binary observations of agent opinions. The authors construct finite abstractions of the model that make this verification problem tractable.

The preprint is available here.

Michael Schaub will join the Discrete Laplacians 2026 workshop starting 22nd of June as a keynote speaker, while Vincent Grande and Bastian Epping contribute talks (registration open until 17.05.26). Looking forward to seeing you there!

We are happy to have Atuhurra Jesse, a PhD student at the Natural Language Processing Lab of NAIST, visiting us for the next six months! During his stay he will be studying the combination of LLMs with knowledge graphs.

Welcome, Jesse!

Damin Kühn’s, Leonie Rompelberg’s and Michael Schaub’s paper “Unconscious elevated bottom-up processing in depression: Insights from dynamic causal modeling with EEG and fMRI” has been published in Journal of Affective Disorders.

In this paper, the authors study unconscious emotional processing in depression using dynamic causal modeling with simultaneous EEG and fMRI measurements.

Michael Schaub coauthored the paper “Hypergraphs and simplicial complexes in focus: A roadmap for future research in higher-order interactions” which has been published in Journal of Physics: Complexity.

This roadmap summarizes the discussions at the Newton Institute Satellite meeting on “Hypergraphs: Theory and Applications”, including a survey on the current state-of-the-art as well as possible directions of future research for higher-order networks.

The paper is available here.

Michael Schaub is coauthor on the paper “Higher order trade-offs in hypergraph community detection” which is now available on arXiv.

This paper develops a unified framework for community detection in non-uniform hypergraphs.

The paper is available here.

We are happy to announce that Jana Hauer will start today as a PhD student in our group! After her successfull Master’s thesis on sampling on product graphs at our chair, she will study how particle-based consensus methods can be applied to solve distributed optimization problems on networks in her PhD.

Welcome, Jana!

Michael and Vincent gave talks at the SALTO Kick-Off Workshop “Higher-order interactions at the crossroads of geometry and topology” at Universite Paris-Saclay.

Michael opened the workshop with a talk on “Topology, Signal processing and Applications”. Vincent presented “Point-Level Topological Representation Learning at the Intersection of Topology and Geometry”.

The workshop brought together researchers working on higher-order combinatorial structures, geometry, and topological data analysis.

The preprint introduces a model for random abstract cell complexes and a method to sample 2-dimensional cell complexes. We’ve updated the preprint after improving the accuracy of the approximate sampling and the presentation in the paper.

We have also highlighted the use case of this approach for (approximately) calculating properties over the cycles on a graph. To this end, the companion python package py-raccoon now exposes intermediate data.

The preprint is available on arXiv and py-raccoon on PyPI.

We are happy to have Daniel Moreno Soto join our group today as a PhD student! With a background in computational neuroscience, he will use spectral methods and lifted dynamics to investigate coding mechanisms in spiking neural networks.

Welcome, Daniel!

We have just minted a new PhD! Michael Scholkemper today successfully defended his thesis “On the Structural Analysis of Nodes in Networks”, covering topics ranging from the assignment of roles to nodes to deep learning on graphs.

We wish him all the best in his new position at the DZNE in Bonn.

Congratulations Dr. Scholkemper!

Alexandre René’s paper “Selecting fitted models under epistemic uncertainty using a stochastic process on quantile functions” is now finally out in Nature Communications!

We are increasingly seeing data-driven methods used to fit scientific models, but methods to compare these models often underestimate relevant uncertainties, leading to overconfident comparisons. This paper examines how one can improve the quantification of uncertainties, especially those arise from modelling approximations or errors, and thus make statements about the most likely generative process underlying those data. The theory can be broadly applied to any type generative model, from graphs to neuroscience.

In the upcoming winter term 2025/26, we are excited to offer a range of courses and seminars in the field of Network Science. We will be teaching the following network-science related seminars:

• Topics in Network Science (Seminar, Bachelor)
• Advanced Topics in Network Science (Seminar, Master)
• Milestones in Network Science (Proseminar, Bachelor)

The two seminars will be held together, with different requirements for Bachelor and Master students. Unfortunately, all seminar slots are already filled and we cannot accommodate late registrations this term.

Additionally, we will offer the following practical lab:

• Network Analytics (Practical Lab, Master)

With a broader topic beyond network science, we will also offer the following lecture:

• Algorithmic Foundations of Data Science (Lecture, Bachelor/Master)

We are looking forward to an exciting term ahead and encourage students to explore these offerings! For more information on each course, please visit the respective links or get in touch.

Happy studying!

Our paper “Faster Inference of Cell Complexes from Flows via Matrix Factorization” got accepted at EUSIPCO 2025.

In this paper, we consider the problem of inferring 2-cells from signals observed on the edges of a graph, s.t. the signals can be represented as a sparse combination of gradient and curl flows (see also our previous paper). We show matrix factorization to lead to an efficient heuristic for inferring said 2-cells.

We are happy to announce the HOOC workshop on higher-order networks. Attendance is free! Go to https://conf.netsci.rwth-aachen.de for more information and registration.

Network analysis has revolutionized our understanding of complex systems, and graph-based methods have emerged as powerful tools to process signals on non-Euclidean domains via graph signal processing and graph neural networks. However, graphs are ill-equipped to encode multi-way and higher-order relations – features that are essential to understanding many systems such as group-dynamics in social systems, multi-gene interactions in genetic data, or multi-way drug interactions.

Accordingly, there is a need for new analytical methods to address the challenges of higher-order data, and a growing body of work in this direction. With this workshop, we especially want to explore current challenges which arise when bridging theory and data. This means on the one hand discussing what higher-order methods have already been used with real-world data, and on the other hand, what challenges currently prevent modelling systems with higher-order interactions.

The workshop will take place from the 11th to the 13th of August 2025. We look forward to welcoming you in Aachen, Germany!

Our paper “HLSAD: Hodge Laplacian-based Simplicial Anomaly Detection” has beeen accepted at KDD 2025, taking place in Toronto, Canada from August 2-7 this year.

HLSAD is a novel event and change-point detection algorithm for time-evolving simplicial complexes. It leverages the Hodge Laplacian to capture higher-order topological features and detect anomalies in the dynamic data by analyzing the evolution of the Hodge Laplacian spectrum. We show the effectiveness of out approach for both graph-lifting and inherently higher-order scenarios.

The preprint is available on arXiv and source code on GitLab.

We have just minted a new PhD! Felix Stamm today successfully defended his thesis “Models and Algorithms for Systematic Network Randomization”, on methods for randomizing graphs while preserving different aspects of their local structure. These were applied to problems both of creating null graph models and anonymizing graph information.

We wish him all the best in his future endeavours.

Congratulations Dr. Stamm!

Our paper “Learning From Simplicial Data Based on Random Walks and 1D Convolutions” has been accepted at ICLR 2024.

In this paper, we propose a learning algorithm on topological domains based on random walks, which are processed by 1D convolutional neural networks. We show that this approach outperforms existing methods such as SCNN and MPSN on several datasets.

The paper is available on OpenReview and source code on GitLab.