arXiv subjects

Josef Hoppe

Publications and source records attributed to Josef Hoppe.

7 recordsLinked to original sources

arXiv2026

Robustness of Reinforcement Learning-Based Congestion Management in Low-Voltage Grids

Increases in photovoltaic generation, charging of electric vehicles and heat-pump demand challenge operating limits in low-voltage distribution grids. This requires curative curtailment methods that can operate under sparse observability, noisy measurements, and imperfect grid models. Unlike prior end-to-end reinforcement-learning approaches for partially observable curtailment, this work decouples congestion detection and control by combining a random-forest violation pre-classifier with an actor-critic controller, and evaluates its robustness to measurement noise and grid-parameter mismatch. The framework is tested on a real low-voltage grid using synthetic future operating scenarios with low observability and controllability. With accurate grid parameters, the controller reduces total violation magnitude by 98.9%, and this performance remains nearly unchanged under the tested measurement-noise settings. Grid-model mismatch proves to be more challenging, but the controller still mitigates most violations under the tested mismatch assumptions.

eess.SY↗

arXiv2025

Faster Inference of Cell Complexes from Flows via Matrix Factorization

We consider the following inference problem: Given a set of edge-flow signals observed on a graph, lift the graph to a cell complex, such that the observed edge-flow signals can be represented as a sparse combination of gradient and curl flows on the cell complex. Specifically, we aim to augment the observed graph by a set of 2-cells (polygons encircled by closed, non-intersecting paths), such that the eigenvectors of the Hodge Laplacian of the associated cell complex provide a sparse, interpretable representation of the observed edge flows on the graph. As it has been shown that the general problem is NP-hard in prior work, we here develop a novel matrix-factorization-based heuristic to solve the problem. Using computational experiments, we demonstrate that our new approach is significantly less computationally expensive than prior heuristics, while achieving only marginally worse performance in most settings. In fact, we find that for specifically noisy settings, our new approach outperforms the previous state of the art in both solution quality and computational speed.

cs.SI↗

arXiv2025

Don't be Afraid of Cell Complexes! An Introduction from an Applied Perspective

Cell complexes (CCs) are a higher-order network model deeply rooted in algebraic topology that has gained interest in signal processing and network science recently. The processing of signals supported on CCs can be described in terms of easily-accessible algebraic or combinatorial notions. However, the commonly presented definition of CCs is grounded in abstract concepts from topology and remains disconnected from the signal processing methods developed for CCs. In this paper, we aim to bridge this gap by providing a simplified definition of CCs that is accessible to a wider audience and can be used in practical applications. Specifically, we first introduce a simplified notion of abstract regular cell complexes (ARCCs). These ARCCs only rely on notions from algebra and are equivalent to regular cell complexes for most practical applications. Second, using this new definition we provide an accessible introduction to (abstract) cell complexes from a perspective of network science and signal processing, including an introduction to central methods and recent developments. Furthermore, as many practical applications work with CCs of dimension 2 and below, we provide an even simpler definition for this case that significantly simplifies understanding and working with CCs in practice.

eess.SP↗

arXiv2024

Topological Trajectory Classification and Landmark Inference on Simplicial Complexes

We consider the problem of classifying trajectories on a discrete or discretised 2-dimensional manifold modelled by a simplicial complex. Previous works have proposed to project the trajectories into the harmonic eigenspace of the Hodge Laplacian, and then cluster the resulting embeddings. However, if the considered space has vanishing homology (i.e., no "holes"), then the harmonic space of the 1-Hodge Laplacian is trivial and thus the approach fails. Here we propose to view this issue akin to a sensor placement problem and present an algorithm that aims to learn "optimal holes" to distinguish a set of given trajectory classes. Specifically, given a set of labelled trajectories, which we interpret as edge-flows on the underlying simplicial complex, we search for 2-simplices whose deletion results in an optimal separation of the trajectory labels according to the corresponding spectral embedding of the trajectories into the harmonic space. Finally, we generalise this approach to the unsupervised setting.

cs.SI↗

arXiv2024

Random Abstract Cell Complexes

We define a model for random (abstract) cell complexes (CCs), similiar to the well-known Erd\H{o}s-R\'enyi model for graphs and its extensions for simplicial complexes. To build a random cell complex, we first draw from an Erd\H{o}s-R\'enyi graph, and consecutively augment the graph with cells for each dimension with a specified probability. As the number of possible cells increases combinatorially -- e.g., 2-cells can be represented as cycles, or permutations -- we derive an approximate sampling algorithm for this model limited to two-dimensional abstract cell complexes. As a basis for this algorithm, we first introduce a spanning-tree-based method that samples simple cycles and allows the efficient approximation of various properties, most notably the probability of occurence of a given cycle. This approximation is of independent interest as it enables the approximation of a wide variety of cycle-related graph statistics using importance sampling. We use this to approximate the number of cycles of a given length on a graph, allowing us to calculate the sampling probability to arrive at a desired expected number of sampled 2-cells. The probability approximation also trivially leads to a sampling algorithm for $2$-cells with a desired sampling probability. We provide some initial analysis into the properties of random CCs drawn from this model. We further showcase practical applications for our random CCs as null models, and in the context of (random) liftings of graphs to cell complexes. The cycle sampling, cycle count estimation, and combined cell sampling algorithms are available in the package `py-raccoon` on the Python Packaging Index.

cs.DS↗

arXiv2024

TopoX: A Suite of Python Packages for Machine Learning on Topological Domains

We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial complexes. TopoX consists of three packages: TopoNetX facilitates constructing and computing on these domains, including working with nodes, edges and higher-order cells; TopoEmbedX provides methods to embed topological domains into vector spaces, akin to popular graph-based embedding algorithms such as node2vec; TopoModelX is built on top of PyTorch and offers a comprehensive toolbox of higher-order message passing functions for neural networks on topological domains. The extensively documented and unit-tested source code of TopoX is available under MIT license at https://pyt-team.github.io/}{https://pyt-team.github.io/.

cs.LG↗

arXiv2023

Representing Edge Flows on Graphs via Sparse Cell Complexes

Obtaining sparse, interpretable representations of observable data is crucial in many machine learning and signal processing tasks. For data representing flows along the edges of a graph, an intuitively interpretable way to obtain such representations is to lift the graph structure to a simplicial complex: The eigenvectors of the associated Hodge-Laplacian, respectively the incidence matrices of the corresponding simplicial complex then induce a Hodge decomposition, which can be used to represent the observed data in terms of gradient, curl, and harmonic flows. In this paper, we generalize this approach to cellular complexes and introduce the flow representation learning problem, i.e., the problem of augmenting the observed graph by a set of cells, such that the eigenvectors of the associated Hodge Laplacian provide a sparse, interpretable representation of the observed edge flows on the graph. We show that this problem is NP-hard and introduce an efficient approximation algorithm for its solution. Experiments on real-world and synthetic data demonstrate that our algorithm outperforms state-of-the-art methods with respect to approximation error, while being computationally efficient.

cs.SI↗