Florian Frantzen

PhD Researcher

Chair of Computational Network Science RWTH Aachen University

Machine learning for simplicial complexes and higher-order systems.

I build practical learning methods for data beyond pairwise graphs.

PhD researcher at RWTH Aachen working on simplicial learning, edge flows, anomaly detection, and open-source research software.

Current focus

Learning from higher-order interactions and turning that work into reusable tools.

Research interests

Simplicial learning Edge flows and random walks Topology-aware anomaly detection Research software and datasets

Research program

Representation

Random-walk and simplicial architectures for higher-order data.

Flows

Edge-flow and Hodge-theoretic methods for structured inference.

Software

Open-source tooling, datasets, and reproducible ML pipelines.

Research

Research directions

My research sits at the intersection of higher-order network science, topological signal processing, and machine learning, with current emphasis on simplicial learning, Hodge-theoretic methods, and anomaly detection.

Current agenda

I develop learning, inference, and detection methods for higher-order systems.

Simplicial
Hodge
Edge Flows
Spectral
Anomalies
Random Walks

Focus

Machine learning on structured data

Simplicial representations, spectral operators, and flow-based inference.

Concretely, this includes representing trajectories as edge flows on simplicial complexes, building random-walk architectures such as SCRaWl for simplicial representation learning, and detecting structural change in time-evolving simplicial complexes with Hodge-Laplacian-based methods such as HLSAD.

01

Theme

Simplicial representation learning

I study how to build learning architectures for simplicial complexes and related higher-order domains, especially when random walks, local neighborhoods, and structured operators offer a better inductive bias than standard graph models.

02

Theme

Flow and Hodge-theoretic methods

A recurring theme in my work is to represent data as edge or cell flows and study it with spectral and Hodge-theoretic tools, linking topological signal processing to machine learning and inference on higher-order systems.

03

Theme

Anomaly detection on evolving higher-order systems

I am interested in detecting structural irregularity and temporal change in higher-order data, from topological outliers in trajectories to anomalies in time-evolving simplicial complexes.

Career

Academic experience

My background combines applied mathematics and machine learning, but my current work is really about how to represent, learn from, and benchmark data with higher-order interactions.

2021 - Present

RWTH Aachen University

PhD Researcher

Pursuing my PhD at the Chair of Computational Network Science, where I work on machine learning and signal processing on simplicial complexes, with particular emphasis on edge flows, anomaly detection, and reusable tooling for higher-order data.

2019 - 2021

RWTH Aachen University

Graduate Studies

Deepened my interests in machine learning, signal processing, and applied mathematics, which still shape how I approach structured data problems today.

2016 - 2019

RWTH Aachen University

Undergraduate Studies

Built the mathematical and computational foundation that later drew me toward geometric methods, topology, and data-driven modeling.

Code Projects

Open-Source Software

A lot of my research shows up as infrastructure: libraries for topological domains, topological deep learning, representation learning, and curated datasets for reproducible higher-order experiments.

Source

GitHub
Dataset Repository ahorn.rwth-aachen.de

AHORN

Stack: TypeScript · Python

A curated, citable repository of simplicial-complex, cell-complex, and hypergraph datasets designed for benchmarking, method development, and reproducible higher-order network science.

Datasets Benchmarking Reproducibility
Python Package github.com/pyt-team/TopoNetX

TopoNetX

Stack: Python

A NetworkX-like Python library for constructing and computing on topological domains, including simplicial, cell, and combinatorial complexes with operators such as boundaries and Hodge Laplacians.

Complexes Hodge Laplacians Data Structures
Python Package github.com/pyt-team/TopoModelX

TopoModelX

Stack: Python

A PyTorch-oriented library for building topological neural networks, making it easier to implement, train, and compare models on topological domains.

PyTorch Topological DL Model prototyping
Python Package github.com/pyt-team/TopoEmbedX

TopoEmbedX

Stack: Python

A representation-learning library for topological domains, with methods such as Cell2Vec, DeepCell, and higher-order Laplacian eigenmap variants for downstream tasks.

Embeddings Cell2Vec Higher-order domains

Publications

Publications

The publications below follow a path from flow-based modeling of trajectories on simplicial complexes, to random-walk architectures for simplicial learning, to higher-order anomaly detection and shared software for topological machine learning.

Profiles

ORCID arXiv

2025

2024

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

Mustafa Hajij, Mathilde Papillon, Florian Frantzen, Jens Agerberg, Ibrahem AlJabea, Rubén Ballester, Claudio Battiloro, Guillermo Bernárdez, Tolga Birdal, Aiden Brent, Peter Chin, Sergio Escalera, Simone Fiorellino, Odin Hoff Gardaa, Gurusankar Gopalakrishnan, Devendra Govil, Josef Hoppe, Maneel Reddy Karri, Jude Khouja, Manuel Lecha, Neal Livesay, Jan Meißner, Soham Mukherjee, Alexander Nikitin, Theodore Papamarkou, Jaro Prílepok, Karthikeyan Natesan Ramamurthy, Paul Rosen, Aldo Guzmán-Sáenz, Alessandro Salatiello, Shreyas N. Samaga, Simone Scardapane, Michael T. Schaub, Luca Scofano, Indro Spinelli, Lev Telyatnikov, Quang Truong, Robin Walters, Maosheng Yang, Olga Zaghen, Ghada Zamzmi, Ali Zia, and Nina Miolane

Journal of Machine Learning Research pp. 1-8

2023

2022

2021

2020