EuLearn: a 3D database for learning Euler characteristics

Figure 1. Representative EuLearn surfaces spanning topological genera 0 through 10.

This repo hosts the code to generate EuLearn surfaces and the geometric deep learning architectures that were trained and evaluated on the EuLearn Dataset.

Database Generator contains the code used to generate EuLearn surfaces from scalar fields via the Marching Cubes algorithm.

Architectures hosts the geometric deep learning models that perform implicit topological data analysis by learning topological invariants from geometric data.

The Sampling folder contains the 3k-vertex point clouds sampled from the benchmark EuLearn dataset. This sampling procedure was used to train the benchmark architectures.

Figure 2. Continuous deformation of the Lissajous singular knot (4,5,7) induced by a sweep of the z-coordinate phase parameter.

Figure 3. EuLearn surface generated from the Lissajous singular knot (4,5,7) with phase parameter φz = π/2.

Citation

If you use EuLearn in your research, please cite:

Pablo Suárez-Serrato, Rodrigo Fritz, Víctor Mijangos, Anayanzi Martínez, Eduardo Velázquez Richards.
«EuLearn: a 3D database for learning Euler characteristics»
Machine Learning: Science and Technology (2026).
http://iopscience.iop.org/article/10.1088/2632-2153/ae622e

You can also copy-paste the BibTex citation:

@article{Suárez-Serrato_2026,
  doi = {10.1088/2632-2153/ae622e},
  url = {https://doi.org/10.1088/2632-2153/ae622e},
  year = {2026},
  month = {may},
  publisher = {IOP Publishing},
  volume = {7},
  number = {3},
  pages = {030601},
  author = {Suárez-Serrato, Pablo and Fritz, Rodrigo and Mijangos, Victor and Martínez, Anayanzi and Velazquez Richards, Eduardo},
  title = {EuLearn: a 3D database for learning Euler characteristics},
  journal = {Machine Learning: Science and Technology}
}