Double projection for reconstructing dynamical systems: between stochastic and deterministic regimes

This repository contains the code and data associated with the paper by Sip et al. (2026). In the paper, we evaluate the capabilities of several methods for dynamical system reconstruction from data, and we propose a novel variant from the dynamical VAE family named double projection dynamical system reconstruction (DPDSR). In particular, we focus on the analysis of the discovered dynamical systems, the role of the noise in the systems, and the nature of their attractors.

Repository structure

The repository is structured as follows:

• conf/ contains the configuration files for the analyzed problems. An example configuration file for a single model and training configuration is conf/example.yaml. The parameter sweeps are described by the .py files (see below on how to use them).
• data/ contains the datasets used in the study.
• dpdsr/ contains the core code.
• run/ is the target directory where the outputs of the runs will be stored.
• scripts/ contains the scripts to train and run the models.
• env.yml describes the Python environment.
• Snakefile describes and serves to execute the study workflow using Snakemake.

Setting up

Create the Python environment with mamba (or equivalently with conda):

mamba env create -f env.yml -n <ENV_NAME>

Running

The training of a single model can be ran by

python scripts/train.py conf/example.yaml -c1

The parameter sweeps are described by the the configuration files following naming scheme conf/<EXPERIMENT>/<DATASET>-<MODEL>.py. They can be ran with Snakemake. The Snakemake worflow for training and evaluation is described by Snakefile. To run the parameter sweeps described by a configuration file execute

export CONF="<PATH_TO_CONFIG_FILE>"
snakemake all

with appropriate Snakemake constraints for your computing environment.

Naming note

For reasons of backward compatibility, in the configuration files and in the code the alternative abbreviation dsrn is used in place of dpdsr.

License

The code is licensed under the MIT license.

References

Sip, V., Breyton, M., Petkoski, S., & Jirsa, V. (2026). Double projection for reconstructing dynamical systems: between stochastic and deterministic regimes. arXiv preprint arXiv:2510.01089. https://doi.org/10.48550/arXiv.2510.01089