Time-Warp-Attend

Dynamical systems across the sciences, from electrical circuits to ecological networks, undergo qualitative and often catastrophic changes in behavior, called bifurcations, when their underlying parameters cross a threshold. Existing methods predict oncoming catastrophes in individual systems but are primarily time-series- based and struggle both to categorize qualitative dynamical regimes across diverse systems and to generalize to real data. To address this challenge, we present here time-warp-attend, a data-driven, physically-informed deep-learning framework for classifying dynamical regimes and characterizing bifurcation boundaries based on the extraction oftopologically invariant features. We focus on the paradigmatic case of the supercritical Hopf bifurcation, which is used to model periodic dynamics across a wide range of applications.

For more information see paper at ICLR 2024.

How to install time-warp-attend

Clone this repository.

Create a clean environment with conda using the environment.yml file from this repository:

conda env create -f environment.yml

Activate the environment and install the package from parent directory:

conda activate twa
pip install -e time-warp-attend

Generate classical,synthetic systems data

To view a few examples of the data generation process, see the notebook notebooks/data.ipynb.

To generate the data used in the paper, run the following commands:

# train datasets
twa generate-dataset --data-dir output/data/simple_oscillator_nsfcl  --train-size 12000 --test-size 1100 --data-name simple_oscillator  --augment-type NSF_CL
twa generate-dataset --data-dir output/data/simple_oscillator_noaug  --train-size 10000 --test-size 1000 --data-name simple_oscillator

# test datasets
twa generate-dataset --data-dir output/data/suphopf --test-size 1000 --data-name suphopf 
twa generate-dataset --data-dir output/data/lienard_poly --test-size 1000 --data-name lienard_poly 
twa generate-dataset --data-dir output/data/lienard_sigmoid --test-size 1000 --data-name lienard_sigmoid 
twa generate-dataset --data-dir output/data/vanderpol --test-size 1000 --data-name vanderpol 
twa generate-dataset --data-dir output/data/bzreaction --test-size 1000 --data-name bzreaction 
twa generate-dataset --data-dir output/data/selkov --test-size 1000 --data-name selkov 

Generate repressilator data

In the notebook notebooks/repressilator.ipynb, we simulate the repressilator regulatory gene network for cell trajectories varying in their transcription rate, $\alpha$, and the ratio of protein and mRNA degradation rates, $\beta$. From these, we generate respective vector fields across pTetR-pLacI phase space.

Generate pancreas data

For the pancreas dataset, vector fields and their corresponding cell cycle score are generated in the notebook notebooks/pancreas.ipynb.

Train models

To train a single model, see the notebook notebooks/train.ipynb.

To run multiple experiments, use the twa train command. For example, to train the models used in the paper, run the following commands:

twa train simple_oscillator_nsfcl output/

Evaluate models

Statistical and visual evaluations of single runs are available in the notebook notebooks/evaluate.ipynb.

Contact

Please get in touch email.