Dynamical systems time series classification

Code and experiments for a time series classifier built on the assumption that series of different classes are generated by distinct dynamical systems (ordinary or stochastic differential equations), whose noisy phase trajectories form the observed data.

Each series is assigned to the class whose dynamics best fit it. The theoretical classifier is asymptotically optimal under suitable noise conditions; in practice the intractable exact trajectories are replaced by conditional expectations from a smoothing problem and unknown vector fields are learned from data with Neural ODEs (NODE). Univariate series are lifted to a phase space via the Takens embedding.

See paper/node_classification_Semkin.tex for the full method and proofs.

Repository structure

.
├── experiment/       # empirical study (see below)
├── paper/            # LaTeX source of the paper and figures
├── diploma/          # thesis based on the paper
├── pyproject.toml    # dependencies (managed with uv)
└── uv.lock

Experiments

Each folder is a self-contained Snakemake pipeline (Snakefile + config.yaml) with field-learning and classification scripts. Results are tracked with MLflow.

Folder	Task
linear_systems	Classify three synthetic linear ODE systems; our classifier vs. k-NN+DTW and LSTM baselines across noise levels
linear_systems_sde	Same task for the SDE version of the systems
basic_motions	Human activity recognition from IMU (BasicMotions), ODE, with acceleration as a control variable
basic_motions_no_control	Ablation of the above without the acceleration control
basic_motions_sde	IMU activity recognition, SDE
basic_motions_sde_no_control	SDE ablation without control
ecg5000	Heart failure detection from univariate ECG (ECG5000) via Takens embedding + NODE
toy	Illustrative examples used for the paper's figures (close vector fields, noise, solver discrepancy)

Setup

Requires Python ≥ 3.12. Install with uv:

uv sync

Running an experiment

Pipelines are run from the repository root (paths in each Snakefile are root-relative), for example:

uv run snakemake -s experiment/linear_systems/Snakefile --cores 1

Authors

• Kirill Semkin
• Vadim Strijov