DaeFinder 1.0.1

A Python package to discover Differential Algebraic Equations from data.

🔎 DaeFinder

Discover the hidden equations inside your data.

DaeFinder is a Scientific Machine Learning toolkit that recovers Differential Algebraic Equations (DAEs) from noisy measurements using a sparse-optimization framework — the SODAs algorithm.

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✨ Why DaeFinder?

Real systems — chemical reaction networks, power grids, mechanical systems — are governed by a mix of differential equations (how things change in time) and algebraic constraints (relationships that always hold). DaeFinder automatically untangles both directly from time-series data:

• 🧩 Decouples algebraic & dynamic relations — finds the constraints and the ODEs.
• 🪶 Model-agnostic by design — plug in any estimator that implements fit() and score() (linear models, regularized regressors, or your own custom optimizer).
• 🔇 Robust to noise — built-in smoothing and derivative estimation (splines, Savitzky–Golay).
• 🧮 Rich feature engineering — polynomial libraries, sparse feature coupling, and SVD analysis.
• ⚡ Parallel discovery — fit many candidate relations concurrently.
• ✅ Tested & current — runs on the latest scientific-Python stack (see Compatibility).

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📝 Citation

If DaeFinder supports your research, please cite the SODAs paper:

M. Jayadharan, C. Catlett, A. N. Montanari, and N. M. Mangan, "SODAs: Sparse Optimization for the Discovery of Differential and Algebraic Equations." Proc. A 1 May 2026; 482 (2337): 20250201. https://doi.org/10.1098/rspa.2025.0201

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📦 Installation

DaeFinder requires Python 3.9+.

pip install DaeFinder

Install the latest development version from source

git clone https://github.com/mjayadharan/DAE-FINDER_dev.git
cd DAE-FINDER_dev
pip install -e .

Dependencies (installed automatically): numpy, scipy, pandas, sympy, scikit-learn, matplotlib, joblib.

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🚀 Quick start

import pandas as pd
from daeFinder import PolyFeatureMatrix, AlgModelFinder

# Your measurements: one column per state variable, one row per time point.
data = pd.DataFrame({"S": ..., "E": ..., "ES": ..., "P": ...})

# 1) Build a candidate library of nonlinear (polynomial) features.
library = PolyFeatureMatrix(degree=2).fit_transform(data)

# 2) Discover sparse algebraic relations among the library terms.
finder = AlgModelFinder(model_id="lasso", alpha=0.01)
finder.fit(library, scale_columns=True)

# ...or fit every candidate in parallel:
finder.fit(library, scale_columns=True, parallelize=True, num_cpu=8)

# 3) Rank and inspect the strongest recovered relations.
print(finder.best_models(num=5))

Working from noisy data? Smooth it and estimate derivatives first:

from daeFinder import smooth_data

smoothed = smooth_data(data, smooth_method="spline", noise_perc=2, derr_order=1)

See the Examples/ folder for full, runnable walkthroughs.

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🧠 How it works

DaeFinder follows the SODAs pipeline:

1. Smooth & differentiate noisy measurements to obtain clean state variables and their time derivatives.
2. Construct a candidate library of nonlinear terms (e.g. polynomial features, coupled features).
3. Sparsely regress library terms against one another to surface algebraic constraints, then against derivatives to surface the dynamics.
4. Refine & simplify the discovered relations into interpretable symbolic equations.

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🔧 Compatibility

DaeFinder is continuously tested across the modern scientific-Python stack:

Component	Supported
Python	3.9 – 3.14
NumPy	1.x and 2.x
pandas	2.x and 3.x
scikit-learn	≥ 1.2 (incl. 1.9)

A GitHub Actions matrix runs the full test suite on every supported Python version. (Recent releases resolved Python 3.13+ exec()/PEP 667, NumPy 2, pandas 3 copy-on-write, and scikit-learn ≥ 1.7 incompatibilities.)

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🧪 Testing

The package ships with a comprehensive regression suite under tests/.

pip install -r tests/requirements-test.txt

pytest                     # run everything
./tests/run_tests.sh       # run all tests + save a timestamped report

See tests/README.md for how to run the suite, read its reports, and add new tests.

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📚 Examples

Step-by-step notebooks live in Examples/, covering:

• A guided walkthrough of the discovery pipeline.
• Chemical reaction networks (Michaelis–Menten enzyme kinetics).
• Nonlinear & double pendulums.
• Power-grid networks.

Some examples need extra data or tools. Data files are included in the repository (download the relevant folders). The power-grid example also requires Matpower 6.0 for power-flow calculations.

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👥 Authors & contributors

Manu Jayadharan · Christina Catlett · Arthur Montanari · Grace Hooper · Niall Mangan · Finn Hagerty · Yuxiang Feng

Developed with the Mangan Group at Northwestern University.

🤝 Contributing

Contributions are welcome! Whether it's a bug report, a feature, a new example, or related research collaboration, please open an issue or reach out to the authors or the Mangan Group.

📬 Contact

• Manu Jayadharan — [e-mail] · [e-mail]
• Niall Mangan — [e-mail]

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Released under the MIT License.