ArticleProceedings. Mathematical, physical, and engineering sciences2022
Stability selection enables robust learning of differential equations from limited noisy data.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 7 papers.
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7 citing papers in PubMed, 24 citations in OpenAlex.
- Nonlinear memory in cell-division dynamics across species.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Integrated path stability selection.Journal of the American Statistical Association · 2025Article
- asteRIa enables robust interaction modeling between chromatin modifications and epigenetic readers.Nucleic acids research · 2024Article
- STENCIL-NET for equation-free forecasting from data.Scientific reports · 2023Article
- Learning hydrodynamic equations for active matter from particle simulations and experiments.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
- Online Weak-form Sparse Identification of Partial Differential Equations.Proceedings of machine learning research · 2022Article
- Stability selection enables robust learning of differential equations from limited noisy data.Proceedings. Mathematical, physical, and engineering sciences · 2022Article
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Authors and funding
4 authors at 2 institutions in 2 countries.
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Abstract
We present a statistical learning framework for robust identification of differential equations from noisy spatio-temporal data. We address two issues that have so far limited the application of such methods, namely their robustness against noise and the need for manual parameter tuning, by proposing stability-based model selection to determine the level of regularization required for reproducible inference. This avoids manual parameter tuning and improves robustness against noise in the data. Our stability selection approach, termed PDE-STRIDE, can be combined with any sparsity-promoting regression method and provides an interpretable criterion for model component importance. We show that the particular combination of stability selection with the iterative hard-thresholding algorithm from compressed sensing provides a fast and robust framework for equation inference that outperforms previous approaches with respect to accuracy, amount of data required, and robustness. We illustrate the performance of PDE-STRIDE on a range of simulated benchmark problems, and we demonstrate the applicability of PDE-STRIDE on real-world data by considering purely data-driven inference of the protein interaction network for embryonic polarization in
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