Stability selection enables robust learning of differential equations from limited noisy data

Research output: Contribution to journalResearch articleContributedpeer-review



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 Caenorhabditis elegans. Using fluorescence microscopy images of C. elegans zygotes as input data, PDE-STRIDE is able to learn the molecular interactions of the proteins.


Original languageEnglish
Article number20210916
Number of pages25
JournalProceedings of the Royal Society of London : Series A, Mathematical, physical and engineering sciences
Issue number2262
Publication statusPublished - Jun 2022

External IDs

PubMedCentral PMC9199075
Scopus 85132361601
unpaywall 10.1098/rspa.2021.0916
WOS 000814371000003
Mendeley 6b1c9678-f6d9-31e0-bafb-031b63248a1a
ORCID /0000-0003-4414-4340/work/142252172