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

Area of Science:

• Computational biology
• Systems biology
• Data science

Background:

• Identifying differential equations from noisy spatio-temporal data is challenging.
• Existing methods often lack robustness against noise and require manual parameter tuning.
• Robust and automated methods are crucial for advancing scientific discovery.

Purpose of the Study:

• To present a statistical learning framework for robust identification of differential equations from noisy spatio-temporal data.
• To address limitations of existing methods regarding noise robustness and parameter tuning.
• To introduce a novel stability-based model selection approach for reproducible inference.

Main Methods:

• Proposed stability-based model selection to determine regularization levels for reproducible inference.
• Developed PDE-STRIDE (Partial Differential Equation - Stability-based Robust Identification of Differential Equations).
• Combined stability selection with iterative hard-thresholding for efficient equation inference.

Main Results:

• PDE-STRIDE demonstrates improved accuracy, reduced data requirements, and enhanced robustness compared to previous methods.
• The approach avoids manual parameter tuning and increases robustness against data noise.
• Successfully applied to simulated benchmark problems and real-world biological data.

Conclusions:

• PDE-STRIDE offers a fast, robust, and accurate framework for differential equation inference from noisy data.
• The method facilitates purely data-driven inference of complex biological networks, such as protein interactions.
• This framework has broad applicability in scientific research where differential equations model dynamic systems.