PDE-STRIDE

PDE-STRIDE identifies differential equations from noisy spatio-temporal datasets to infer mechanistic interactions such as protein interaction networks underlying processes like embryonic polarization.

Key Features:

• Stability-Based Model Selection: Employs stability selection to enhance robustness to noise and automatically determine the appropriate level of regularization for reproducible inference.
• Integration with Sparsity-Promoting Regression: Can be integrated with any sparsity-promoting regression method to select relevant PDE terms.
• Iterative Hard-Thresholding Algorithm: Combines stability selection with the iterative hard-thresholding algorithm from compressed sensing to provide fast and robust differential equation inference.
• Automated Parameter Tuning: Eliminates the need for manual parameter tuning by using algorithmic selection of regularization parameters.
• Interpretable Component Importance: Provides an interpretable criterion for assessing the importance of different components within inferred models.
• Improved Speed and Accuracy: Demonstrates enhanced speed and accuracy of model identification relative to previous approaches.

Scientific Applications:

• Benchmarking and Simulation: In simulations, outperforms existing approaches by requiring less data while maintaining high accuracy and robustness against noise.
• Protein Interaction Network Inference: Applied to fluorescence microscopy images of Caenorhabditis elegans zygotes to infer molecular interactions among proteins involved in embryonic polarization.

Methodology:

Uses stability selection, integration with sparsity-promoting regression methods, and the iterative hard-thresholding algorithm from compressed sensing applied to fluorescence microscopy images of Caenorhabditis elegans zygotes to infer molecular interactions.