Learning physically consistent differential equation models from data using group sparsity.

Area of Science:

• Computational Biology
• Systems Biology
• Statistical Learning

Background:

• Data-driven modeling is valuable but can yield physically inconsistent models in biology due to noise and variability.
• Incorporating prior knowledge from physical principles is crucial for biologically plausible models.
• Existing methods may not adequately enforce constraints like conservation laws or symmetries.

Purpose of the Study:

• To develop a statistical learning framework for inferring differential-equation models from data.
• To enforce physical constraints such as conservation laws, model equivalence, and symmetries.
• To generate biologically plausible and physically consistent models.

Main Methods:

• Utilizing a group-sparse regression framework.
• Implementing the group iterative hard thresholding algorithm.
• Employing stability selection for parameter tuning and model inference.

Main Results:

• Demonstrated the ability to enforce conservation laws, model equivalence, and symmetries.
• Successfully inferred physically consistent models from noisy biological data.
• Showcased the benefits of incorporating prior knowledge into data-driven modeling.

Conclusions:

• The proposed framework enables the learning of interpretable and physically consistent differential-equation models.
• Enforcing prior knowledge significantly improves the biological plausibility and reliability of data-driven models.
• This approach offers a robust method for advancing systems biology research through accurate model inference.