Achieving Occam's razor: Deep learning for optimal model reduction

Area of Science:

• Scientific modeling across diverse domains including astrophysics, physiology, and neuroscience.
• Application of computational methods to fundamental scientific inquiry.

Background:

• Mathematical models are crucial in all scientific fields.
• Model complexity can lead to parameter estimation errors and ambiguous conclusions.
• Occam's razor principle advocates for parsimonious models.

Purpose of the Study:

• To leverage deep learning for applying Occam's razor to model parameters.
• Introduce a novel method, FixFit, for characterizing and predicting model behavior.
• Quantify model complexity and enable unique data fitting.

Main Methods:

• Utilized a feedforward deep neural network with a bottleneck layer (FixFit).
• Characterized model behavior based on input parameters.
• Applied FixFit to Kepler orbit, blood glucose regulation, and multi-scale brain models.

Main Results:

• FixFit quantifies model complexity.
• Enables unique fitting of data to models.
• Provides an unbiased method for hypothesis discrimination.
• Successfully recovered parameters for known models and identified parameters in complex systems.

Conclusions:

• Deep learning offers a powerful approach to model parsimony.
• FixFit enhances the reliability and interpretability of scientific models.
• The method has broad applicability in reducing model complexity and guiding research directions.