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

Botond B Antal1, Anthony G Chesebro1, Helmut H Strey1,2

  • 1Department of Biomedical Engineering, Stony Brook University, Stony Brook, New York, United States of America.

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|July 18, 2024
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Summary
This summary is machine-generated.

Deep learning, using the FixFit method, applies Occam's razor to scientific models by reducing complexity and improving data fitting. This approach enhances model accuracy and aids in hypothesis discrimination across diverse scientific fields.

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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.