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Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study
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Improving model fidelity and sensitivity for complex systems through empirical information theory.

Andrew J Majda1, Boris Gershgorin

  • 1Department of Mathematics and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA. jonjon@cims.nyu.edu

Proceedings of the National Academy of Sciences of the United States of America
|June 8, 2011
PubMed
Summary

This study introduces an information theoretic framework to enhance complex system models. It improves model fidelity and sensitivity, crucial for accurate scientific predictions despite inherent model errors.

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Area of Science:

  • Complex Systems Analysis
  • Scientific Modeling
  • Information Theory

Background:

  • Contemporary science and engineering often rely on complex dynamical equations for analysis and prediction.
  • These models frequently exhibit significant errors compared to real-world phenomena, impacting accuracy.
  • Improving both model fidelity and sensitivity is essential for reliable scientific insights.

Purpose of the Study:

  • To develop a systematic information theoretic framework to enhance model fidelity and sensitivity for complex systems.
  • To address simultaneous improvements in both aspects of model error.
  • To provide a robust methodology for evaluating and refining imperfect scientific models.

Main Methods:

  • Development of a novel information theoretic framework.
  • Utilization of perturbation formulas and multimodel ensembles.
  • Testing the framework with a suite of unambiguous test models, including linear stochastic and nonlinear atmospheric tracer models.

Main Results:

  • Demonstrated the framework's ability to improve model fidelity and sensitivity simultaneously.
  • Identified natural barriers to improving sensitivity in imperfect models with perfect equilibrium fidelity.
  • Showcased the role of spatial resolution and stochastic forcing in enhancing information-theoretic measures.

Conclusions:

  • The proposed information theoretic framework offers a systematic approach to refining complex system models.
  • Effective improvement of model fidelity and sensitivity is achievable through this framework.
  • Stochastic forcing plays a critical role in enhancing imperfect models for better scientific predictions.