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Renormalized Mori-Zwanzig-reduced models for systems without scale separation.

Panos Stinis1

  • 1Department of Mathematics , University of Minnesota , Minneapolis, MN 55455, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|August 23, 2016
PubMed
Summary

Developing accurate reduced models for complex systems is challenging due to scale separation issues. This work surveys Mori-Zwanzig-reduced models, inspired by physics concepts, for systems lacking clear scale separation.

Keywords:
Mori–Zwanzigmodel reductionrenormalization

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Area of Science:

  • Computational Physics
  • Applied Mathematics
  • Complex Systems Modeling

Background:

  • Model reduction is crucial for complex systems but often expensive.
  • A key challenge is the vast range of spatial and temporal scales.
  • Reduced models often require handling variables without clear scale separation.

Purpose of the Study:

  • To survey recent advancements in constructing Mori-Zwanzig-reduced models.
  • To address model reduction for systems lacking spatial or temporal scale separation.
  • To explore physics-inspired approaches for complex system modeling.

Main Methods:

  • Surveying recent results on Mori-Zwanzig-reduced models.
  • Applying concepts of scale dependence and renormalization.
  • Developing reduced models for systems with interacting scales.

Main Results:

  • Mori-Zwanzig-reduced models offer a framework for systems without scale separation.
  • Physics concepts like renormalization provide insights into model construction.
  • Effective reduced models can be built even when scales are intertwined.

Conclusions:

  • Mori-Zwanzig-reduced models are a promising approach for complex systems.
  • The integration of physics concepts aids in tackling scale challenges.
  • This methodology advances the field of model reduction for intricate systems.