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Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations.

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This study introduces a new method for Dynamic Mode Decomposition (DMD) to analyze data from adaptive mesh refinement (AMR) simulations. This approach allows for feature extraction from complex systems with varying data dimensions, improving dynamic system analysis.

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Adaptive mesh refinement and coarseningDimensionality reductionDynamic mode decompositionMesh projection

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Area of Science:

  • * Computational fluid dynamics
  • * Data-driven modeling
  • * Scientific computing

Background:

  • * Dynamic Mode Decomposition (DMD) is a key technique for analyzing dynamical systems by extracting spatio-temporal structures.
  • * Standard DMD requires data snapshots of consistent dimensionality, which is often not met in adaptive mesh refinement (AMR) simulations.
  • * Adaptive mesh refinement/coarsening (AMR/C) schemes generate simulation data with varying mesh topologies and dimensions, posing challenges for traditional DMD.

Purpose of the Study:

  • * To develop a novel strategy enabling DMD to process data from AMR/C simulations with heterogeneous dimensionality.
  • * To project adaptive snapshots onto a common reference function space for compatibility with DMD.
  • * To validate the proposed DMD strategy on complex AMR/C simulations and assess its reconstruction and extrapolation capabilities.

Main Methods:

  • * Projection of adaptive snapshots onto a unified reference function space.
  • * Application of Dynamic Mode Decomposition (DMD) to the transformed data.
  • * Validation using diverse AMR/C simulations: COVID-19 SEIRD model, gravity currents, and bubble rising phenomena.
  • * Evaluation of DMD's efficiency in reconstructing dynamics and extrapolating future states.

Main Results:

  • * Successful application of DMD to extract coherent structures from AMR/C simulation data with varying dimensions.
  • * Demonstrated ability of the proposed method to reconstruct system dynamics and relevant quantities of interest.
  • * Validated DMD's capability for short-term future state extrapolation in epidemiological and fluid dynamics models.

Conclusions:

  • * The proposed projection strategy effectively extends DMD's applicability to complex AMR/C simulations.
  • * This method enhances the analysis of dynamical systems producing non-uniform data.
  • * The approach offers a robust tool for understanding and predicting the behavior of complex physical and biological systems.