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Model reduction using a posteriori analysis.

Jonathan P Whiteley¹

¹Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX13QD, United Kingdom. Jonathan.Whiteley@comlab.ox.ac.uk

Mathematical Biosciences

|February 2, 2010

Summary

This summary is machine-generated.

This study introduces a new method to pinpoint crucial mathematical model components affecting biological system behavior. It uses a posteriori error analysis to identify key terms for accurate functional predictions in complex models.

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Area of Science:

Computational Biology
Mathematical Modeling
Systems Physiology

Background:

Biological and physiological systems are frequently modeled using large, non-linear ordinary differential equation systems.
Observed behaviors often correspond to linear functionals of these complex model solutions.

Purpose of the Study:

To develop an automated technique for identifying critical terms within mathematical models.
To determine which model components significantly influence specific linear functionals of the solution.

Main Methods:

The study adapts concepts from a posteriori error analysis, commonly used in finite element analysis.
This approach identifies influential regions in the computational domain and solution components.

Main Results:

The technique successfully identifies key mathematical terms responsible for specific functional outputs.
Demonstrated effectiveness on a model problem and a cell-level cardiac electrophysiology model, reproducing known results.

Conclusions:

The developed method automates the identification of essential model components for accurate functional prediction.
This technique enhances understanding and efficiency in analyzing complex biological mathematical models.