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Quantifying uncertainty in partially specified biological models: how can optimal control theory help us?
M W Adamson1, A Y Morozov2, O A Kuzenkov3
1Department of Mathematics , University of Leicester , Leicester LE1 7RH , UK.
Proceedings. Mathematical, Physical, and Engineering Sciences
|October 8, 2016
Summary
Mathematical models in biology face uncertainty due to simplified functions. This study introduces a new framework using optimal control theory to project function spaces, enabling robust uncertainty analysis in biological models.
Area of Science:
- Mathematical Biology
- Computational Biology
- Systems Biology
Background:
- Biological models are simplified representations with inherent uncertainty in function specification.
- Structural sensitivity in models, where different functions yield varied predictions, critically impacts reliability.
- Existing frameworks struggle to address uncertainty propagation from model functions to predictions.
Purpose of the Study:
- To develop a novel framework for uncertainty analysis in biological models.
- To address the challenge of projecting infinite-dimensional function spaces into lower dimensions using biological constraints.
- To enable more flexible and user-friendly uncertainty quantification for biological models.
Main Methods:
- Utilizing partially specified models where functions are not rigidly defined.
- Employing optimal control theory to construct functions that satisfy specified global properties.
- Projecting function spaces while incorporating biological constraints to manage complexity.
Main Results:
- Demonstration of a powerful technique for function space projection.
- Successful application of optimal control theory for constructing biologically relevant functions.
- Establishment of a method to handle uncertainty arising from model function specification.
Conclusions:
- The proposed framework offers a flexible approach to uncertainty analysis in biological modeling.
- Optimal control theory provides a viable solution for the projection challenge in partially specified models.
- This method enhances the reliability and interpretability of predictions from complex biological models.
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