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Hyper-differential sensitivity analysis for inverse problems governed by ODEs with application to COVID-19 modeling.
Mason Stevens1, Isaac Sunseri1, Alen Alexanderian1
1Department of Mathematics, North Carolina State University, Raleigh, NC, United States of America.
Mathematical Biosciences
|August 15, 2022
Summary
This study introduces enhanced methods for sensitivity analysis in inverse problems, crucial for understanding parameter uncertainty in models like COVID-19. The new approach quantifies uncertainty in estimated parameters, improving model reliability.
Area of Science:
- Mathematical modeling
- Computational science
- Applied mathematics
Background:
- Inverse problems governed by ordinary differential equations (ODEs) often involve uncertain parameters.
- Understanding the sensitivity of inverse problem solutions to these uncertain parameters and experimental setups is critical for applications.
- Existing Hyper-differential sensitivity analysis (HDSA) methods offer tools for sensitivity analysis.
Purpose of the Study:
- To extend HDSA methods for quantifying uncertainty in estimated parameters within ODE-governed inverse problems.
- To develop efficient methods for approximating statistical properties of estimated parameters using a linear approximation.
- To explore the application of this linear model for approximate global sensitivity analysis and parameter screening.
Main Methods:
- Development of a linear approximation to the inverse problem solution.
- Application of the linear approximation for efficient statistical property estimation of parameters.
- Utilizing the linear model for approximate global sensitivity analysis.
- Computational studies using a COVID-19 model as a case study.
Main Results:
- The proposed linear approximation effectively quantifies uncertainty in estimated parameters.
- The method efficiently approximates statistical properties of parameters.
- Computational studies demonstrated sensitivity to uncertain parameters and measurement types in a COVID-19 model.
- The linear approximation proved effective for uncertainty quantification and parameter screening.
Conclusions:
- The extended HDSA methods provide robust tools for uncertainty quantification in ODE-governed inverse problems.
- The linear approximation model offers an efficient approach for analyzing parameter sensitivity and uncertainty.
- This work enhances the reliability and interpretability of inverse problem solutions in scientific applications, exemplified by the COVID-19 model.
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