Project Info
Automated Sensitivity Analysis for Dynamical Systems
Mike Mikucki
mikucki@mines.edu
Performing forward sensitivity analysis has been an integral component of mathematical modeling, yet its implementation becomes increasingly difficult with a model's complexity. For a system of N differential equations with K parameters, a system of NK differential equations are required. Even writing down this system of equations is cumbersome, let alone solving them. A software package called SENSAI built in MATLAB automates this process, but is now inaccessible due to software updates. This project seeks to update and improve the automation process, both in determining and solving the sensitivity equations. Further applications include automation of the sensitivity of any model quantity of interest with respect to any parameter, such as but not limited to the basic reproduction number in infectious disease models.
More Information:
Grand Challenge: Not applicable.
Transient Sensitivity Analysis for Nonlinear Population Models. https://besjournals.onlinelibrary.wiley.com/doi/10.1111/j.2041-210X.2011.00108.x
Primary Contacts:
Mike Mikucki, AMS
Student Preparation
Qualifications
Mathematical modeling with systems of differential equations and systems of difference equations. Numerical solution of systems of differential equations. Programming in Python and MATLAB (functions, loops, vectors, automatic differentiation).
TIME COMMITMENT (HRS/WK)
4-5
SKILLS/TECHNIQUES GAINED
Sensitivity analysis for mathematical modeling, including interpretation of results in the context of the model. Software development and increase in programming skills.
MENTORING PLAN
The overall product is a large undertaking, so it is very important to give the students manageable small stepping stones toward the goal. I will meet with the student on a weekly or as-needed basis for incremental checkpoints of the project, ensuring that the incremental step is successful before giving the student another larger task. Various reading on background material (math and/or programming) may also be required.
PREFERRED STUDENT STATUS
Sophomore
Junior
Senior