ma-code

This repository complements the work done in my master's thesis

"The Role of Bifurcations in Parameter Estimation: Application to the Klausmeier Vegetation Model with Random Coefficients".

The code implements uncertainty quantification (UQ) and parameter estimation tools from [2] and applies them to the Klausmeier vegetation model in its ODE form [1]. The goal is to systematically assess parameter identifiability and uncertainty around the model bifurcation, expanding the work of [3]. We treat the model in a Bayesian setting and try to estimate posterior parameter distributions using Gaussian approximation of the posterior.

The following are implemented (amongst others):

• Global sensitvity analysis using Sobol indices
• Solution and UQ assessment of the inverse problem
• Forward UQ with Monte Carlo simulations
• Simulation of model trajectories and bifurcation behavior

In src/ all the functionalities are implemented; notebooks/ contains all experiments conducted in Jupyter notebooks; plots/ stores all resulting plots.

Main references:

_{[1] Klausmeier, C. A. (1999). "Regular and irregular patterns in semiarid vegetation." Science, 284(5421), pp. 1826-1828.
[2] Piazzola, C., et al. (2021). "A note on tools for prediction under uncertainty and identifiability of SIR-like dynamical systems for epidemiology." In: Mathematical Biosciences 332 (2021), p. 108514.
[3] Roesch, E., & Stumpf, M. P. H. (2019). "Parameter inference in dynamical systems with co-dimension 1 bifurcations." Royal Society Open Science, 6(10).}