Numerical Methods for Parameter Estimation in Dynamical Systems Using Measurements at Bifurcation Points

Traditional approaches to parameter estimation typically rely on measurements of observables over multiple points in time. However, obtaining such data can be challenging or even infeasible for many experimental systems, particularly those that operate on a fast timescale. Therefore, in this talk, I will introduce an alternative approach to parameter estimation - one that uses the values of applied external controls at bifurcation points, instead of time-series data to calibrate mathematical models.

We will start our discussion by formulating the parameter estimation problem as a constrained nonlinear least-squares problem that can be solved using the generalized Gauss-Newton method. Since this method relies on good initial guesses for effective convergence, we will then present our systematic and robust numerical strategy for initializing the optimization variables. Finally, we will discuss how standard optimal experimental design techniques can also be extended to our bifurcation-based framework to identify new measurement points that can reduce the uncertainty in the parameter estimates.