Dresden 2026 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 41: Poster: Nonlinear Dynamics, Granular Matter, and Machine Learning

DY 41.4: Poster

Mittwoch, 11. März 2026, 15:00–18:00, P5

On Uncertainty Quantification in Parameter Estimation of Ordinary Differential Equation Initial Value Problems — •Oliver Strebel — Angelstr. 17, 75392 Deckenpfronn

Parameter estimation tasks for ordinary differential equation initial value problems (ODE-IVP) arise, when solution data for the ODE-IVP are given and for a given model the parameters and initial values are estimated. From the mathematical definition of the ODE-IVP it follows that uncertainty due to noise in the data and from a misfit of the model is reflected in the parameters and initial values alone. This uncertainty determines the uncertainty in the solution curves of the ODE-IVP. It is shown that simple Monte Carlo simulations, using the standard nonlinear regression measure, are well-suited for uncertainty quantification (UQ) in ODE-IVPs. This approach also uncovers practical identifiability issues related to the parameters and initial conditions. Additionally, the limitations of the method, such as its sensitivity to initial conditions and computational feasibility, are discussed.

Keywords: ordinary differential equation; parameter estimation; uncertainty quantification; practical identifiability