Abstract
Approximate ordinary differential equation models are commonly used when the original dynamics are complex, uncertain, or deliberately perturbed for sensitivity analysis.
In this talk, I will present joint work with Tatjana Petrov on a method for constructing finite-time, coordinate-wise error tubes around a supplied same-dimensional approximation.
Our construction combines a defect measuring the mismatch between the original and approximate vector fields with a logarithmic-norm bound controlling how this mismatch is amplified or damped by the dynamics. A scalar comparison equation yields an error radius in a weighted quadratic metric, which is then converted into upper and lower bounds for the physical state variables. Importantly, constructing the tube does not require solving the original system. We illustrate the approach using chemical reaction networks and show how the resulting bounds can quantify the reliability of parameter-perturbed models and support finite-time robustness and sensitivity analysis.
About the speaker
Iman Mehrabinezhad is a mathematician and postdoctoral researcher at the University of Trieste. His research interests include nonlinear dynamical systems, contraction metrics, and numerical analysis, with applications in mathematical biology. His current work focuses on model reduction and error bounds for biochemical reaction networks.