Yuto Miyatake (Osaka University, Japan) - Data Science
Date: - Location: Eurecom
We investigate the problem of parameter estimation in ordinary differential equation (ODE) models using noisy observations. Traditional approaches often involve fitting numerical solutions, such as those obtained via Euler or Runge-Kutta methods, to the observed data. However, these methods do not account for discretization errors inherent in numerical integration, thereby limiting the accuracy of the parameter estimates. In this context, quantifying discretization errors can significantly improve both the accuracy and the reliability evaluation of the parameter estimates. Although the literature on numerical analysis does not offer straightforward methods for quantifying these errors, we propose novel approaches to address this gap. In this talk, we introduce several models that treat discretization error as a random variable. We demonstrate that the variance of this random variable can be effectively updated using isotonic regression algorithms. Furthermore, we show that this updated variance provides a reliable quantification of the actual discretization error for several test problems. Brief bio: I have been an Associate Professor at the Cybermedia Center, Osaka University, since 2018. Prior to this, I was an Assistant Professor at Nagoya University, following the completion of my Ph.D. in 2015 from the University of Tokyo. My research interests lie in applied mathematics, specifically: + Numerical analysis of differential equations, with a focus on Geometric Integration + Numerical linear algebra, including continuous optimizations + Computational uncertainty quantification + Applications across various fields such as science, engineering, and informatics.
