6 papers
Bayesian Inference of Discretization Error Means in ODEs via Ensemble Kalman Filtering
Shoji Toyota, Yuto Miyatake
We propose a Bayesian framework to quantify discretization errors in numerical solutions of ODE models based on observational data. The discretization error is modeled as a random…
Accelerating SAV-based optimization via randomized low-rank Hessian approximation
Ryo Sagawa, Daisuke Furihata, Yuto Miyatake
We propose a new optimization method, the Nyström-enhanced relaxed scalar auxiliary variable method (N-RSAV), which incorporates curvature information into the RSAV framework to ac…
An error control framework for computing the exponential of matrices arising from the finite element discretization
Fuminori Tatsuoka, Yuto Miyatake, Tomohiro Sogabe
Several methods for computing the action of the matrix exponential are expressed by substituting into a rational appro…
Joint Bayesian Inference of Parameter and Discretization Error Uncertainties in ODE Models
Shoji Toyota, Yuto Miyatake
We address the problem of Bayesian inference for parameters in ordinary differential equation (ODE) models based on observational data. Conventional approaches in this setting typi…
Quantifying uncertainty in the numerical integration of evolution equations based on Bayesian isotonic regression
Yuto Miyatake, Kaoru Irie, Takeru Matsuda
This paper presents a new Bayesian framework for quantifying discretization errors in numerical solutions of ordinary differential equations. By modelling the errors as random vari…
On the B-series composition theorem
John C. Butcher, Taketomo Mitsui, Yuto Miyatake +1
The B-series composition theorem has been an important topic in numerical analysis of ordinary differential equations for the past-half century. Traditional proofs of this theorem…