3 papers
math.NA2024
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…
cs.LG2024
Structure-Preserving Physics-Informed Neural Networks With Energy or Lyapunov Structure
Haoyu Chu, Yuto Miyatake, Wenjun Cui +2
Recently, there has been growing interest in using physics-informed neural networks (PINNs) to solve differential equations. However, the preservation of structure, such as energy…
math.NA2022
Structure-preserving numerical methods for constrained gradient flows of planar closed curves with explicit tangential velocities
Tomoya Kemmochi, Yuto Miyatake, Koya Sakakibara
In this paper, we consider numerical approximation of constrained gradient flows of planar closed curves, including the Willmore and the Helfrich flows. These equations have energy…