2 citations · 2 across the 3 of their papers we have counts for
10 papers
High-order linearly implicit schemes conserving quadratic invariants
Shun Sato, Yuto Miyatake, John C. Butcher
In this paper, we propose linearly implicit and arbitrary high-order conservative numerical schemes for ordinary differential equations with a quadratic invariant. Many differentia…
Symplectic Adjoint Method for Exact Gradient of Neural ODE with Minimal Memory
Takashi Matsubara, Yuto Miyatake, Takaharu Yaguchi
A neural network model of a differential equation, namely neural ODE, has enabled the learning of continuous-time dynamical systems and probabilistic distributions with high accura…
Computing the matrix fractional power with the double exponential formula
Fuminori Tatsuoka, Tomohiro Sogabe, Yuto Miyatake +2
Two quadrature-based algorithms for computing the matrix fractional power are presented in this paper. These algorithms are based on the double exponential (DE) formula, whic…
Generalization of partitioned Runge--Kutta methods for adjoint systems
Takeru Matsuda, Yuto Miyatake
This study computes the gradient of a function of numerical solutions of ordinary differential equations (ODEs) with respect to the initial condition. The adjoint method computes t…
A Parallelizable Energy-Preserving Integrator MB4 and Its Application to Quantum-Mechanical Wavepacket Dynamics
Tsubasa Sakai, Shuhei Kudo, Hiroto Imachi +3
In simulating physical systems, conservation of the total energy is often essential, especially when energy conversion between different forms of energy occurs frequently. Recently…
A fully discrete curve-shortening polygonal evolution law for moving boundary problems
Koya Sakakibara, Yuto Miyatake
We consider the numerical integration of moving boundary problems with the curve-shortening property, such as the mean curvature flow and Hele-Shaw flow. We propose a fully discret…