48 citations · 71 across the 17 of their papers we have counts for
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Elucidating the Conformal Structure of the Brinkman Penalisation Method for Geometry-Adapted, Structure-Preserving Operator Learning of Hamiltonian PDEs
Teo Deveney, Baige Xu, Takaharu Yaguchi
The Brinkman penalisation method embeds boundary-value problems on complex domains into a simple computational box by modeling the solid region as a strongly dissipative medium, av…
An Error Analysis Framework for Neural Network Modeling of Dynamical Systems
Shunpei Terakawa, Takashi Matsubara, Takaharu Yaguchi
We propose a theoretical framework for investigating a modeling error caused by numerical integration in the learning process of dynamics. Recently, learning equations of motion to…
Symplecticity of coupled Hamiltonian systems
Shunpei Terakawa, Takaharu Yaguchi
We derived a condition under which a coupled system consisting of two finite-dimensional Hamiltonian systems becomes a Hamiltonian system. In many cases, an industrial system can b…
Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics
Nobuki Takayama, Takaharu Yaguchi, Yi Zhang
Definite integrals with parameters of holonomic functions satisfy holonomic systems of linear partial differential equations. When we restrict parameters to a one dimensional curve…
Deep Energy-Based Modeling of Discrete-Time Physics
Takashi Matsubara, Ai Ishikawa, Takaharu Yaguchi
Physical phenomena in the real world are often described by energy-based modeling theories, such as Hamiltonian mechanics or the Landau theory, which yield various physical laws. R…
Preserving multiple first integrals by discrete gradients
Morten Dahlby, Brynjulf Owren, Takaharu Yaguchi
We consider systems of ordinary differential equations with known first integrals. The notion of a discrete tangent space is introduced as the orthogonal complement of an arbitrary…