482 citations · 604 across the 16 of their papers we have counts for
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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…
KAM Theory Meets Statistical Learning Theory: Hamiltonian Neural Networks with Non-Zero Training Loss
Yuhan Chen, Takashi Matsubara, Takaharu Yaguchi
Many physical phenomena are described by Hamiltonian mechanics using an energy function (the Hamiltonian). Recently, the Hamiltonian neural network, which approximates the Hamilton…
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…