no code implementations • 14 Feb 2024 • Yusuke Tanaka, Takaharu Yaguchi, Tomoharu Iwata, Naonori Ueda

The operator learning has received significant attention in recent years, with the aim of learning a mapping between function spaces.

no code implementations • 26 Jul 2023 • Takashi Matsubara, Takaharu Yaguchi

However, the solutions to PDEs are inherently infinite-dimensional, and the distance between the output and the solution is defined by an integral over the domain.

no code implementations • 1 Oct 2022 • Takashi Matsubara, Takaharu Yaguchi

However, these models incorporate the underlying structures, and in most situations where neural networks learn unknown systems, these structures are also unknown.

no code implementations • NeurIPS 2021 • Yuhan Chen, Takashi Matsubara, Takaharu Yaguchi

In this study, we propose a model that learns the symplectic form from data using neural networks, thereby providing a method for learning Hamiltonian equations from data represented in general coordinate systems, which are not limited to the generalized coordinates and the generalized momenta.

no code implementations • 22 Feb 2021 • Yuhan Chen, Takashi Matsubara, Takaharu Yaguchi

To apply the KAM theory, we provide a generalization error bound for Hamiltonian neural networks by deriving an estimate of the covering number of the gradient of the multi-layer perceptron, which is the key ingredient of the model.

1 code implementation • NeurIPS 2021 • Takashi Matsubara, Yuto Miyatake, Takaharu Yaguchi

The symplectic adjoint method obtains the exact gradient (up to rounding error) with memory proportional to the number of uses plus the network size.

no code implementations • 22 Dec 2020 • Mizuka Komatsu, Takaharu Yaguchi

As the parameters of unidentifiable models cannot be uniquely determined from the given data, it is difficult to examine the systems described by such models.

1 code implementation • NeurIPS 2020 • 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.

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