48 citations · 71 across the 17 of their papers we have counts for
19 papers
Dirac-Interconnected Neural Elements: Discovering Modularity in Physical Systems Without Reduction
Reiho Li, Razmik Arman Khosrovian, Takaharu Yaguchi +2
Deep learning has shown remarkable success in the data-driven modeling of dynamical systems. Much of its success is attributed not to the flexibility of neural networks but to indu…
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…
Horizon-Aware Early Event Prediction for Tokamak Disruption Alarms
Takeshi Koshizuka, Takaharu Yaguchi
Disruption predictors must warn the plasma control system early enough for the intended response, and the required warning time differs between mitigation and avoidance. We view a…
CoSynFlow: Conformal Symplectic Neural Flows for Cross-System Prediction of Dissipative Hamiltonian Dynamics
Baige Xu, Takaharu Yaguchi
Learning solution operators for differential equations is a central problem in scientific machine learning. However, many neural operator methods optimize prediction accuracy witho…
Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems
Yeang Makara, Yusuke Tanaka, Takashi Matsubara +1
The modeling and simulation of infinite-dimensional Hamiltonian systems are central problems in mathematical physics and engineering, however they pose significant computational an…
Approximation of Maximally Monotone Operators : A Graph Convergence Perspective
Takashi Furuya, Yury Korolev, Takaharu Yaguchi
Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-includ…
Learning Hamiltonian Density Using DeepONet
Baige Xu, Yusuke Tanaka, Takashi Matsubara +1
In recent years, deep learning for modeling physical phenomena which can be described by partial differential equations (PDEs) have received significant attention. For example, for…
Poisson-Dirac Neural Networks for Modeling Coupled Dynamical Systems across Domains
Razmik Arman Khosrovian, Takaharu Yaguchi, Hiroaki Yoshimura +1
Deep learning has achieved great success in modeling dynamical systems, providing data-driven simulators to predict complex phenomena, even without known governing equations. Howev…
Neural Operators Meet Energy-based Theory: Operator Learning for Hamiltonian and Dissipative PDEs
Yusuke Tanaka, Takaharu Yaguchi, Tomoharu Iwata +1
The operator learning has received significant attention in recent years, with the aim of learning a mapping between function spaces. Prior works have proposed deep neural networks…
Number Theoretic Accelerated Learning of Physics-Informed Neural Networks
Takashi Matsubara, Takaharu Yaguchi
Physics-informed neural networks solve partial differential equations by training neural networks. Since this method approximates infinite-dimensional PDE solutions with finite col…
FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantities
Takashi Matsubara, Takaharu Yaguchi
Many real-world dynamical systems are associated with first integrals (a.k.a. invariant quantities), which are quantities that remain unchanged over time. The discovery and underst…
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…
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…
Method for estimating hidden structures determined by unidentifiable state-space models and time-series data based on the Groebner basis
Mizuka Komatsu, Takaharu Yaguchi
In this study, we propose a method for extracting the hidden algebraic structures of model parameters that are uniquely determined by observed time-series data and unidentifiable s…
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…