Updated on 2026/07/07

Information

 

写真a

 
YAGUCHI TAKAHARU
 
Organization
Institute of Mathematics for Industry Division of Advanced Mathematics Technology Professor
Graduate School of Mathematics Department of Mathematics（Concurrent）
School of Sciences Department of Mathematics（Concurrent）
Title
Professor
Contact information
メールアドレス
External link

Research Areas

  • Natural Science / Applied mathematics and statistics

Research Interests・Research Keywords

  • Research theme： 社会ネットワーク解析

    Keyword： 社会ネットワーク解析

    Research period： 2026

  • Research theme： Machine Learning

    Keyword： Machine Learning

    Research period： 2026

  • Research theme： 数理モデリング

    Keyword： 数理モデリング

    Research period： 2026

  • Research theme： Numerical Analysis

    Keyword： Numerical Analysis

    Research period： 2026

  • Research theme： Geometric Mechanics

    Keyword： Geometric Mechanics

    Research period： 2026

  • Research theme： Morphological Computing

    Keyword： Morphological Computing

    Research period： 2026

Awards

  • 学長表彰（財務貢献者）

    2024.10   神戸大学  

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  • 学長表彰（財務貢献者）

    2023.10   神戸大学  

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  • JSIAM Letters Paper Award

    2023.9   JSIAM Letters Paper Award   Causal inference for empirical dynamical systems based on persistent homology

    Hiroaki Bando, Shizuo Kaji, Takaharu Yaguchi

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Papers

  • UEPI: Universal Energy-Behavior-Preserving Integrators for Energy Conservative/Dissipative Differential Equations Reviewed

    Elena Celledoni, Brynjulf Owren, Chong Shen, Baige Xu, Takaharu Yaguchi

    Advances in Neural Information Processing Systems   38   2025.12

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  • A posteriori error estimation of numerical solutions of PINNs for the Navier–Stokes equations under the Dirichlet boundary condition with external force Reviewed

    Baige Xu, Takaharu Yaguchi

    International Journal of Mathematics for Industry   17 ( 1 )   2025.12   （ ISSN:26613352 ）

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：International Journal of Mathematics for Industry  

    In this paper, we present an a posteriori error estimation for numerical solutions of Physics-Informed Neural Networks (PINNs) for the Navier–Stokes equations under the Dirichlet boundary condition with external force. The main theorem provides a computable upper bound for the solution error via explicit indicators derived from the equation residual and initial error, both observable during the training of PINNs. This enables reliability assessment of numerical solutions of PINNs for fluid flows.

    DOI： 10.1142/S2661335225500108

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  • Hyperbolic partial differential equations generalize LSSL with the HiPPO matrix Reviewed

    Atsushi Takabatake, Takaharu Yaguchi

    Japan Journal of Industrial and Applied Mathematics   42 ( 3 )   1207 - 1229   2025.9   （ ISSN:09167005 ）

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Japan Journal of Industrial and Applied Mathematics  

    The LSSL with HiPPO matrix is a model for the modeling of time series data that can handle long-range dependencies. In a previous paper, we showed that the LSSL with HiPPO matrix can be expressed as a discretization of a partial differential equation. In this paper, we generalize this result. We show the LSSL with HiPPO matrix can be regarded as another discretization of the partial differential equation under another condition as well, and also propose a generalization of the HiPPO matrix by different discretizations of partial differential equations. Our result can extend existing state-space models to infinite-dimensional settings. In addition, we perform thorough numerical experiments to evaluate the proposed generalized model and confirm that the performance of the model can certainly be improved by this generalization.

    DOI： 10.1007/s13160-025-00731-4

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  • Energy-Consistent Neural Operators for Hamiltonian and Dissipative Partial Differential Equations Reviewed

    Proc. of the 28th International Conference on Artificial Intelligence and Statistics (AISTATS2025)   2025.5

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  • Number Theoretic Accelerated Learning of Physics-Informed Neural Networks Reviewed

    Matsubara T., Yaguchi T.

    Proceedings of the Aaai Conference on Artificial Intelligence   39 ( 1 )   595 - 603   2025.4   （ ISSN:21595399 ISBN:157735897X, 9781577358978 ）

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    Language：English   Publisher：Proceedings of the Aaai Conference on Artificial Intelligence  

    Physics-informed neural networks solve partial differential equations by training neural networks. Since this method approximates infinite-dimensional PDE solutions with finite collocation points, minimizing discretization errors by selecting suitable points is essential for accelerating the learning process. Inspired by number theoretic methods for numerical analysis, we introduce good lattice training and periodization tricks, which ensure the conditions required by the theory. Our experiments demonstrate that GLT requires 2-7 times fewer collocation points, resulting in lower computational cost, while achieving competitive performance compared to typical sampling methods.

    DOI： 10.1609/aaai.v39i1.32040

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  • Deep Energy-Based Discrete-Time Physical Model for Reproducing Energetic Behavior Reviewed

    Takashi Matsubara, Takehiro Aoshima, Ai Ishikawa, Takaharu Yaguchi

    IEEE Transactions on Neural Networks and Learning Systems   36 ( 8 )   15400 - 15412   2025   （ ISSN:2162237X ）

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：IEEE Transactions on Neural Networks and Learning Systems  

    Modeling and simulating physical phenomena, especially those governed by partial differential equations (PDEs), pose significant challenges in computational physics and scientific machine learning. While neural network approaches have made strides in learning continuous-time dynamics, they have struggled with discrete-time scenarios and often fail to adhere to fundamental laws of physics, such as the conservation of energy and mass. This study addresses this gap by introducing a novel deep energy-based discrete-time model. In the real world, energy-based modeling theories like Hamiltonian mechanics and the Landau theory are pivotal, as they support various laws of physics. By integrating differential geometric structures into neural networks as coefficient matrices, our model successfully simulates the conservation and dissipation laws of energy and mass. Furthermore, we propose an automatic discrete differentiation algorithm, which enables neural networks to utilize the discrete gradient method, ensuring adherence to these laws in discrete-time settings. This capability also facilitates the identification of such laws directly from data by learning matrices that represent geometric structures. These advantages are verified using simulation results of physical phenomena, namely the 1- and 2-D Korteweg–de Vries (KdV) equation and the Cahn–Hilliard equation.

    DOI： 10.1109/TNNLS.2025.3529516

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  • POISSON-DIRAC NEURAL NETWORKS FOR MODELING COUPLED DYNAMICAL SYSTEMS ACROSS DOMAINS Reviewed

    Khosrovian R.A., Yaguchi T., Yoshimura H., Matsubara T.

    13th International Conference on Learning Representations Iclr 2025   84440 - 84468   2025   （ ISBN:9798331320850 ）

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    Language：English   Publisher：13th International Conference on Learning Representations Iclr 2025  

    Deep learning has achieved great success in modeling dynamical systems, providing data-driven simulators to predict complex phenomena, even without known governing equations. However, existing models have two major limitations: their narrow focus on mechanical systems and their tendency to treat systems as monolithic. These limitations reduce their applicability to dynamical systems in other domains, such as electrical and hydraulic systems, and to coupled systems. To address these limitations, we propose Poisson-Dirac Neural Networks (PoDiNNs), a novel framework based on the Dirac structure that unifies the port-Hamiltonian and Poisson formulations from geometric mechanics. This framework enables a unified representation of various dynamical systems across multiple domains as well as their interactions and degeneracies arising from couplings. Our experiments demonstrate that PoDiNNs offer improved accuracy and interpretability in modeling unknown coupled dynamical systems from data.

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  • FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantities Reviewed International journal

    T. Matsubara, T. Yaguchi

    Proc. of The Eleventh International Conference on Learning Representations (ICLR2023)   11   2023.5

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  • The Symplectic Adjoint Method: Memory-Efficient Backpropagation of Neural-Network-Based Differential Equations Reviewed

    Takashi Matsubara, Yuto Miyatake, Takaharu Yaguchi

    IEEE Transactions on Neural Networks and Learning Systems   35 ( 8 )   1 - 13   2023   （ ISSN:2162-237X eISSN:2162-2388 ）

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Institute of Electrical and Electronics Engineers (IEEE)  

    The combination of neural networks and numerical integration can provide highly accurate models of continuous-time dynamical systems and probabilistic distributions. However, if a neural network is used n times during numerical integration, the whole computation graph can be considered as a network n times deeper than the original. The backpropagation algorithm consumes memory in proportion to the number of uses times of the network size, causing practical difficulties. This is true even if a checkpointing scheme divides the computation graph into subgraphs. Alternatively, the adjoint method obtains a gradient by a numerical integration backward in time; although this method consumes memory only for single-network use, the computational cost of suppressing numerical errors is high. The symplectic adjoint method proposed in this study, an adjoint method solved by a symplectic integrator, obtains the exact gradient (up to rounding error) with memory proportional to the number of uses plus the network size. The theoretical analysis shows that it consumes much less memory than the naive backpropagation algorithm and checkpointing schemes. The experiments verify the theory, and they also demonstrate that the symplectic adjoint method is faster than the adjoint method and is more robust to rounding errors.

    DOI： 10.1109/tnnls.2023.3242345

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  • Robustness of Operator Learning Methods with MLP-Based Kolmogorov-Arnold Networks Reviewed

    Dehami Kiryu, Atsushi Takabatake, Takaharu Yaguchi

    The AAAI-26 Workshop on Artificial Intelligence for Cyber Security (AICS)   2026.1

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  • Infinite-Dimensional HiPPO Provides an Explicit Formula for LSSLs Reviewed

    Atsushi Takabatake, Takaharu Yaguchi

    NeurIPS2025 Workshop MATH-AI 2025   2025.12

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  • 【社会的孤立・孤独を広く深く捉え,つなげる(2)】社会的つながりへの介入による超高齢社会のウェルビーイングの実現　介入の理論・方法・評価

    増本 康平, 原田 和弘, 谷口 隆晴, 打田 篤彦, 近藤 徳彦

    心理学評論   68 ( 2 )   149 - 166   2025.10   （ ISSN:0386-1058 ）

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    Language：Japanese   Publisher：心理学評論刊行会  

  • Learning Discrete Integral Operators and Energy-Preserving Numerical Schemes for Nonlocal Hamiltonian Equations Reviewed

    Toki Shinogi, Chong Shen, Baige Xu, Takaharu Yaguchi

    ICICE Proceeding Series: 2025 International Symposium on Nonlinear Theory and Its Applications   2025.10

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  • Port-Hamiltonian Neural Networks for Learning Coupled Systems and Their Interactions Reviewed

    Razmik Arman Khosrovian, Takaharu Yaguchi, Takashi Matsubara

    NeurIPS 2024 Workshop on Machine Learning and the Physical Sciences   2024.12

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  • A New Approach to Designing Robust Hamiltonian Neural Networks by Regularisation Reviewed

    Dehami Kiryu, Baige Xu, Takashi Matsubara, Takaharu Yaguchi

    Proc. of 2024 International Symposium on Nonlinear Theory and Its Applications (NOLTA2024)   2024.12

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  • Learning Difference and Summation Operators for Discretization of Nonlocal Hamiltonian Partial Differential Equations Using Neural Networks Reviewed

    Toki Shinogi, Baige Xu, Takaharu Yaguchi

    Proc. of 2024 International Symposium on Nonlinear Theory and Its Applications (NOLTA2024)   2024.12

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  • Hyperbolic-PDE-Based Neural Network Architecture Reviewed

    Atsushi Takabatake, Baige Xu, Takaharu Yaguchi

    Proc. of 2024 International Symposium on Nonlinear Theory and Its Applications (NOLTA2024)   2024.12

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  • Application of the Kernel Method to Learning Symplectic Forms Reviewed

    Taisei Ueda, Baige Xu, Takashi Matsubara, Takaharu Yaguchi

    Proc. of 2024 International Symposium on Nonlinear Theory and Its Applications (NOLTA2024)   2024.12

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  • Loss Function for Deep Learning to Model Dynamical Systems Reviewed

    Yoshida T., Yaguchi T., Matsubara T.

    IEICE Transactions on Information and Systems   E107.D ( 11 )   1458 - 1462   2024.11   （ ISSN:09168532 ）

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    Language：English   Publisher：IEICE Transactions on Information and Systems  

    Accurately simulating physical systems is essential in various fields. In recent years, deep learning has been used to automatically build models of such systems by learning from data. One such method is the neural ordinary differential equation (neural ODE), which treats the output of a neural network as the time derivative of the system states. However, while this and related methods have shown promise, their training strategies still require further development. Inspired by error analysis techniques in numerical analysis while replacing numerical errors with modeling errors, we propose the error-analytic strategy to address this issue. Therefore, our strategy can capture long-term errors and thus improve the accuracy of long-term predictions.

    DOI： 10.1587/transinf.2023EDL8064

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  • Algebraic design of physical computing system Reviewed

    Mizuka Komatsu, Takaharu Yaguchi, Kohei Nakajima

    Physica D: Nonlinear Phenomena   470   134382 - 134382   2024.10   （ ISSN:0167-2789 ）

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    Recently, computational techniques that employ physical systems (physical computing systems) have been developed. To utilize physical computing systems, their design strategy is important. Although there are practical learning-based methods and theoretical approaches, no general method exists that provides specific design guidelines for given systems with rigorous theoretical support. In this paper, we propose a novel algebraic design framework for a physical computing system, which is capable of extracting specific design guidelines. Our approach describes input–output relationships algebraically and relates them to given target tasks. Two theorems are presented in this paper. The first theorem offers a basic strategy for algebraic design. The second theorem explores the “replaceability” of such systems. Their possible implementations are investigated through experiments. In particular, the design of inputs of a system so that it generates multiple target time-series and the replacement of stationary or non-stationary target systems by a given system that is designed algebraically are included. The proposed framework is shown to have the potential of designing given physical computing systems with theoretical support.

    DOI： 10.1016/j.physd.2024.134382

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  • Improved input points estimate for identifying nonlinear dynamic systems in DeepONet Reviewed

    Dehami Kiryu, Baige Xu, Takaharu Yaguchi

    Proc. of CAI2024 Workshop on Scientific Machine Learning and Its Industrial Applications (SMLIA2024)   2024.6

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  • Learning Coupled Systems and their Connectivity Using Port-Hamiltonian Neural Networks Reviewed

    Razmik Arman Khosrovian, Takaharu Yaguchi, Takashi Matsubara

    Proc. of CAI2024 Workshop on Scientific Machine Learning and Its Industrial Applications (SMLIA2024)   2024.6

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  • Modeling Error and Nonuniqueness of the Continuous-Time Models Learned via Runge–Kutta Methods Reviewed

    Shunpei Terakawa, Takaharu Yaguchi

    Mathematics   12 ( 8 )   2024.4

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Mathematics  

    In the present study, we consider continuous-time modeling of dynamics using observed data and formulate the modeling error caused by the discretization method used in the process. In the formulation, a class of linearized dynamics called Dahlquist’s test equations is used as representative of the target dynamics, and the characteristics of each discretization method for various dynamics are taken into account. The family of explicit Runge–Kutta methods is analyzed as a specific discretization method using the proposed framework. As a result, equations for predicting the modeling error are derived, and it is found that there can be multiple possible models obtained when using these methods. Several learning experiments using a simple neural network exhibited consistent results with theoretical predictions, including the nonuniqueness of the resulting model.

    DOI： 10.3390/math12081190

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  • Sparse Estimation for Hamiltonian Mechanics Reviewed

    Yuya Note, Masahito Watanabe, Hiroaki Yoshimura, Takaharu Yaguchi, Toshiaki Omori

    Mathematics   12 ( 7 )   974 - 974   2024.3   （ eISSN:2227-7390 ）

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：MDPI AG  

    Estimating governing equations from observed time-series data is crucial for understanding dynamical systems. From the perspective of system comprehension, the demand for accurate estimation and interpretable results has been particularly emphasized. Herein, we propose a novel data-driven method for estimating the governing equations of dynamical systems based on machine learning with high accuracy and interpretability. The proposed method enhances the estimation accuracy for dynamical systems using sparse modeling by incorporating physical constraints derived from Hamiltonian mechanics. Unlike conventional approaches used for estimating governing equations for dynamical systems, we employ a sparse representation of Hamiltonian, allowing for the estimation. Using noisy observational data, the proposed method demonstrates a capability to achieve accurate parameter estimation and extraction of essential nonlinear terms. In addition, it is shown that estimations based on energy conservation principles exhibit superior accuracy in long-term predictions. These results collectively indicate that the proposed method accurately estimates dynamical systems while maintaining interpretability.

    DOI： 10.3390/math12070974

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  • Algebraic Design of Physical Computing System for Time-Series Generation Reviewed International journal

    M. Komatsu, T. Yaguchi, K. Nakajima

    NeurIPS2023 Workshop: Machine Learning with New Compute Paradigms   2023.12

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  • Application of the Neural Operator for Physical Simulations of GENERIC Systems Reviewed International journal

    B. Xu, T. Matsubara, T. Yaguchi

    IEICE Proceedings Series   76   419 - 421   2023.9

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  • Super Resolution of Numerical Solutions of Nonlinear Elliptic Equations by DeepONet Reviewed International journal

    C. Yuhan, T. Matsubara, T. Yaguchi

    IEICE Proceedings Series   76   370 - 373   2023.9

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  • Generalization Error Analysis of Discrete Hamiltonian Neural Networks Reviewed International journal

    N. Ogawa, C. Yuhan, T. Matsubara, T. Yaguchi

    IEICE Proceedings Series   76   259 - 262   2023.9

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  • Equivalence Class Learning for GENERIC Systems Reviewed International journal

    Baige Xu, Yuhan Chen, Takashi Matsubara, Takaharu Yaguchi

    ICML Workshop on New Frontiers in Learning, Control, and Dynamical Systems   2023.7

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  • Variational Principle and Variational Integrators for Neural Symplectic Forms Reviewed International journal

    Yuhan Chen, Baige Xu, Takashi Matsubara, Takaharu Yaguchi

    ICML Workshop on New Frontiers in Learning, Control, and Dynamical Systems   2023.7

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  • Good Lattice Accelerates Physics-Informed Neural Networks Reviewed International journal

    Takashi Matsubara, Takaharu Yaguchi

    1st Workshop on the Synergy of Scientific and Machine Learning Modeling at ICML2023   2023.7

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  • 幾何学的深層科学技術計算 -深層学習による物理モデリング・シミュレーション- Invited

    松原 崇, 陳 鈺涵, 谷口 隆晴

    応用物理   91 ( 10 )   629 - 633   2022.10

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  • KAM Theory Meets Statistical Learning Theory: Hamiltonian Neural Networks with Non-zero Training Loss Reviewed

    Chen Y., Matsubara T., Yaguchi T.

    Proceedings of the 36th Aaai Conference on Artificial Intelligence Aaai 2022   36   6322 - 6332   2022.6   （ ISBN:1577358767, 9781577358763 ）

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    Language：English   Publisher：Proceedings of the 36th Aaai Conference on Artificial Intelligence Aaai 2022  

    Many physical phenomena are described by Hamiltonian mechanics using an energy function (the Hamiltonian). Recently, the Hamiltonian neural network, which approximates the Hamiltonian as a neural network, and its extensions have attracted much attention. This is a very powerful method, but its use in theoretical studies remains limited. In this study, by combining the statistical learning theory and Kolmogorov–Arnold–Moser (KAM) theory, we provide a theoretical analysis of the behavior of Hamiltonian neural networks when the learning error is not completely zero. A Hamiltonian neural network with non-zero errors can be considered as a perturbation from the true dynamics, and the perturbation theory of the Hamilton equation is widely known as the KAM theory. 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. This error bound gives a sup-norm bound on the Hamiltonian that is required in the application of the KAM theory.

    DOI： 10.1609/aaai.v36i6.20582

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  • Symplecticity of coupled Hamiltonian systems Reviewed

    Shunpei Terakawa, Takaharu Yaguchi

    JSIAM Letters   14   37 - 40   2022.3   （ ISSN:1883-0609 eISSN:1883-0617 ）

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：The Japan Society for Industrial and Applied Mathematics  

    DOI： 10.14495/jsiaml.14.37

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  • Causal inference for empirical dynamical systems based on persistent homology

    Bando Hiroaki, Kaji Shizuo, Yaguchi Takaharu

    JSIAM Letters   14 ( 0 )   69 - 72   2022   （ ISSN:18830609 eISSN:18830617 ）

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    Language：English   Publisher：The Japan Society for Industrial and Applied Mathematics  

    <p>Given two correlated systems, detecting causality between them from observed data is an important but challenging task. Combining two mathematical techniques, delay coordinate embedding and persistent homology, we propose a novel causal inference method for data comprising a pair of scalar time series that are observed from two possibly coupled deterministic dynamical systems. The idea is to encode the topology of the dynamics in the form of the persistent homology of the reconstructed attractors and compare the involved systems by a metric defined on the persistent homology.</p>

    DOI： 10.14495/jsiaml.14.69

    CiNii Research

  • Causal inference for empirical dynamical systems based on persistent homology Reviewed

    Bando, H; Kaji, S; Yaguchi, T

    JSIAM LETTERS   14   69 - 72   2022   （ ISSN:1883-0609 eISSN:1883-0617 ）

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  • Variational Integrator for Hamiltonian Neural Networks Reviewed

    Yuhan Chen, Takashi Matsubara, Takaharu Yaguchi

    Proceedings of the 2022 International Symposium on Nonlinear Theory and its Applications (NOLTA2022)   2022

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  • Secure Communication Systems Based on Synchronization of Chaotic Vibration of Wave Equations Reviewed

    Hideki Sano, Masashi Wakaiki, Takaharu Yaguchi

    Journal of Signal Processing   2022

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  • Learning GENERIC Systems Using Neural Symplectic Forms Reviewed

    Baige Xu, Yuhan Chen, Takashi Matsubara, Takaharu Yaguchi

    Proceedings of the 2022 International Symposium on Nonlinear Theory and its Applications (NOLTA2022)   2022

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  • Imbalance-Aware Learning for Deep Physics Modeling Reviewed

    Takahito Yoshida, Takaharu Yaguchi, Takashi Matsubara

    ICLR2022 Workshop on AI for Earth and Space Science (ai4earth)   2022

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Presentations

  • Navier–Stokes 方程式に対する PINNs の解の誤差解析

    徐百歌, 谷口隆晴

    日本数学会2025年度年会  2025.3 

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    Event date： 2025.3

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 幾何学的深層科学技術計算 Invited

    谷口隆晴

    日本数学会2025年度年会  2025.3 

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    Event date： 2025.3

    Language：Japanese   Presentation type：Oral presentation (invited, special)  

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  • An Infinite Dimensional LSSL with Infinite Dimensional HiPPO

    Atsushi Takabatake, Takaharu Yaguchi

    International Conference on Scientific Computing and Machine Learning 2025  2025.3 

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    Event date： 2025.3

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Refinement of the average vector field method for Hamiltonian systems using neural networks

    Chong Shen, Baige Xu, Elena Celledoni, Brynjulf Owren, Takaharu Yaguchi

    International Conference on Scientific Computing and Machine Learning 2025  2025.3 

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    Event date： 2025.3

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Modeling Coupled Systems by Neural Networks with Poisson Structures and Ports

    Razmik Khosrovian, Takaharu Yaguchi, Hiroaki Yoshimura, Takashi Matsubara

    International Conference on Scientific Computing and Machine Learning 2025  2025.3 

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    Event date： 2025.3

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Learning Hamiltonian Partial Differential Equations Using DeepONet with a Symplectic Branch Network

    Makara Yeang, Yusuke Tanaka, Takashi Matsubara, Takaharu Yaguchi

    International Conference on Scientific Computing and Machine Learning 2025  2025.3 

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    Event date： 2025.3

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  • Learning Hamiltonian Density Using DeepONet for Modeling Wave Equations

    Baige Xu, Yusuke Tanaka, Takashi Matsubara, Takaharu Yaguchi

    International Conference on Scientific Computing and Machine Learning 2025  2025.3 

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    Event date： 2025.3

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Energy-consistent Neural Operator Learning

    Yusuke Tanaka, Takaharu Yaguchi, Tomoharu Iwata, Naonori Ueda

    International Conference on Scientific Computing and Machine Learning 2025  2025.3 

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    Event date： 2025.3

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Model Reduction of Neural Operators by Infinite-Dimensional Singular Value Decomposition Invited International conference

    Takaharu Yaguchi

    Workshop on Dynamical Systems and Machine Learning  2025.2 

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    Event date： 2025.2

    Language：English   Presentation type：Oral presentation (invited, special)  

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  • Ge-Marsden の定理に基づくSympNets の改良の試み

    瀋翀, 徐百歌, Elena Celledoni, Brynjulf Owren, 谷口隆晴

    日本応用数理学会環瀬戸内応用数理研究部会第28回シンポジウム  2024.12 

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    Event date： 2024.12

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • On a posteriori estimates of physics-informed neural networks for solving partial differential equations Invited International conference

    Takaharu Yaguchi

    Geometric Structures and Differential Equations -- Symmetry, Singularity, and Dynamical Systems --  2024.12 

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    Event date： 2024.12

    Language：English   Presentation type：Oral presentation (invited, special)  

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  • An error bound of PINNs for solving differential equations International conference

    Takashi Matsubara, Takaharu Yaguchi

    International Conference on Scientific Computation and Differential Equations (SciCADE) 2024  2024.7 

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  • Operator Learning of Hamiltonian Density for Modeling Nonlinear Waves International conference

    Baige Xu, Yusuke Tanaka, Takashi Matsubara, Takaharu Yaguchi

    International Conference on Scientific Computation and Differential Equations (SciCADE) 2024  2024.7 

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    Event date： 2024.7

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  • Neural Operators for Hamiltonian and Dissipative PDEs International conference

    Yusuke Tanaka, Takaharu Yaguchi, Tomoharu Iwata, Naonori Ueda

    International Conference on Scientific Computation and Differential Equations (SciCADE) 2024  2024.7 

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    Event date： 2024.7

    Language：English   Presentation type：Poster presentation  

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  • Improved estimate of the number of input points of DeepONet International conference

    Dehami Kiryu, Baige Xu, Takaharu Yaguchi

    International Conference on Scientific Computation and Differential Equations (SciCADE) 2024  2024.7 

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    Event date： 2024.7

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  • Enhancing Modeling Accuracy via Discriminating Hamiltonian Systems International conference

    Yuhan Chen, Takaharu Yaguchi

    International Conference on Scientific Computation and Differential Equations (SciCADE) 2024  2024.7 

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    Event date： 2024.7

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  • Physics-Informed Neural Networksの誤差解析について

    松原崇, 谷口隆晴

    第29回計算工学講演会  2024.6 

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  • PINNによってエネルギー保存則・エントロピー増大則を保つGENERIC系の作用素学習

    徐百歌, 松原崇, 谷口隆晴

    第29回計算工学講演会  2024.6 

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  • 幾何学的深層科学技術計算 ～深層学習による物理モデリング・ シミュレーション～ Invited

    谷口隆晴

    数学と諸分野の連携にむけた若手数学者交流会2023  2023.3 

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    Event date： 2023.3

    Language：Japanese   Presentation type：Oral presentation (invited, special)  

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  • ニューラルシンプレクティック形式と変分原理の両立性について

    陳 鈺涵, 松原 崇, 谷口 隆晴

    日本数学会2022年度秋季総合分科会  2022.9 

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    Event date： 2022.9

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  • 神経ネットワーク動画像からのモデリングの試み

    安田 諒子, 松原 崇, 谷口 隆晴

    日本数学会2022年度秋季総合分科会  2022.9 

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  • 一般化 Dissipative SymODEN の GENERIC 形式

    徐 百歌, 陳 鈺涵, 松原 崇, 谷口 隆晴

    日本数学会2022年度秋季総合分科会  2022.9 

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  • GENERICシステムに対する構造保存型深層物理モデル

    徐 百歌, 陳 鈺涵, 松原 崇, 谷口 隆晴

    日本応用数理学会2022年度年会  2022.9 

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  • 複数の研究分野の連携と数理科学 Invited

    谷口 隆晴

    日本応用数理学会2022年度年会  2022.9 

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  • 深層学習を用いてデータから力学系の第一積分を発見し保存するモデル化法

    松原 崇, 谷口 隆晴

    日本応用数理学会2022年度年会  2022.9 

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  • 交流アンケートデータからのネットワーク特徴量推定について

    徐 百歌, 谷口隆晴, 増本康平, 原田 和弘, 近藤 徳彦, 岡田 修一

    日本応用数理学会2022年度年会  2022.9 

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  • Learning GENERIC Systems Using Neural Symplectic Forms

    Baige Xu, Yuhan Chen, Takashi Matsubara, Takaharu Yaguchi

    International Conference on Scientific Computation and Differential Equations (SciCADE) 2022  2022.7 

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    Event date： 2022.7

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  • Theoretical analysis of approximation properties of Hamiltonian neural networks

    Yuhan Chen, Takashi Matsubara, Takaharu Yaguchi

    International Conference on Scientific Computation and Differential Equations (SciCADE) 2022  2022.7 

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  • Neural symplectic form and coordinate-free learning of Hamiltonian dynamics

    Yuhan Chen, Takashi Matsubara, Takaharu Yaguchi

    International Conference on Scientific Computation and Differential Equations (SciCADE) 2022  2022.7 

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  • 射影法を用いて系の第一積分を発見し保存するNeural ODE

    松原崇, 谷口隆晴

    電子情報通信学会 情報論的学習理論と機械学習研究会(IBISML)  2022.6 

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    Event date： 2022.6

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  • アンバランスを考慮した深層学習による物理系の学習

    吉田崇人, 谷口隆晴, 松原崇

    2022年度 第36回人工知能学会全国大会(JSAI2022)  2022.6 

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  • Imbalance-aware lossを用いた深層学習による物理系の学習

    吉田 崇人, 谷口 隆晴, 松原 崇

    電子情報通信学会 NOLTAソサイエティ大会  2022.6 

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  • Neural Symplectic 形式によるGENERICシステムの学習

    徐 百歌, 陳 鈺涵, 松原 崇, 谷口 隆晴

    第27回計算工学講演会  2022.6 

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  • Geometric Deep Energy- Based Models for Physics Invited

    Takashi Matsubara, Yuhan Chen, Takaharu Yaguchi

    Geometric Deep Energy- Based Models for Physics, Workshop on Functional Inference and Machine Intelligence (FIMI2022), 2022  2022.3 

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  • Learning Physical Systems with Imbalance-Aware Deep Learning

    Takahito Yoshida, Takaharu Yaguchi, Takashi Matsubara

    電子情報通信学会技術研究報告 複雑コミュニケーションサイエンス研究会(CCS)  2022.3 

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  • ニューラルシンプレクティック形式とその応用

    陳鈺涵, 徐百歌, 松原崇, 谷口隆晴

    日本応用数理学会第18 回研究部会連合発表会  2022.3 

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  • 社会的つながりの次 数分布からの交流ネットワーク生成モデルの提案

    浅野広大, 谷口隆晴, 増本康平, 原田和弘, 近藤徳彦, 岡田修一

    日本応用数理学会第18 回研究 部会連合発表会  2022.3 

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  • 非線形波動のモデリングのためのハミルトニアン密度の作用素学習

    徐百歌, 田中佑典, 松原崇, 谷口隆晴

    日本応用数理学会2024年度年会  2024.9 

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  • 言語のための状態空間モデルによるハミルトン力学の時系列予測の試み

    徐 百歌, 谷口 隆晴

    日本数学会2025年度年会  2025.9 

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  • 複数のハミルトン系を同時に学習するシンプレクティックニューラルネットワーク

    徐 百歌, 谷口 隆晴

    日本応用数理学会 2025年度年会  2025.9 

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  • 物理システムにおける深層学習のための損失関数

    吉田崇人, 谷口隆晴, 松原崇

    2023年度 第37回 人工知能学会全国大会 (JSAI2023)  2023.6 

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  • 無限次元ハミルトン系を学習するための近似的なシンプレクティックニューラル作用素

    YEANG MAKARA, 田中 佑典, 松原 崇, 谷口 隆晴

    日本数学会2025年度年会  2025.9 

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  • 深層科学技術計算：深層学習の物理モデリング・シミュレーションへの応用 Invited

    谷口隆晴

    Plasma Simulator Symposium 2024  2024.9 

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  • 深層科学技術計算の最新動向 ー幾何学的深層科学技術計算ー Invited

    谷口隆晴

    第35回計算力学講演会  2022.11 

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  • 深層科学技術計算とそれを支える数学 Invited

    谷口隆晴

    MfIP連携探索ワークショップ「数学を軸とする新たな価値創造に向けて」  2024.4 

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  • 深層科学技術計算 Invited

    谷口隆晴

    第49回ASE研究会開催  2024.10 

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  • 深層物理モデルにおける数値解析技術の応用について Invited

    谷口隆晴

    IMI研究集会「新時代における高性能科学技術計算法の探究」  2023.11 

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  • 深層学習の物理モデリング・シミュレーションへの応用における最近の話題 Invited

    谷口 隆晴

    日本応用数理学会 2025年度年会  2025.9 

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  • 波動方程式のハミルトニアン密度のDeepONetによる作用素学習

    徐百歌, 田中佑典, 松原崇, 谷口隆晴

    第27回情報論的学習理論ワークショップ (IBIS2024)  2024.11 

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  • 末梢血造血幹細胞動員データ解析のためのグレブナー基底による変数分 類手法

    徐百歌,谷口隆晴,片山義雄

    日本数学会2023年度秋季総合分科会  2023.9 

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  • 拡散モデルを利用したPINNsに対する適応的学習

    市山 琴美, 谷口 隆晴

    環瀬戸内応用数理研究部会 第29回シンポジウム  2025.12 

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  • 幾何学的深層学習 Invited

    Yuhan Chen, 徐百歌,松原崇,谷口隆晴

    RIMS研究集会「新時代における高性能科学技術計算法の探究」  2023.10 

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  • 幾何学的力学と深層学習の連携による物理現象の構造保存型モデリング Invited

    谷口隆晴

    第25回情報論的学習理論ワークショップ (IBIS2022)  2022.11 

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  • 在変数をもつハミルトニアンニューラルネットワークのハミルトン構造をもたないデータへの適用について

    延安歩美, 安田諒子, 松原崇, 谷口隆晴

    日本応用数理学会環瀬戸内応用数理研究部会第26回シンポジウム  2022.12 

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  • 作用素学習のハミルトン系の学習への応用 Invited

    谷口 隆晴

    2025年度 RIMS共同研究「機械学習の数理的研究」  2025.11 

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  • ハミルトン系に対するカーネル法によるモデリング

    植田大晴, 松原崇, 谷口隆晴

    日本応用数理学会環瀬戸内応用数理研究部会第26回シンポジウム  2022.12 

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  • ニューラルネットワークを用いたハミルトン系のAverage Vector Field法の改良

    Celledoni Elena, Owren Brynjulf, Shen Chong, Xu Baige, 谷口 隆晴

    第30回計算工学講演会 (JSCES30)  2025.6 

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  • カーネル法によるハミルトン系の学習と乱択化による高速化

    植田大晴, 松原崇, 谷口隆晴

    第28回計算工学講演会  2023.6 

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  • アクティブエイジングプロジェクトにおける社会ネットワーク解析 Invited

    谷口隆晴

    持続的環境エネルギー社会共創研究機構 研究所間交流会  2023.9 

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  • Structure-preserving methods for a class of dissipative differential equations Invited International conference

    Takaharu Yaguchi

    REMODEL-DSC Workshop on Machine Learning and Physics  2024.8 

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  • Structure-Preserving Learning for GENERIC systems International conference

    Baige Xu, Yuhan Chen, Takashi Matsubara, and Takaharu Yaguchi

    10th International Congress on Industrial and Applied Mathematics (ICIAM2023)  2023.8 

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  • On the weak form of the finite element exterior calculus on manifolds Invited

    Takaharu Yaguchi

    REMODEL-DSC Workshop on Machine Learning and Geometric Methods  2025.11 

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  • Numerical integrators for learning neural ordinary differential equation models Invited International conference

    Takaharu Yaguchi

    BIRS Workshop: Structured Machine Learning and Time–Stepping for Dynamical Systems  2024.2 

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  • Neural symplectic form and its variational principle International conference

    Takaharu Yaguchi

    Maths4DL Deep Learning for Computational Physics conference  2023.7 

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  • Neural Operators for Learning Hamiltonian Systems Invited

    Takaharu Yaguchi

    Workshop on Mathematics for Machine Learning and Its Application to Industry  2025.4 

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  • Navier-Stokes方程式に対するPINNsの残差学習による事後誤差推定

    Jackaman James, 徐 百歌, 谷口 隆晴

    日本応用数理学会 2025年度年会  2025.9 

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  • Machine Learning Methods for Learning Physical Systems and Related Problems Invited

    Takaharu Yaguchi

    Workshop on Functional Inference and Machine Intelligence  2026.3 

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  • Learning infinite dimensional Hamiltonian systems via shear-type neural operators

    YEANG MAKARA, 田中 佑典, 松原 崇, 谷口 隆晴

    第28回情報論的学習理論ワークショップ (IBIS2025)  2025.11 

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  • Learning Hamiltonian Systems Using Neural Networks Invited

    Takaharu Yaguchi

    KSIAM 2025 Annual Meeting  2025.11 

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  • Hyperbolic Partial Differential Equations Derived From Hippo Matrices International conference

    Atsushi Takabatake, Baige Xu, Takaharu Yaguchi

    REMODEL-DSC Workshop on Machine Learning and Physics  2024.8 

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  • Geometric numerical integrators for a class of dissipative differential equations Invited

    Takaharu Yaguchi

    REMODEL-DSC Workshop on Machine Learning and numerical analysis  2025.4 

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  • Geometric Neural Network Models for Physics Invited

    Takaharu Yaguchi

    REMODEL-DSC Workshop on Geometry, Inverse Problems and Machine Learning  2026.1 

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  • Geometric Integrators for Neural Symplectic Forms International conference

    Yuhan Chen, Takashi Matsubara, and Takaharu Yaguchi

    10th International Congress on Industrial and Applied Mathematics (ICIAM2023)  2023.8 

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  • Geometric Deep Energy-Based Models for Physics Invited International conference

    Takaharu Yaguchi

    REMODEL-DSC Workshop on Structure-Preserving Numerical Methods and Machine Learning  2024.8 

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  • Geometric Deep Energy-Based Models for Physics Invited International conference

    Takaharu Yaguchi

    Cambridge Image Analysis Sminar  2024.5 

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  • DeepONet による非線形力学系の解の予測における入力点数の評価の改良

    桐生デハミ,徐百歌,谷口隆晴

    日本応用数理学会環瀬戸内応用数理研究部会第27回シンポジウム  2023.12 

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  • DeepONet による発展型偏微分方程式の学習

    岩田実莉,入江凜,久田正樹,松原崇,谷口隆晴

    日本応用数理学会環瀬戸内応用数理研究部会第27回シンポジウム  2023.12 

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  • Deep Learning Models for Physical Modeling Invited International conference

    Takaharu Yaguchi

    The Data Science seminar in University of Birmingham  2024.5 

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  • Deep Discrete-Time Models for Physics Invited International conference

    Takaharu Yaguchi

    The DNA (Differential Equations and Numerical Analysis) Seminar  2024.5 

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  • CoSyNN: Conformal symplectic neural networks for learning dissipative Hamiltonian systems

    徐 百歌, 谷口 隆晴

    第28回情報論的学習理論ワークショップ (IBIS2025)  2025.11 

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  • Application of the Kernel Method to Learning Hamiltonian Equations International conference

    Taisei Ueda, Takashi Matsubara, and Takaharu Yaguchi

    10th International Congress on Industrial and Applied Mathematics (ICIAM2023)  2023.8 

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  • Application of Infinite-Dimensional Singular Value Decomposition to Model Reduction of Neural Operators Invited

    Takaharu Yaguchi

    REMODEL-DSC Workshop on Differential equations, Geometry and Machine Learning  2025.12 

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  • Application of DeepONet for learning Hamiltonian PDEs International conference

    Baige Xu, Yusuke Tanaka, Takashi Matsubara, Takaharu Yaguchi

    REMODEL-DSC Workshop on Machine Learning and Physics  2024.8 

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  • An Extension of SympNets for Learning of Multiple Hamilton Systems Invited

    Takaharu Yaguchi

    Forum "Math for Industry"  2025.8 

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  • An error bound of physics-informed neural networks for solving differential equations Invited International conference

    Takaharu Yaguchi

    PhysML Workshop 2024  2024.5 

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    Language：English   Presentation type：Oral presentation (invited, special)  

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Professional Memberships

  • Institute of Electrical and Electronics Engineers

    2020.5 - Present

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  • 日本流体力学会

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  • 日本数学会

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  • 日本応用数理学会

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  • American Institute of Aeronautics and Astronautics

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Committee Memberships

  • Neural Information Processing Systems (NeurIPS)   Area Chair  

    2026.4 - Present   

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  • International Conference on Machine Learning (ICML)   Area Chair  

    2025.11 - Present   

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  • International Conference on Learning Representations (ICLR)   Area Chair  

    2025.9 - Present   

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  • 日本学術会議   計算音響学小委員会 委員  

    2015.5 - 2024.3   

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    Committee type：Academic society

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  • 28th International Conference on Artificial Neural Networks, Programme Committee  

       

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Research Projects

  • 保存則・散逸則を考慮した Physics-Informed Neural Networksの理論解析

    Grant number：25K15148  2025.4 - 2028.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    谷口 隆晴

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    Grant type：Scientific research funding

    近年の深層学習による発展はめざましく，様々な分野に応用が進んでいる．特に，物理シミュレーションについても応用が始まっており，シミュレーションを加速することで，気象予測や製品開発などが加速すると期待されている．一方，深層学習はブラックボックスと言われることも多く，信頼性が高い方法とはいえない．本研究では，特に，物理法則を保つような深層学習手法に着目し，物理法則を入れることで，どの程度，精度が高まるのかを明らかにすることを目指す．

    CiNii Research

  • A longitudinal study of aging changes in emotion regulation, trust, and social connectedness

    Grant number：23K22352  2024.4 - 2026.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    増本 康平, 谷口 隆晴, 佐藤 幸治, 原田 和弘

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    Grant type：Scientific research funding

    超高齢社会の問題の解決には，社会的つながりが必要不可欠である。感情調整は，良い人間関係の構築において中核的な役割を担う心理機能であり，加齢による低下がみられずむしろ向上する。しかしながら，高齢期の感情調整機能が社会的つながりに及ぼす影響は明確ではない。そこで本研究では，下記の2つを目的とした研究を実施する。
    目的1：高齢期の感情調整機能が社会的つながりに及ぼす影響を縦断データを用いて検討する。
    目的2：高齢期の感情調整が社会的つながりの基盤である「他者への信頼」に及ぼす影響を心理実験により明らかにする。

    CiNii Research

  • Method for extracting conserved quantities of black box differential equation models and its application to network analysis

    Grant number：20K11693  2020.4 - 2024.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    Yaguchi Takaharu

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    Grant type：Scientific research funding

    In recent years, black-box differential equation models such as neural ordinary differential equations have been attracting much attention. Because such models do not admit symbolic representations, it is difficult to investigate their properties, including the existence of conservation laws.
    In this study we constructed a data-driven method that finds conserved quantities for black-box differential equation models. More precisely, conserved quantities are modeled by neural networks, and the neural networks representing the conserved quantity are trained so that the model accuracy is improved when the black-box model is modified so that this quantity is conserved. We numerically confirmed that conservation laws can be certainly extracted from various differential equation models using this method. We developed a statistical method for the analysis of structural changes in networks.

    CiNii Research

  • Development of the quantitative measurements for social network, and effects of neighborhood social network intervention on mental and physical health of older adults.

    Grant number：20K20319  2018.6 - 2023.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Challenging Research (Pioneering)

    Okada Shuichi

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    Grant type：Scientific research funding

    We developed quantitative method for measurement of the social network using wearable device and considered about the reliability of an objective effects of the neighborhood intervention for the promotion of the social network and the association with health, the social relations index evaluated by social network and inventory survey. As a result, the relationship between total utterance time for measured by wearable device and the utterance time by the self-entry was significantly correlation in a walking lesson.
    In addition, the extroversion of TIPI-J in group for total utterance time more than 30 minutes was significantly higher than that in group for total utterance time within 30 minutes.

    CiNii Research

Outline of Social Contribution and International Cooperation activities

  • We organize the International Conference on Scientific Computing and Machine Learning to promote scientific machine learning. We also participate in Horizon Europe and JST ASPIRE, and are conducting joint research with research groups in the United Kingdom, Norway, the Netherlands, and other countries.