arXiv subjects

Takaharu Yaguchi

Publications and source records attributed to Takaharu Yaguchi.

17 recordsLinked to original sources

arXiv2026

Horizon-Aware Early Event Prediction for Tokamak Disruption Alarms

Reliable disruption prediction is essential for the safe operation of future tokamaks. Existing full-distribution survival methods model the complete residual time-to-disruption distribution, whereas operational decisions primarily depend on disruption risk within a finite prediction horizon. This mismatch motivates introducing Early Event Prediction (EEP) objectives into survival-based disruption prediction. We take Deep Survival Machines (DSM) as the full-distribution baseline and propose applying two established EEP methods to tokamak disruption prediction: Temporal Label Smoothing (TLS), which directly predicts disruption probability within a finite horizon, and survTLS, which additionally models the event-time distribution within that horizon. Using a common causal encoder, we compare these methods on DIII-D, Alcator C-Mod, and EAST. We distinguish threshold-free deadline ranking from validation-selected fixed-policy alarm performance and evaluate prediction horizons and encoder architectures. TLS achieves the best mean alarm performance on DIII-D and EAST, whereas all methods perform poorly on Alcator C-Mod. survTLS does not consistently outperform DSM, suggesting that directly learning horizon-level event probability is more effective than modeling detailed within-horizon event-time distributions in the present setting. Finally, the selected prediction horizons and encoder-ablation results vary across devices, reflecting differences in disruption characteristics.

physics.plasm-ph↗

arXiv2026

CoSynFlow: Conformal Symplectic Neural Flows for Cross-System Prediction of Dissipative Hamiltonian Dynamics

Learning solution operators for differential equations is a central problem in scientific machine learning. However, many neural operator methods optimize prediction accuracy without explicitly enforcing the geometric structure of the dynamics. Structure-preserving models such as SympNets and Symplectic Neural Flows address this issue for conservative Hamiltonian systems by preserving the symplectic form. In dissipative Hamiltonian systems with conformal symplectic structure, however, the symplectic form evolves according to a conformal factor determined by the dissipation. We propose CoSynFlow, a conformal symplectic neural flow for learning continuous-time solution maps of dissipative Hamiltonian dynamics. CoSynFlow composes symplectic shear maps with explicit conformal scaling, preserving the conformal symplectic structure by construction. By conditioning it on a finite-dimensional Hamiltonian descriptor and the dissipation parameter, a single trained model predicts solution maps for unseen systems without retraining. CoSynFlow keeps the structure error at machine precision, attains the lowest long-horizon error, and admits physics-informed training.

cs.LG↗

arXiv2026

Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems

The modeling and simulation of infinite-dimensional Hamiltonian systems are central problems in mathematical physics and engineering, however they pose significant computational and structural challenges for standard data-driven architectures. In this work, we introduce the Symplectic Neural Operator, a neural operator architecture designed to preserve the symplectic structure intrinsic to Hamiltonian PDEs. We provide a theoretical characterization of their symplecticity and establish a rigorous long-term stability result based on the combination of symplectic structure preservation and learning accuracy. Numerical experiments on canonical Hamiltonian PDEs corroborate this theoretical result and show that SNOs exhibit improved energy behavior compared with non-structure-preserving neural operators.

math.DS↗

arXiv2026

Approximation of Maximally Monotone Operators : A Graph Convergence Perspective

Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-including differential operators-are discontinuous or set-valued, and lie outside classical approximation frameworks. We propose a paradigm shift by formulating approximation via graph convergence (Painlevé-Kuratowski convergence), which is well-suited for closed operators. We show that uniform and $L^p$ approximation are fundamentally inadequate in this setting. Focusing on maximally monotone operators, we prove that any such operator can be approximated in the sense of local graph convergence by continuous encoder-decoder architectures, and further construct structure-preserving approximations that retain maximal monotonicity via resolvent-based parameterizations.

cs.LG↗

arXiv2026

Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics

Definite integrals with parameters of holonomic functions satisfy holonomic systems of linear partial differential equations. When we restrict parameters to a one dimensional curve, the system becomes a linear ordinary differential equation (ODE) with respect to a curve in the parameter space. We can evaluate the integral by solving the linear ODE numerically. This approach to evaluate numerically definite integrals is called the holonomic gradient method (HGM) and it is useful to evaluate several normalizing constants in statistics. We will discuss and compare methods to solve linear ODE's to evaluate normalizing constants.

math.NA↗

arXiv2025

Learning Hamiltonian Density Using DeepONet

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 learning Hamiltonian mechanics, methods based on deep neural networks such as Hamiltonian Neural Networks (HNNs) and their variants have achieved progress. However, existing methods typically depend on the discretization of data, and the determination of required differential operators is often necessary. Instead, in this work, we propose an operator learning approach for modeling wave equations. In particular, we present a method to compute the variational derivatives that are needed to formulate the equations using the automatic differentiation algorithm. The experiments demonstrated that the proposed method is able to learn the operator that defines the Hamiltonian density of waves from data with unspecific discretization without determination of the differential operators.

cs.LG↗

arXiv2024

Number Theoretic Accelerated Learning of Physics-Informed Neural Networks

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.

cs.LG↗

arXiv2024

Poisson-Dirac Neural Networks for Modeling Coupled Dynamical Systems across Domains

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.

cs.LG↗

arXiv2024

Neural Operators Meet Energy-based Theory: Operator Learning for Hamiltonian and Dissipative PDEs

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 (DNNs) for learning such a mapping, enabling the learning of solution operators of partial differential equations (PDEs). However, these works still struggle to learn dynamics that obeys the laws of physics. This paper proposes Energy-consistent Neural Operators (ENOs), a general framework for learning solution operators of PDEs that follows the energy conservation or dissipation law from observed solution trajectories. We introduce a novel penalty function inspired by the energy-based theory of physics for training, in which the energy functional is modeled by another DNN, allowing one to bias the outputs of the DNN-based solution operators to ensure energetic consistency without explicit PDEs. Experiments on multiple physical systems show that ENO outperforms existing DNN models in predicting solutions from data, especially in super-resolution settings.

stat.ML↗

arXiv2023

FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantities

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 understanding of first integrals are fundamental and important topics both in the natural sciences and in industrial applications. First integrals arise from the conservation laws of system energy, momentum, and mass, and from constraints on states; these are typically related to specific geometric structures of the governing equations. Existing neural networks designed to ensure such first integrals have shown excellent accuracy in modeling from data. However, these models incorporate the underlying structures, and in most situations where neural networks learn unknown systems, these structures are also unknown. This limitation needs to be overcome for scientific discovery and modeling of unknown systems. To this end, we propose first integral-preserving neural differential equation (FINDE). By leveraging the projection method and the discrete gradient method, FINDE finds and preserves first integrals from data, even in the absence of prior knowledge about underlying structures. Experimental results demonstrate that FINDE can predict future states of target systems much longer and find various quantities consistent with well-known first integrals in a unified manner.

cs.LG↗

arXiv2022

KAM Theory Meets Statistical Learning Theory: Hamiltonian Neural Networks with Non-Zero Training Loss

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 an $L^\infty$ bound on the Hamiltonian that is required in the application of the KAM theory.

math.DS↗

arXiv2021

An Error Analysis Framework for Neural Network Modeling of Dynamical Systems

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 describe dynamics from data using neural networks has been attracting attention. During such training, numerical integration is used to compare the data with the solution of the neural network model; however, discretization errors due to numerical integration prevent the model from being trained correctly. In this study, we formulate the modeling error using the Dahlquist test equation that is commonly used in the analysis of numerical methods and apply it to some of the Runge--Kutta methods.

math.NA↗

arXiv2021

Symplecticity of coupled Hamiltonian systems

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 be modeled as a coupled system of some subsystems. Although it is known that symplectic integrators are suitable for discretizing Hamiltonian systems,the composition of Hamiltonian systems may not be Hamiltonian. In this paper, focusing on a property of Hamiltonian systems, that is, the conservation of the symplectic form, we provide a condition under which two Hamiltonian systems coupled with interactions compose a Hamiltonian system.

math.NA↗

arXiv2021

Symplectic Adjoint Method for Exact Gradient of Neural ODE with Minimal Memory

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 accuracy. The neural ODE uses the same network repeatedly during a numerical integration. The memory consumption of the backpropagation algorithm is proportional to the number of uses times the network size. This is true even if a checkpointing scheme divides the computation graph into sub-graphs. Otherwise, the adjoint method obtains a gradient by a numerical integration backward in time. Although this method consumes memory only for a single network use, it requires high computational cost to suppress numerical errors. This study proposes the symplectic adjoint method, which is an adjoint method solved by a symplectic integrator. The symplectic adjoint method obtains the exact gradient (up to rounding error) with memory proportional to the number of uses plus the network size. The experimental results demonstrate that the symplectic adjoint method consumes much less memory than the naive backpropagation algorithm and checkpointing schemes, performs faster than the adjoint method, and is more robust to rounding errors.

cs.LG↗

arXiv2020

Method for estimating hidden structures determined by unidentifiable state-space models and time-series data based on the Groebner basis

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 state-space models, explicitly and exhaustively. State-space models are often constructed based on the domain, for example, physical or biological. Such models include parameters that are assigned specific meanings in relation to the system under consideration, which is examined by estimating the parameters using the corresponding data. 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. To overcome this difficulty, multiple possible sets of parameters are estimated and analysed in the exiting approaches; however, in general, all the possible parameters cannot be explored; therefore, considerations on the system using the estimated parameters become insufficient. In this study, focusing on certain structures determined by the observed data and models uniquely, even if they are unidentifiable, we introduce the concept of parameter variety. This is newly defined and proven to form algebraic varieties, in general. A computational algebraic method that relies on the Groebner basis for deriving the explicit representation of the varieties is presented along with the supporting theory. Furthermore, its application in the analysis of a model that describes virus dynamics is presented. With this, new insight on the dynamics overlooked by the conventional approach are discovered, confirming the applicability of our idea and the proposed method.

eess.SY↗

arXiv2020

Deep Energy-Based Modeling of Discrete-Time Physics

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. Recent developments in neural networks have enabled the mimicking of the energy conservation law by learning the underlying continuous-time differential equations. However, this may not be possible in discrete time, which is often the case in practical learning and computation. Moreover, other physical laws have been overlooked in the previous neural network models. In this study, we propose a deep energy-based physical model that admits a specific differential geometric structure. From this structure, the conservation or dissipation law of energy and the mass conservation law follow naturally. To ensure the energetic behavior in discrete time, we also propose an automatic discrete differential algorithm that enables neural networks to employ the discrete gradient method.

math.NA↗

arXiv2011

Preserving multiple first integrals by discrete gradients

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 set of discrete gradients. Integrators which exactly conserve all the first integrals simultaneously are then defined. In both cases we start from an arbitrary method of a prescribed order (say, a Runge-Kutta scheme) and modify it using two approaches: one based on projection and one based one local coordinates. The methods are tested on the Kepler problem.

math.NA↗