Pseudo-Hamiltonian neural networks with state-dependent external forces

Eidnes, Sølve; Stasik, A.; Sterud, Camilla; Bøhn, Eivind; Riemer-Sørensen, Signe

doi:10.1016/j.physd.2023.133673

Cited by 12 publications

(12 citation statements)

References 19 publications

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“…This approach has a significant disadvantage in terms of computational costs, especially in the PDE setting. In addition, predictions can only be made for a predefined spatio-temporal discretization when applied to PDEs [16,40].…”

Section: Related Workmentioning

confidence: 99%

Event Report: NTT Communication Science Laboratories Open House 2022

Tanaka¹,

Sano²,

Wu³

et al. 2022

NTT Technical Review

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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. KeywordsOperator learning • Energy-based theory • Hamiltonian mechanics • Partial differential equations * Citation: Authors. Title. Pages.... DOI:000000/11111.2 Note that PIML refers to the field of machine learning for exploiting various forms of physics knowledge and is distinct from PINNs that directly use PDEs, which is one approach in PIML.

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Section: Related Workmentioning

confidence: 99%

Event Report: NTT Communication Science Laboratories Open House 2022

Tanaka¹,

Sano²,

Wu³

et al. 2022

NTT Technical Review

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“…Zhang et al (2024) [16] observed dynamics with noise in observational data through Hamiltonian mechanics and proposed the Hamiltonian neuron Koopman operator (HNKO), which incorporates mathematical knowledge to automatically discover and maintain conservation laws. Eidnes et al (2023) [17] proposed a hybrid machine-learning approach using Hamiltonian formulations for mechanical systems, whether conservative or non-conservative. Additionally, they introduced pseudo-Hamiltonian algorithms as a generalization of the Hamiltonian formulation through a pH formulation.…”

Section: Introductionmentioning

confidence: 99%

Development of a Conservative Hamiltonian Dynamic System for the Early Detection of Leaks in Pressurized Pipelines

Ladino-Moreno,

García-Ubaque,

Zamudio-Huertas

2024

Civ Eng J

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In this study, we propose an innovative approach for real-time leakage detection in pipelines by integrating conservative Hamiltonian equations and experimental Internet of Things (IoT) technologies. The proposed method combines a hybrid model that utilizes sensors and IoT devices to acquire real-time data and solves the coupled system of Hamiltonian equations using the ODE45 numerical integration method. Spectral frequency analysis is an essential part of this method, as it reveals specific patterns in the pressure and flow signals. The findings highlighted 95% accuracy in leak detection, which was validated through a comparison of the theoretical and experimental data. The novelty of this approach lies in its ability to maintain constant total system energy, thereby enabling continuous monitoring for early leak detection. As an improvement, the proper handling of sensor signals is emphasized, underscoring its contribution to the efficient management of water resources in potable water distribution systems. Doi: 10.28991/CEJ-2024-010-04-01 Full Text: PDF

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“…Much of the literature has focused on Hamiltonian or Lagrangian formulations of (1), beginning with [23,8,10]. In [17,20], it is demonstrated how a pseudo-Hamiltonian formulation can be utilized in the model structure to separate the internal dynamics and external forces acting on the system. This pseudo-Hamiltonian formulation is a generalization of the port-Hamiltonian formulation [54], which is again a generalization of the Hamiltonian formulation.…”

mentioning

confidence: 99%

“…• We argue for using symmetric numerical integrators in the training of the model and demonstrate superior performance over existing methods, especially on noisy data. The implementation of the PHSI models is done in Python and builds on the phlearn package introduced in [20]. Code to reproduce numerical experiments from the paper is published at https://github.com/SINTEF/PHSI.…”

mentioning

confidence: 99%

“…Especially relevant for this paper are the generalizations of the Hamiltonian formulation allowing for damping, disturbances acting on the system, or interaction with other systems. In addition to those that use the term port-Hamiltonian [15,17] or pseudo-Hamiltonian [20,19], several papers consider a specific generalization of Hamiltonian systems that fall under the definition of pseudo-Hamiltonian systems applied in this paper, whether they aim to learn external forces [18] or not [60,59,58]. Our motivation for the pseudo-Hamiltonian formulation comes from the long history of modeling mechanical systems by studying the conservation of energy, momentum, mass, and other quantities [2,38,24].…”

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confidence: 99%

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Pseudo-Hamiltonian system identification

Holmsen,

Eidnes,

Riemer-Sørensen

2024

JCD

Self Cite

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Identifying the underlying dynamics of physical systems can be challenging when only provided with observational data. In this work, we consider systems that can be modelled as first-order ordinary differential equations. By assuming a certain pseudo-Hamiltonian formulation, we are able to learn the analytic terms of internal dynamics even if the model is trained on data where the system is affected by unknown damping and external disturbances. In cases where it is difficult to find analytic terms for the disturbances, a hybrid model that uses a neural network to learn these can still accurately identify the dynamics of the system as if under ideal conditions. This makes the models applicable in some situations where other system identification models fail. Furthermore, we propose to use a fourth-order symmetric integration scheme in the loss function and avoid actual integration in the training, and demonstrate on varied examples how this leads to increased performance on noisy data.

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Pseudo-Hamiltonian neural networks with state-dependent external forces

Cited by 12 publications

References 19 publications

Event Report: NTT Communication Science Laboratories Open House 2022

Event Report: NTT Communication Science Laboratories Open House 2022

Development of a Conservative Hamiltonian Dynamic System for the Early Detection of Leaks in Pressurized Pipelines

Pseudo-Hamiltonian system identification

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