An overview on recent machine learning techniques for Port Hamiltonian systems

Cherifi, Karim

doi:10.1016/j.physd.2020.132620

Cited by 12 publications

(9 citation statements)

References 28 publications

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“…Of course, neural networks based upon this formulation have been developed in the last years [99,100,101,102,103,104]. They all share the more or less the same ingredients and are based upon the formulation just discussed.…”

Section: Deconstructing Inductive Biasesmentioning

confidence: 99%

Thermodynamics of learning physical phenomena

Chinesta¹

2022

Preprint

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Thermodynamics could be seen as an expression of physics at a high epistemic level. As such, its potential as an inductive bias to help machine learning procedures attain accurate and credible predictions has been recently realized in many fields. We review how thermodynamics provides helpful insights in the learning process. At the same time, we study the influence of aspects such as the scale at which a given phenomenon is to be described, the choice of relevant variables for this description or the different techniques available for the learning process.

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Section: Deconstructing Inductive Biasesmentioning

confidence: 99%

Thermodynamics of learning physical phenomena

Chinesta¹

2022

Preprint

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“…BPNN is developed from the forward perceptron network, and is a very mature and reliable neural network [19].…”

Section: Back Propagation Neural Network (Bpnn)mentioning

confidence: 99%

Predicting Temperature-induced Deflection and Abnormality Recognition of Cable-stayed Bridge Based on Machine Learning

Sun¹,

Sun²,

Wang³

et al. 2022

Journal of Compurters

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<p>The vertical deflection of the main girder on a cable-stayed bridge is a direct reflection of the vertical stiffness of bridge structure, which represents the comprehensive mechanical performance of cable-stayed bridge. Compared with the deflection caused by vehicles, the deflection caused by temperature is often more significant and the change frequency is very low, which is easy to extract from raw data, and can be used as an index to evaluate the state of cable-stayed bridge. To obtain the control value for recognizing the abnormal deflection, it is necessary to establish an accurate input-output relationship between temperature and temperature-induced deflection. However, because of the high-order nonlinear relationship between the temperature and the temperature-induced deflection, the traditional linear regression is not accurate enough in modeling this relationship. To establish a high-precision model for the deflection, this paper uses the machine learning tools with the highly nonlinear fitting performance to further model the project. Considering both the precision and modeling efficiency, the Long-Short Term Memory (LSTM) network can build the optimal model between temperature and temperature-induced deflection. Use the regression value output by LSTM as the control value combining with the statistical pattern of t-test, the 6% abnormal deflection can be recognized. The 6% sensitivity can help to recognize bridge abnormalities earlier. </p> <p> </p>

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“…The port-Hamiltonian [17][18][19][20][21] is a well studied formalism that generalizes Hamilton's equations to incorporate energy dissipation and an external control input to a dynamical system. Hamilton's equations in the port-Hamiltonian framework are represented as:…”

Section: B Port-hamiltonian Frameworkmentioning

confidence: 99%

“…Defining a network to accurately learn and predict the dynamics of such systems from position and momentum data is therefore of critical practical interest. We address this challenge by embedding the port-Hamiltonian formalism [17][18][19][20][21] into neural networks. We show that the structure of this formulation can be used to uncover the underlying Hamiltonian, force and damping terms given position and momentum data and as such, can be used to accurately predict the long-range trajectories of many forced/damped systems.…”

Section: Introductionmentioning

confidence: 99%

Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems

Desai,

Mattheakis,

Sondak

et al. 2021

Preprint

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Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant improvement over other approaches in predicting trajectories of physical systems. These methods generally tackle autonomous systems that depend implicitly on time or systems for which a control signal is known apriori. Despite this success, many real world dynamical systems are non-autonomous, driven by time-dependent forces and experience energy dissipation. In this study, we address the challenge of learning from such non-autonomous systems by embedding the port-Hamiltonian formalism into neural networks, a versatile framework that can capture energy dissipation and time-dependent control forces. We show that the proposed port-Hamiltonian neural network can efficiently learn the dynamics of nonlinear physical systems of practical interest and accurately recover the underlying stationary Hamiltonian, time-dependent force, and dissipative coefficient. A promising outcome of our network is its ability to learn and predict chaotic systems such as the Duffing equation, for which the trajectories are typically hard to learn.

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An overview on recent machine learning techniques for Port Hamiltonian systems

Cited by 12 publications

References 28 publications

Thermodynamics of learning physical phenomena

Thermodynamics of learning physical phenomena

Predicting Temperature-induced Deflection and Abnormality Recognition of Cable-stayed Bridge Based on Machine Learning

Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems

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