Neural network approach for the calculation of potential coefficients in quantum mechanics

Ossandón, Sebastián; Reyes, Carlos M.; Cumsille, Patricio

doi:10.1016/j.cpc.2017.01.006

Cited by 6 publications

(4 citation statements)

References 13 publications

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“…We denote by t the image of under T . Let t be the value of (22) for the domain t , = 0 . With 0 , the derivative of at t = 0, is linearized as…”

Section: Shape Derivative Of the Average Pressure Responsementioning

confidence: 99%

“…Suppose that the interval [λ min , λ max ] does not contain any eigenvalue κ i for which ψ i = 0. Then the shape derivative of the objective function (22) is given by…”

Section: Shape Derivative Of the Average Pressure Responsementioning

confidence: 99%

“…The paper [25] focuses on the nonlinear partial differential equations. Some other network inspired approaches in the study of PDEs are [5,6,21,22].…”

Section: Introductionmentioning

confidence: 99%

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A Feedforward Neural Network for Modeling of Average Pressure Frequency Response

2022

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The Helmholtz equation has been used for modeling the sound pressure field under a harmonic load. Computing harmonic sound pressure fields by means of solving Helmholtz equation can quickly become unfeasible if one wants to study many different geometries for ranges of frequencies. We propose a machine learning approach, namely a feedforward dense neural network, for computing the average sound pressure over a frequency range. The data are generated with finite elements, by numerically computing the response of the average sound pressure, by an eigenmode decomposition of the pressure. We analyze the accuracy of the approximation and determine how much training data is needed in order to reach a certain accuracy in the predictions of the average pressure response.

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“…We denote by t the image of under T . Let t be the value of (22) for the domain t , = 0 . With 0 , the derivative of at t = 0, is linearized as…”

Section: Shape Derivative Of the Average Pressure Responsementioning

confidence: 99%

“…Suppose that the interval [λ min , λ max ] does not contain any eigenvalue κ i for which ψ i = 0. Then the shape derivative of the objective function (22) is given by…”

Section: Shape Derivative Of the Average Pressure Responsementioning

confidence: 99%

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A Feedforward Neural Network for Modeling of Average Pressure Frequency Response

2022

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“…More recently, in Ossandón and Reyes [12] and Ossandón et al [13], the authors solve, respectively, inverse eigenvalue problems for the linear elasticity operator and for the anisotropic Laplace operator. Also, in Ossandón et al [14], the authors solve an inverse problem, using a neural network approach, in order to calculate the potential coefficients associated with the Hamiltonian operator in quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Neural network solution to an inverse problem associated with the eigenvalues of the Stokes operator

Ossandón¹,

Barrientos²,

Reyes³

2017

Comptes Rendus. Mécanique

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Viscosity and density coefficients Inverse problems Eigenvalues of the Stokes operator Finite element methodA numerical method, based on the design of two artificial neural networks, is presented in order to approximate the viscosity and density features of fluids from the eigenvalues of the Stokes operator. The finite element method is used to solve the direct problem by training a first artificial neural network. A nonlinear map of eigenvalues of the Stokes operator as a function of the viscosity and density of the fluid under study is then obtained. This relationship is later inverted and refined by training a second artificial neural network, solving the aforementioned inverse problem. Numerical examples are presented in order to show the effectiveness and the limitations of this methodology.

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Machine Learning Control Design for Elastic Composite Materials

Ossandón

Barrientos

Reyes

2021

Computational Science – ICCS 2021

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Neural network approach for the calculation of potential coefficients in quantum mechanics

Cited by 6 publications

References 13 publications

A Feedforward Neural Network for Modeling of Average Pressure Frequency Response

A Feedforward Neural Network for Modeling of Average Pressure Frequency Response

Neural network solution to an inverse problem associated with the eigenvalues of the Stokes operator

Machine Learning Control Design for Elastic Composite Materials

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