Stochastic gradient descent for optimization for nuclear systems

Williams, Austin; Walton, Noah M.; Maryanski, Austin; Bogetic, Sandra; Hines, Wes. J.; Sobes, Vladimir

doi:10.1038/s41598-023-32112-7

Cited by 2 publications

(3 citation statements)

References 14 publications

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“…Like NNs, the training process for PINNs corresponds to the minimization problem min P J(X; P). Training of network parameters P is carried out using a gradient descent approach such as Adam [75] or L-BFGS-B (limited memory algorithm Broyden-Fletcher-Goldfarb-Shanno) [76]. However, the required number of iterations depends highly on the problem "(e.g., smoothness of the solution)" see [57].…”

Section: Te Combined Adam and L-bfgs-b Optimizationmentioning

confidence: 99%

Exploring Physics‐Informed Neural Networks for the Generalized Nonlinear Sine‐Gordon Equation

Deresse,

Dufera

2024

Applied Computational Intelligence and Soft Computing

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The nonlinear sine-Gordon equation is a prevalent feature in numerous scientific and engineering problems. In this paper, we propose a machine learning-based approach, physics-informed neural networks (PINNs), to investigate and explore the solution of the generalized non-linear sine-Gordon equation, encompassing Dirichlet and Neumann boundary conditions. To incorporate physical information for the sine-Gordon equation, a multiobjective loss function has been defined consisting of the residual of governing partial differential equation (PDE), initial conditions, and various boundary conditions. Using multiple densely connected independent artificial neural networks (ANNs), called feedforward deep neural networks designed to handle partial differential equations, PINNs have been trained through automatic differentiation to minimize a loss function that incorporates the given PDE that governs the physical laws of phenomena. To illustrate the effectiveness, validity, and practical implications of our proposed approach, two computational examples from the nonlinear sine-Gordon are presented. We have developed a PINN algorithm and implemented it using Python software. Various experiments were conducted to determine an optimal neural architecture. The network training was employed by using the current state-of-the-art optimization methods in machine learning known as Adam and L-BFGS-B minimization techniques. Additionally, the solutions from the proposed method are compared with the established analytical solutions found in the literature. The findings show that the proposed method is a computational machine learning approach that is accurate and efficient for solving nonlinear sine-Gordon equations with a variety of boundary conditions as well as any complex nonlinear physical problems across multiple disciplines.

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Section: Te Combined Adam and L-bfgs-b Optimizationmentioning

confidence: 99%

Exploring Physics‐Informed Neural Networks for the Generalized Nonlinear Sine‐Gordon Equation

Deresse,

Dufera

2024

Applied Computational Intelligence and Soft Computing

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“…We perform fitting and calculation using the Adam gradient method. Unlike the conventional gradient descent method, the Adam gradient can automatically adjust the step size at each iteration as follows [21][22][23][24][25]:…”

Section: Mean Elements Of Space Debrismentioning

confidence: 99%

where

= 0.9,

= 0.999,

= 1 × 10 −8 ,

, and

;

is an orbit element,

is the partial derivative of the RMSE with respect to element

, and t is the number of iterations.…”

Section: Calculation Of Ballistic Coefficients From Optical Angle Mea...mentioning

confidence: 99%

Ballistic Coefficient Calculation Based on Optical Angle Measurements of Space Debris

Ding,

Li,

Liu

et al. 2023

Sensors

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Atmospheric drag is an important factor affecting orbit determination and prediction of low-orbit space debris. To obtain accurate ballistic coefficients of space debris, we propose a calculation method based on measured optical angles. Angle measurements of space debris with a perigee height below 1400 km acquired from a photoelectric array were used for orbit determination. Perturbation equations of atmospheric drag were used to calculate the semi-major-axis variation. The ballistic coefficients of space debris were estimated and compared with those published by the North American Aerospace Defense Command in terms of orbit prediction error. The 48 h orbit prediction error of the ballistic coefficients obtained from the proposed method is reduced by 18.65% compared with the published error. Hence, our method seems suitable for calculating space debris ballistic coefficients and supporting related practical applications.

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Stochastic gradient descent for optimization for nuclear systems

Cited by 2 publications

References 14 publications

Exploring Physics‐Informed Neural Networks for the Generalized Nonlinear Sine‐Gordon Equation

Exploring Physics‐Informed Neural Networks for the Generalized Nonlinear Sine‐Gordon Equation

Ballistic Coefficient Calculation Based on Optical Angle Measurements of Space Debris

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