Physics-Informed Deep Neural Networks for Transient Electromagnetic Analysis

Noakoasteen, Oameed; Wang, Shu; Peng, Zhen; Christodoulou, C.G.

doi:10.1109/ojap.2020.3013830

Cited by 47 publications

(22 citation statements)

References 32 publications

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“…It is important that a dataset is properly scaled for training, as mentioned in the literatures, e.g. [19], [20]. In this study, the scaling of the input and output to a NN is performed as preprocessing and post-processing for the proposed method.…”

Section: B Deep Learing Approachmentioning

confidence: 99%

“…Note that γ and ρn are included even in the scaled PDE (23). From ( 9) and ( 19), the PEC-BC of the scaled SC field is given by 𝑒 𝑧 = 0 (24) It should be mentioned that the input (x,y) is scaled to (X,Y) with s0 in (17), and the output Ez is scaled to ez with E0 in (19), and the absolute value of the right-hand side in the PDE ( 23) is scaled to B. This scaling is performed as pre-processing.…”

Section: A Data and Equation Scalingmentioning

confidence: 99%

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Physics-Informed Neural Network Method for Space Charge Effect in Particle Accelerators

Fujita¹

2021

IEEE Access

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The electromagnetic coupling of a charged particle beam with vacuum chambers is of great interest for beam dynamics studies in the design of a particle accelerator. A deep learning-based method is proposed as a mesh-free numerical approach for solving the field of space charges of a particle beam in a vacuum chamber. Deep neural networks based on the physical model of a relativistic particle beam with transversally nonuniform charge density moving in a vacuum chamber are constructed using this method. A partial differential equation with the Lorentz factor, transverse charge density, and boundary condition is embedded in its loss function. The proposed physics-informed neural network method is applied to round, rectangular, and elliptical vacuum chambers. This is verified in comparison with analytical solutions for coupling impedances of a round Gaussian beam and an elliptical bi-Gaussian beam. The effects of chamber geometries, charge density, beam offset, and energy on the beam coupling impedance are demonstrated.

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Section: B Deep Learing Approachmentioning

confidence: 99%

Section: A Data and Equation Scalingmentioning

confidence: 99%

Physics-Informed Neural Network Method for Space Charge Effect in Particle Accelerators

Fujita¹

2021

IEEE Access

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“…PINN has resulted in excitement on the use of machine learning algorithms for solving physical systems and optimizing their characteristic parameters given data. PINNs have now been applied to solve a variety of problems including fluid mechanics [54,33,20,72,10,55,46,57], solid mechanics [24,56,23,21], heat transfer [11,48,76], electro-chemistry [53,43,32], electro-magnetics [16,13,49], geophysics [7,63,62,66], and flow in porous media [19,1,6,60,34,5,64] (for a detailed review, see [35]). A few libraries have also been developed for solving PDEs using PINNs, including SciANN [22], DeepXDE [44], SimNet [25], and NeuralPDE [77].…”

Section: Introductionmentioning

confidence: 99%

Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential training

Haghighat,

Amini,

Juanes

2021

Preprint

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Physics-informed neural networks (PINNs) have received significant attention as a unified framework for forward, inverse, and surrogate modeling of problems governed by partial differential equations (PDEs). Training PINNs for forward problems, however, pose significant challenges, mainly because of the complex non-convex and multi-objective loss function. In this work, we present a PINN approach to solving the equations of coupled flow and deformation in porous media for both single-phase and multiphase flow. To this end, we construct the solution space using multi-layer neural networks. Due to the dynamics of the problem, we find that incorporating multiple differential relations into the loss function results in an unstable optimization problem, meaning that sometimes it converges to the trivial null solution, other times it moves very far from the expected solution. We report a dimensionless form of the coupled governing equations that we find most favourable to the optimizer. Additionally, we propose a sequential training approach based on the stress-split algorithms of poromechanics. Notably, we find that sequential training based on stress-split performs well for different problems, while the classical strain-split algorithm shows an unstable behaviour similar to what is reported in the context of finite element solvers. We use the approach to solve benchmark problems of poroelasticity, including Mandel's consolidation problem, Barry-Mercer's injection-production problem, and a reference two-phase drainage problem. The Python-SciANN codes reproducing the results reported in this manuscript will be made publicly available at https://github.com/sciann/sciann-applications.

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“…Due to these advantages, LSTMs are widely used in different areas (e.g., natural language processing) [44]. These interesting properties have also been successfully exploited to predict the evolution of field values in transient electrodynamics [45] and for buried object detection from ground penetrating radar signals [46].…”

Section: Introductionmentioning

confidence: 99%

Microwave Tomography With LSTM-Based Processing of the Scattered Field

Fedeli

2021

IEEE Open J. Antennas Propag.

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The quantitative inspection of unknown targets or bodies by means of microwave tomography requires a proper modeling of the field scattered by the structures under test, which in turn depends on several factors related to the adopted antennas and measurement configuration. In this article, a multifrequency tomographic approach in nonconstant-exponent Lebesgue spaces is enhanced by a preliminary step that processes the measured scattered field with a neural network based on long short-term memory cells. In the considered cases, this approach allows dealing with measurements in three-dimensional settings obtained with non-ideal antennas and measurement points, while retaining a canonical two-dimensional formulation of the inverse problem. The adopted data-driven model is trained with a set of simulations of cylindrical targets performed with a finite-difference time domain method, considering a simplified bistatic measurement configuration as an initial case study. The inversion procedure is then validated with numerical simulations involving cylindrical and spherical structures.INDEX TERMS Microwave imaging, inverse scattering, long short-term memory.

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Physics-Informed Deep Neural Networks for Transient Electromagnetic Analysis

Cited by 47 publications

References 32 publications

Physics-Informed Neural Network Method for Space Charge Effect in Particle Accelerators

Physics-Informed Neural Network Method for Space Charge Effect in Particle Accelerators

Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential training

Microwave Tomography With LSTM-Based Processing of the Scattered Field

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