Physics-Informed Neural Networks for Solving Parametric Magnetostatic Problems

Beltrán-Pulido, Andrés; Bilionis, Ilias; Aliprantis, Dionysios

doi:10.1109/tec.2022.3180295

Cited by 28 publications

(11 citation statements)

References 31 publications

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“…To overcome this potential issue, Beltran-Pulido et al propose the minimization of the integral on the coupling field coenergy instead which is equivalent to solving the weak formulation of Eqs. ( 2) and (3) [10]. We obtain…”

Section: B Physical Modelmentioning

confidence: 91%

“…Due to the different orders of magnitudes present in the problem, a nondimensionalization scheme similar to the one used in [10] is applied to rescale variables and constants to numerically similar ranges via…”

Section: B Physical Modelmentioning

confidence: 99%

“…( 5) is minimized on the set of training points (r i , z i ), cf. [10]. Consequently, we obtain the following loss function for the weak solution:…”

Section: A Fully Connected Pinn (Fc-pinn)mentioning

confidence: 99%

“…In the field of electromagnetics, PINNs have already been applied to predict the magnetic flux distribution based on a given magnetization [8], and in a hybrid setup combined with data for simple electro-and magneto-static problems [9]. More recent results demonstrate their potential for the design of a single coil or choke [10], or coil systems used for induction heating and hardening [11], [12]. The aforementioned examples use Fully Connected Neural Networks (FCNNs) as basic architecture to approximate the physics and allow only limited degrees of freedom in their geometric setups.…”

Section: Introductionmentioning

confidence: 99%

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Physics-Informed Neural Networks for Magnetostatic Problems on Axisymmetric Transformer Geometries

Brendel,

Medvedev,

Rosskopf

2024

IEEE J. Emerg. Sel. Top. Ind. Electron.

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Physics-Informed Neural Networks (PINNs) have shown their potential for solving direct problems in many engineering domains including electromagnetics. We employ fully connected and convolutional PINNs in order to predict the magnetic vector potential and resulting inductances and coupling for axisymmetric transformer geometries commonly used in inductive power systems. Both approaches are compared quantitatively and validated against reference solutions obtained from a numerical solver. Fully connected PINNs tend to train faster and more accurate for single geometries, whereas convolutional PINNs show an outperformance in terms of their generalization capability and are able to predict inductances and coupling for a wide range of transformer geometries accurately in a matter of milliseconds. The combination of high accuracy and fast inference paves the way for PINN-based topology optimization in the field of power electronics.

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Section: B Physical Modelmentioning

confidence: 91%

Section: B Physical Modelmentioning

confidence: 99%

“…( 5) is minimized on the set of training points (r i , z i ), cf. [10]. Consequently, we obtain the following loss function for the weak solution:…”

Section: A Fully Connected Pinn (Fc-pinn)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Physics-Informed Neural Networks for Magnetostatic Problems on Axisymmetric Transformer Geometries

Brendel,

Medvedev,

Rosskopf

2024

IEEE J. Emerg. Sel. Top. Ind. Electron.

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show abstract

“…[26,27]. Importantly, PINNs are very well suited for solving parametric PDEs [28], i.e. for situations where the solution to the governing PDE is required for different scenarios (e.g.…”

Section: Physics Informed Neural Network (Pinns)mentioning

confidence: 99%

Single-Track Thermal Analysis of Laser Powder Bed Fusion Process: Parametric Solution Through Physics-Informed Neural Networks

Hosseini¹,

Ghanbari²,

Müller³

et al. 2023

Preprint

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Transfer learning‐based physics‐informed neural networks for magnetostatic field simulation with domain variations

Lippert,

von Tresckow,

De Gersem

et al. 2024

Int J Numerical Modelling

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Physics‐informed neural networks (PINNs) provide a new class of mesh‐free methods for solving differential equations. However, due to their long training times, PINNs are currently not as competitive as established numerical methods. A promising approach to bridge this gap is transfer learning (TL), that is, reusing the weights and biases of readily trained neural network models to accelerate model training for new learning tasks. This work applies TL to improve the performance of PINNs in the context of magnetostatic field simulation, in particular to resolve boundary value problems with geometrical variations of the computational domain. The suggested TL workflow consists of three steps. (a) A numerical solution based on the finite element method (FEM). (b) A neural network that approximates the FEM solution using standard supervised learning. (c) A PINN initialized with the weights and biases of the pre‐trained neural network and further trained using the deep Ritz method. The FEM solution and its neural network‐based approximation refer to an computational domain of fixed geometry, while the PINN is trained for a geometrical variation of the domain. The TL workflow is first applied to Poisson's equation on different 2D domains and then to a 2D quadrupole magnet model. Comparisons against randomly initialized PINNs reveal that the performance of TL is ultimately dependent on the type of geometry variation considered, leading to significantly improved convergence rates and training times for some variations, but also to no improvement or even to performance deterioration in other cases.

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Physics-Informed Neural Networks for Solving Parametric Magnetostatic Problems

Cited by 28 publications

References 31 publications

Physics-Informed Neural Networks for Magnetostatic Problems on Axisymmetric Transformer Geometries

Physics-Informed Neural Networks for Magnetostatic Problems on Axisymmetric Transformer Geometries

Single-Track Thermal Analysis of Laser Powder Bed Fusion Process: Parametric Solution Through Physics-Informed Neural Networks

Transfer learning‐based physics‐informed neural networks for magnetostatic field simulation with domain variations

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