Magnetostatics and micromagnetics with physics informed neural networks

Kovacs, Alexander; Exl, Lukas; Kornell, Alexander; Fischbacher, Johann; Hovorka, Markus; Gusenbauer, Markus; Breth, Leoni; Oezelt, Harald; Praetorius, Dirk; Suess, Dieter; Schrefl, T.

doi:10.1016/j.jmmm.2021.168951

Cited by 37 publications

(20 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The multifidelity simulation technique, which is a combination of low-fidelity and high-fidelity simulations using PINN, was studied by Penwarden et al [42] to reduce the computational cost. Kovacs et al [43] used PINN to solve magnetostatic and micromagnetic problems. The design of electromagnetic metamaterials using PINN was proposed by Fang and Zhan [44].…”

Section: Surrogate Modelmentioning

confidence: 99%

State-of-the-Art Review of Design of Experiments for Physics-Informed Deep Learning

Das¹,

Tesfamariam²

2022

Preprint

View full text Add to dashboard Cite

This paper presents a comprehensive review of the design of experiments used in the surrogate models. In particular, this study demonstrates the necessity of the design of experiment schemes for the Physics-Informed Neural Network (PINN), which belongs to the supervised learning class. Many complex partial differential equations (PDEs) do not have any analytical solution; only numerical methods are used to solve the equations, which is computationally expensive. In recent decades, PINN has gained popularity as a replacement for numerical methods to reduce the computational budget. PINN uses physical information in the form of differential equations to enhance the performance of the neural networks. Though it works efficiently, the choice of the design of experiment scheme is important as the accuracy of the predicted responses using PINN depends on the training data. In this study, five different PDEs are used for numerical purposes, i.e., viscous Burger's equation, Shrödinger equation, heat equation, Allen-Cahn equation, and Korteweg-de Vries equation. A comparative study is performed to establish the necessity of the selection of a DoE scheme. It is seen that the Hammersley sampling-based PINN performs better than other DoE sample strategies.

show abstract

Section: Surrogate Modelmentioning

confidence: 99%

State-of-the-Art Review of Design of Experiments for Physics-Informed Deep Learning

Das¹,

Tesfamariam²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…7.B, an ensemble of neurons generated mathematically to mimic neuronal clustering in two rows. The next step was to explore the vector field of those neurons that may reflect their electromagnetic activity projected in 2D by using the gradient of on the differentiable manifolds for more details and for Laplacian vector field, see below [13] Fig. 7.C.…”

Section: The Assumed Model For Neuronal Clustering and Its Vector Fieldmentioning

confidence: 99%

Geometrical modelling of neuronal clustering and development

Rafati

Ardalan

Vontell

et al. 2022

Heliyon

View full text Add to dashboard Cite

“…The boundary value problem corresponding to the heat equation can also be defined by Eq. (25). We consider problems on the square domain Ω with [x l , x r ] = [0, 2] and the hole radius r = 0.6 and T 0 = 5.…”

Section: Heat Transfer Problem Of Square Plate With a Hole In The Middlementioning

confidence: 99%

“…PINN was shown to behave well in solving both the forward and inverse problems of various kinds of PDE with very little data, such as phase field equation [13,14,15,16], stochastic PDE [17,18,19,20], and fractional PDE [21]. In addition, PINN is useful in several engineering applications, such as biomedical problems [22], materials [23,24,25], or solid mechanics [26]. PINN also found rich applications in computational fluid mechanics [27,28,29,30,31].…”

Section: Introductionmentioning

confidence: 99%

Hybrid Finite Difference with the Physics-informed Neural Network for solving PDE in complex geometries

Zixue¹,

Wei²,

Zhou³

et al. 2022

Preprint

View full text Add to dashboard Cite

The physics-informed neural network (PINN) is effective in solving the partial differential equation (PDE) by capturing the physics constraints as a part of the training loss function through the Automatic Differentiation (AD). This study proposes the hybrid finite difference with the physics-informed neural network (HFD-PINN) to fully use the domain knowledge. The main idea is to use the finite difference method (FDM) locally instead of AD in the framework of PINN. In particular, we use AD at complex boundaries and the FDM in other domains. The hybrid learning model shows promising results in experiments. To use the FDM locally in the complex boundary domain and avoid the generation of background mesh, we propose the HFD-PINN-sdf method, which locally uses the finite difference scheme at random points. In addition, the signed distance function is used to avoid the difference scheme from crossing the domain boundary. In this paper, we demonstrate the performance of our proposed methods and compare the results with the different number of collocation points for the Poisson equation, Burgers equation. We also chose several different finite difference schemes, including the compact finite difference method (CDM) and crank-nicolson method (CNM), to verify the robustness of HFD-PINN. We take the heat conduction problem and the heat transfer problem on the irregular domain as examples to demonstrate the efficacy of our framework. In summary, HFD-PINN, especially HFD-PINN-sdf, are more instructive and efficient, significantly when solving PDEs in complex geometries.

show abstract

Magnetostatics and micromagnetics with physics informed neural networks

Cited by 37 publications

References 36 publications

State-of-the-Art Review of Design of Experiments for Physics-Informed Deep Learning

State-of-the-Art Review of Design of Experiments for Physics-Informed Deep Learning

Geometrical modelling of neuronal clustering and development

Hybrid Finite Difference with the Physics-informed Neural Network for solving PDE in complex geometries

Contact Info

Product

Resources

About