Approximating Steady-State Maxwell’s Equations via Physics-Informed Neural Networks

(welcome applications for the research internship positions in a form of Master thesis)

Supported by the Emerging Talents Initiative No. 5500168 (ETI) at Friedrich-Alexander-Universität Erlangen-Nürnberg.

Duration: 2022 – now

In recent years, Physics-Informed Neural Networks (PINNs) have started to arise frequently in many areas of science and engineering. PINNs are revolutionizing the way many physics-related problems are solved by combining classic Neural Networks explicitly with the underlying Physics of a certain problem.

This is a collaboration with Fraunhofer IISB, Erlangen.

People involved

Scope / Goal

In recent years, Physics-Informed Neural Networks (PINNs) have started to arise frequently in many areas of science and engineering. PINNs are revolutionizing the way many physics-related problems are solved by combining classic Neural Networks explicitly with the underlying Physics of a certain problem.

The intrinsic Machine-Learning (ML) nature of PINNs enables huge speed-ups for simulations at inference time (i.e., after training) while the introduced Physics ensure the conservation of the physical laws behind the problem.

We consider a Use-Case from Power-Electronics, more specifically the topology optimization of a ferrit core for a choke or coil, which requires accurate and fast prediction of magnetic flux and field intensity inside the system.

This task is tackled by:

• Deriving an adequate mathematical description based on the steady-state Maxwell Equations (2D symmetric) with corresponding Initial- and Boundary-Conditions [1].

• Enhancing frameworks such as Nvidia Modulus for reproducible training, evaluation and visualization of PINNs [2].

• Application of Hyperparameter-Tuning and other ML-Enhancing Techniques like Loss-Balancing for PINNs [3]. This Project is a collaboration with Fraunhofer IISB, Erlangen.


[1] J. Lima, D. Psaltis. MaxwellNet: Physics-driven deep neural network training based on Maxwell’s equations, https://aip.scitation.org/doi/pdf/10.1063/5.0071616

[2] A Framework for Developing Physics Machine Learning Neural Network Models, https://developer.nvidia.com/modulus

[3] Bischof et al., „Multi-Objective Loss Balancing for Physics-Informed Deep Learning“, 2110.09813.pdf (arxiv.org)


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