Conference Agenda

new class of neural networks has been recently introduced to solve problems based on some physical model. Such networks are called “Physical-Informed Neural Networks” (PINN). PINN are trained not based on input-output data, but rather by explicitly enforcing the model physical laws. More in detail, they are trained to minimize the “equations residual” in the physical model in each point of the domain rather than the discrepancy with known data. In this contribution, we propose to formulate the equations of ElectroMagnetism (EM) embedded in a PINN by using a weak formulation approach. This helps convergence of the training process, thanks to the lower derivation order required in the error computation. In addition, the presence of different materials in the domain is easily treated. In this digest, the approach is described in its fundamentals, and a simple example is presented.

This paper proposes a scheme of applying data augmentation to improve the accuracy of machine learning for optimal design of electromagnetic devices, where an inductor design with neural network (NN) is considered as a concrete example. The data set is augmented by introducing perturbative noise to geometric parameters, while keeping the inductance, core loss, and magnetic saturation capacity to their original values. Through K-fold cross-validation and Pearson correlation coefficient, it has been demonstrated that the NN model with data augmentation achieves higher accuracy than the one without data augmentation.

Open boundaries 2-D magnetostatic field problems pose significant challenges for traditional numerical methods due to their high computational complexity. This paper proposes MagOpenNet, a novel implementation of self-adaptive physical-informed neural networks (PINNs) for solving these problems. MagOpenNet introduces the concept of the Infinite Element Method (IEM) and adjusts its architecture to address the complexities of interior and exterior domain predictions. The preliminary results state that MagOpenNet reduces 22.5% the computation time while maintaining 98% accuracy compared to traditional numerical methods.

Building on the graph-neural network architecture proposed by Hao Zhang et al. [1], we propose a novel physics-informed neural network (PINN) approach for efficiently solving the Helmholtz equation in two dimensions. By viewing the computational mesh as a graph, we employ an encoder-processor-decoder architecture that learns local interactions among mesh nodes while simultaneously enforcing the underlying physical laws through a PDE-informed loss term. This novelty lies in leveraging graph neural networks (GNNs) to incorporate geometric domain information for accurate and scalable numerical computation of electromagnetic fields. Numerical experiments confirm the model’s ability to replicate the known exact solution to within reasonable error, suggesting that this PINN-GNN synergy has the potential for fast solutions to electromagnetic-wave-related PDEs compared to more traditional numerical methods.