Uncertainty Quantification in PEEC Method: A Physics-Informed Neural Networks-Based Polynomial Chaos Expansion

Abstract

In this article, we propose a novel machine learning approach for uncertainty quantification (UQ) within the partial equivalent element circuit (PEEC) framework, employing physics-informed neural networks (PINNs)-based polynomial chaos expansion (PCE) scheme. Initially, the PEEC method is formulated via the electrical field integral equations and current continuity equations. Subsequently, random parameters are introduced to construct corresponding stochastic equations, thereby facilitating the generation of input–output data pairs for the training process. Then, by utilizing the PCE methodology, a mapping function is established. Next, the PINN-based approach is adopted to compute the coefficients of the polynomial bases, leveraging the matrix constructed from training data. Finally, this proposed approach enables the determination of stochastic parameters for quantities of interest within the PEEC method. The numerical examples involving the transmission lines are provided to verify the efficiency of the proposed method. It is found that the uncertainty is well quantified in each case. Compared to the traditional MCM, the proposed method can make UQ in the PEEC method 20 times faster. Hence, our work offers a practical machine learning approach for quantifying uncertainty, which could also be extended to other computational electromagnetic methods.