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

This paper proposes a novel approach to uncertainty quantification (UQ) in the partial equivalent element circuit (PEEC) method through a physics-informed neural networks (PINNs)-based polynomial chaos expansion (PCE) scheme. Initially, the PEEC method is formulated via the electrical field integral equations and continuity equations. Subsequently, random parameters are introduced to construct stochastic equations, generating input and output observations for training data. The PCE method is then employed to establish a mapping function. To calculate the coefficients of polynomial bases, a PINNs-based method is applied, utilizing the constructed matrix derived from the training data. Finally, this methodology enables the determination of stochastic parameters for quantities of interest within the PEEC method. The numerical example involving a transmission line is provided to verify the efficiency of the proposed method. It is found that the uncertainty is well quantified in all cases.