PDNFormer: Fast, Accurate, and Scalable Impedance Estimator for Grid-Type Multilayered Power Distribution Networks With Multipower Domains

In this article, we propose a fast, accurate and scalable impedance estimation framework, PDNFormer, for grid-type multi-layered power distribution networks (PDNs) with multi-power domains. The proposed model independently predicts the real and imaginary parts of the impedance in the proposed signed-dB (sdB) representation based on given PDN configurations. Through a post-processing transformation, the predicted real and imaginary parts are converted into the corresponding magnitude and phase, from which the complex impedance is finally recovered. PDNFormer leverages attention and convolutional blocks to capture both local geometric patterns and global inter-domain and inter-layer dependencies. Compared to the previous work, the proposed framework incorporates enhanced neural sub-modules to handle PDN descriptors, including port positions, scale factor, and grid direction. Trained and validated on a dataset of 621,312 samples, our framework predicts each impedance response within 22.2 μs on a GPU and approximately 1.3 ms on a CPU. This corresponds to a runtime improvement of more than five orders of magnitude compared to conventional electromagnetic (EM) simulations, while maintaining high estimation accuracy, achieving an average mean absolute error (MAE) of 3.44 dBΩ in magnitude and 0.25 rad in phase on test samples. The scalability of our framework is also validated on unseen PDN configurations with increased PDN size and number of metal layers, as well as diverse scale factors beyond the training range. A rational fitting–based causality evaluation shows that the causality error metric (CEM) remains below 0.01, confirming that the generated Z-parameters maintain causal consistency within a practically reasonable range. This work can support power integrity (PI) optimization frameworks as a fast surrogate estimator for preliminary screening and design exploration, complementing conventional EM simulations.