Explainable Machine Learning for Multilayer Planar Winding Inductance Estimation

Wound rotor synchronous motors have emerged as a strong alternative that eliminates dependence on REEs. However, WRSM design requires the simultaneous optimization of numerous geometric and electromagnetic parameters, and the high computational cost of conventional finite element analysis severely limits the rapid exploration of the large parameter space. Although there are machine-learning-based surrogate modeling studies in the literature, they generally compare only a limited number of models, exclude deep learning architectures, and do not provide a comprehensive benchmark specific to WRSM. In this study, the performance of a total of eight machine learning and deep learning models from four different algorithmic families was systematically compared for the prediction of WRSM torque and motor efficiency. On a dataset of 3351 samples generated using Latin Hypercube Sampling in the Motor-CAD simulation environment, each model was trained with 10 different random seed values and tuned via Optuna hyperparameter optimization. Different from the existing literature, this study jointly offers a broad model spectrum including recent deep learning architectures such as FT Transformer, a multi-seed reproducibility protocol, and a Pareto analysis of the computational cost-accuracy trade-off. The results revealed that neural-network-based models systematically outperform tree-based models. The FT-Transformer model achieved the highest single-model accuracy with R^2 = 0.9928, producing predictions in 0.33 milliseconds and thus obtaining several orders of magnitude speedup compared to FEA. Model performances were evaluated in a multidimensional manner using R^2, MAE, RMSE, and MAPE metrics.

As capacitance extraction accuracy of rule-based pattern matching becomes difficult to sustain at advanced nodes, a growing trend emerges to develop deep-learning-based 2D capacitance models. However, existing MLP- and CNN-based methods constrain their input to fixed metal-layer combinations in a specific process node, limiting their usability in practice. Recognizing the inherent similarity between capacitance matrix and the prevailing attention mechanism, we propose AttentionCap, a customized Transformer for capacitance matrix learning, with a Gram representation framework, a physics-aligned symmetric-attention output layer, and a novel normalized Laplacian loss. We also introduce a process-node embedding to enable multi-node learning. Trained on synthetic data, AttentionCap attains 0.67%/3.99% self/coupling-capacitance error on unseen real designs under a multi-layer and multi-node setting, surpassing the CNN-Cap baseline with 4.6$\times$/5.7$\times$ lower self/coupling error and 192$\times$ faster inference speed. A pretrained AttentionCap accurately transfers to an unseen node with only 5K samples and 4K finetuning steps. With sufficient accuracy on unseen real designs and strong transferability to new process nodes, AttentionCap offers highly practical value for modern EDA workflows. Code and data are available at https://github.com/THU-numbda/AttentionCap.

Explaining Machine Learning (ML) results in a transparent and user-friendly manner remains a challenging task of Explainable Artificial Intelligence (XAI). In this paper, we present a method to enhance the interpretability of ML models by using a Knowledge Graph (KG). We store domain-specific data along with ML results and their corresponding explanations, establishing a structured connection between domain knowledge and ML insights. To make these insights accessible to users, we designed a selective retrieval method in which relevant triplets are extracted from the KG and processed by a Large Language Model (LLM) to generate user-friendly explanations of ML results. We evaluated our method in a manufacturing environment using the XAI Question Bank. Beyond standard questions, we introduce more complex, tailored questions that highlight the strengths of our approach. We evaluated 33 questions, analyzing responses using quantitative metrics such as accuracy and consistency, as well as qualitative ones such as clarity and usefulness. Our contribution is both theoretical and practical: from a theoretical perspective, we present a novel approach for effectively enabling LLMs to dynamically access a KG in order to improve the explainability of ML results. From a practical perspective, we provide empirical evidence showing that such explanations can be successfully applied in real-world manufacturing environments, supporting better decision-making in manufacturing processes.