Physics-informed DeepONet with modal coordinate encoding for predicting dynamic responses of unseen motor housings

This study proposes a unified physics-informed machine-learning (PIML) framework for predicting the dynamic responses of traction motor housings under unseen geometric conditions. The framework incorporates three key forms of physical priors into a neural network. First, an observation bias is introduced through modal coordinate encoding, which embeds both geometric characteristics and excitation-dependent modal contributions into the neural network. Second, an inductive bias is incorporated by deploying a separable deep operator network architecture, which effectively learns nonlinear operator mappings and generalizes them to unseen housing geometries. Third, a learning bias is enforced by embedding the governing equations of structural dynamics into the training process to ensure physically consistent predictions. Novel training strategies are also employed to enhance convergence and numerical stability during physics-informed training. Quantitative evaluations and ablation studies demonstrate the effectiveness of the proposed framework, achieving a mean MAPE of 3.32 % across the full test set and outperforming conventional neural networks. A design-optimization application further confirms that the proposed framework improves computational efficiency compared with conventional finite element analysis. Overall, this study establishes a robust framework for accelerating AI-driven design optimization and advancing intelligent structural engineering methodologies.