Scalable parametric acoustic field prediction via hierarchical physics-informed deep operator network with modal compression

We propose a hierarchical transfer learning framework for physics-informed deep operator networks augmented with modal compression to enable fast, accurate, and generalizable prediction of parametric fields governed by partial differential equations (PDEs). The proposed approach integrates physical constraints into the training process through PDE residual-based loss and interface boundary condition loss. Furthermore, we introduce a hierarchical transfer learning strategy across spatial resolution and dimensionality levels, allowing for knowledge reuse from low-fidelity fields to high-fidelity physical fine-tuned domains. To efficiently encode spatial variability, the trunk network is constructed using reduced-order modal bases, while binary masking is employed to distinguish between internal and external domains. Numerical examples on complex acoustic problems demonstrate that the proposed framework achieves high accuracy under various parametric values. Moreover, the proposed framework demonstrates exceptional generalization to new source configurations not seen during training, confirming its function as a solution operator. This work presents a physically robust and highly expandable approach for real-time field prediction in complex engineering systems.