用预训练加速声场插值，实时性提升千倍以上

Numerous machine learning-based sound field interpolation methods have been proposed. In particular, physics-informed neural networks (PINNs) can accurately interpolate sound fields from a small number of microphones. However, their high computational cost and long training time pose practical challenges for applications requiring real-time processing or online learning. To address this, we propose a hybrid framework that combines PINN-based pre-training with a physics-informed extreme learning machine (PIELM) tailored for acoustic fields. By replacing iterative PINN fine-tuning for each target sound field with closed-form output-layer adaptation using hidden-layer weights pre-trained by PINN, the proposed method efficiently interpolates unknown sound fields from limited observations. Simulation results under simplified one-dimensional free-field conditions demonstrate that, given a pre-trained model, the proposed method achieves interpolation accuracy comparable to that of PINN-based fine-tuning while reducing the adaptation time by more than three orders of magnitude.