Physics-Enhanced Probabilistic Generative Modeling for Sparse Measurement-Based Sound Field Reconstruction

To address the ill-posedness and generalization challenges associated with sound field reconstruction under sparse measurement conditions， this paper proposes a physics-constrained generative reconstruction framework. Specifically， the proposed method employs a plane wave decomposition model to represent the spatial sound field， transforming it into plane wave spectrum coefficients. Utilizing a conditional invertible neural network （CINN） as the backbone， the model learns the conditional posterior probability distribution from sparse observations to spectrum coefficients using large-scale simulation data， effectively modeling the uncertainty inherent in the inverse problem. During the inference phase on real-world data， a fine-tuning mechanism based on Helmholtz equation residuals is introduced as a physical constraint to correct the generated results and enforce physical consistency. Experimental results on the MeshRIR dataset demonstrate that the proposed method significantly outperforms mainstream baselines， including physics-informed neural networks， generative adversarial networks， and the original CINN， in terms of both normalized mean squared error and modal assurance criterion.