Physically informed complex neural network for sound source localization in reverberant environments

Accurate localization of acoustic sources in reverberant environments is important for low-noise mechanical design, yet remains challenging due to multipath reflections and environmental uncertainty. In this study, a physically informed complex neural network is proposed, in which acoustic transfer functions derived from the image source method or the free-field Green’s function are used as input features. By preserving both magnitude and phase information through complex-domain operations, the model incorporates physical priors while leveraging the representation capability of deep learning to reduce reverberation-induced distortions. Unlike conventional methods that rely heavily on idealized assumptions, the proposed approach learns to compensate for discrepancies between physically modeled and observed acoustic responses. The model is evaluated under different reverberation times and source frequencies. The results show more favorable localization accuracy and sidelobe suppression than those of conventional deconvolution methods and recent deep-learning baselines such as FISTA-Net within the tested conditions. Additional ablation studies further demonstrate the contributions of complex-valued learning and physically informed modeling to the observed performance. Experimental validation in a controlled enclosed acoustic space also supports the feasibility of the proposed framework.