<p>High-fidelity inversion of the sound speed profile is critical for reliable oceanic environmental sensing. However, the prohibitive computational cost of traditional matched-field inversion (MFI) and the limited physical interpretability of purely data-driven methods have led to a persistent trade-off between efficiency and accuracy. To address these limitations, we propose the deep modal neural operator (DeepMNO), a physics-informed architecture that is mathematically isomorphic to normal mode theory. By employing a decoupled branch-trunk architecture to independently process environmental descriptors and synthesize spatial basis functions, DeepMNO encapsulates the physics of discrete modal expansion directly within its parametric space. Furthermore, a cascaded optimization framework is introduced to implement a “global search to local refinement” strategy, shifting the computational burden to facilitate near-real-time environmental characterization. Numerical assessments using WOA18-derived datasets reveal that the framework achieves a root-mean-square error of 0.07 m/s at a signal-to-noise ratio (SNR) of 10 dB. Notably, the inversion latency is reduced to 4.7 s, marking an over 35-fold acceleration compared to conventional iterative MFI. Moreover, the framework demonstrates strong robustness even under a low SNR of −5 dB. The results confirm that projecting acoustic observations onto a differentiable physical manifold—represented by the learned operator—effectively reconciles computational tractability with physical rigor in complex underwater acoustic waveguides.</p>