Researchers propose DVL-DeepONet, a physics-guided deep neural operator framework designed to enhance autonomous underwater vehicle navigation under degraded sensing conditions. The system addresses challenges arising from noisy or incomplete Doppler velocity log measurements and the absence of inertial sensors in low-cost platforms. It estimates velocity vectors through three operational scenarios: noise-resilient estimation with coupled sensors, DVL-only learning, and beam measurement recovery. By mapping temporal observations to vehicle velocity while enforcing physical consistency constraints, the model maintains robustness during environmental disturbances. The framework was validated using real-world AUV experiments covering a cumulative path length of approximately 10,000 meters. Experimental results demonstrate that DVL-DeepONet architectures outperform baseline model-based and learning-based algorithms by 40%.