Abstract: Objectives Hybrid crawling-swimming Autonomous Underwater Vehicles (AUVs) possess the unique capability to traverse both the water column and the seabed, yet their operation is plagued by drastic, nonlinear dynamic changes during configuration shifting (morphing), posing significant challenges for safe and stable control. To address this, this paper proposes a novel adaptive control framework. Methods We present a novel Dual-Loop Symbolic Adaptive Control (DSAC) architecture. In the slow adaptation loop (~0.1 Hz), a Large Language Model (LLM) functions as a “physics reasoner,” generating structural priors based on configuration semantics to guide a Symbolic Regression (SR) engine. In the fast control loop (100 Hz), a Lyapunov-based safety filter verifies the stability of the generated model before updating the controller. Results Experimental results in a high-fidelity simulator across diverse morphing scenarios (gradual, step, sinusoidal) demonstrate that our framework autonomously discovers configuration-dependent drag laws, reducing tracking error by approximately 25% compared to robust Model Reference Adaptive Control (MRAC) and PID baselines, while ensuring theoretical stability during complex mode transitions. Conclusions The proposed DSAC framework effectively addresses three major challenges in morphing AUV dynamics modeling: unknown model structure, low search efficiency, and poor physical plausibility. By integrating LLM-guided symbolic discovery with rigorous stability verification, it achieves a unified balance between adaptability and stability.