To accurately capture sharp features like shock and expansion waves in high-speed compressible flows, we introduce the OL-AAF (operator learning method with adaptive activation function), a novel framework designed to learn solution operators for parametric governing equations for high speed shock tube problems and airfoil flows. The primary novelty of the neural network lies in a layer-wise gated bridge branch that establishes interaction information channels between the latent representations of neural networks. By utilizing learnable gating parameters to adaptively modulate coupled hidden features at every layer, the architecture’s representational capacity is markedly increased. The approximation ability of the network is also improved by an adaptive Z-shape-ReLU activation function in the basis function network’s terminal layers. Through the simultaneous optimization of its positive-axis slope and truncation threshold, Z-shape-ReLU counteracts the numerical ‘blurring’ typical of SiLU or other activation functions, ensuring high-fidelity approximations of strong discontinuities. Validated against high-speed shock tube and airfoil flow datasets, the OL-AAF framework outperforms DeepONet in shock-position accuracy and displays strong generalization. This study gains a robust architectural template for high-speed, data-driven aerodynamic prediction. To address discrepancies in physical equations, an enhanced fine-tuning module integrated with physical constraints is proposed. Physical equation residuals are calculated via a point-based query strategy to enable efficient gradient computation, which are then mapped into the latent feature space for iterative refinement. The fine-tuning workflow adopts a self-supervised learning paradigm, ensuring adherence to physical consistency without compromising the core characteristics of the generated fields. Experimental results demonstrate that this physics-informed fine-tuning framework achieves a substantial reduction in physical inaccuracies.