Abstract: Accurate prediction of formation pore pressure is essential to predict fluid flow and manage hydrocarbon production in petroleum engineering. Recent deep learning technique has been receiving more interest due to the great potential to deal with pore pressure prediction. However, most of the traditional deep learning models are less efficient to address generalization problems. To fill this technical gap, in this work, we developed a new adaptive physics-informed deep learning model with high generalization capability to predict pore pressure values directly from seismic data. Specifically, the new model, named CGP-NN, consists of a novel parametric features extraction approach (1DCPP), a stacked multilayer gated recurrent model (multilayer GRU), and an adaptive physics-informed loss function. Through machine training, the developed model can automatically select the optimal physical model to constrain the results for each pore pressure prediction. The CGP-NN model has the best generalization when the physics-related metric λ=0.5. A hybrid approach combining Eaton and Bowers methods is also proposed to build machine-learnable labels for solving the problem of few labels. To validate the developed model and methodology, a case study on a complex reservoir in Tarim Basin was further performed to demonstrate the high accuracy on the pore pressure prediction of new wells along with the strong generalization ability. The adaptive physics-informed deep learning approach presented here has potential application in the prediction of pore pressures coupled with multiple genesis mechanisms using seismic data.