This paper presents a framework for manipulating Deformable Linear Objects (DLOs) using a neural network (NN) to model their dynamics. The framework aims to address the challenges of DLO manipulation, such as unpredictable configuration, high-dimensional state space, and complex nonlinear dynamics. The NN is trained to mimic the DLO dynamics using an analytical model and a dataset generated with various parameters. During the online phase, the NN is used to estimate the optimal manipulation actions and simultaneously adapt the model parameters to better capture the dynamics of the real-world DLO. The effectiveness of the framework is demonstrated through experiments on different DLOs and surfaces, showing improved performance compared to existing methods. The contributions of the paper include an NN-based DLO dynamics approximation, efficient gradient-based action prediction and parameter estimation, and experimental validation on real-world DLOs. The framework is evaluated using a robotic setup with a Panda Robot, a parallel-jaw gripper, and a Photoneo Motioncam3D, and it successfully manipulates ropes on different surfaces. The results highlight the adaptability and efficiency of the proposed method, with the NN model outperforming other architectures in terms of prediction accuracy and generalization.This paper presents a framework for manipulating Deformable Linear Objects (DLOs) using a neural network (NN) to model their dynamics. The framework aims to address the challenges of DLO manipulation, such as unpredictable configuration, high-dimensional state space, and complex nonlinear dynamics. The NN is trained to mimic the DLO dynamics using an analytical model and a dataset generated with various parameters. During the online phase, the NN is used to estimate the optimal manipulation actions and simultaneously adapt the model parameters to better capture the dynamics of the real-world DLO. The effectiveness of the framework is demonstrated through experiments on different DLOs and surfaces, showing improved performance compared to existing methods. The contributions of the paper include an NN-based DLO dynamics approximation, efficient gradient-based action prediction and parameter estimation, and experimental validation on real-world DLOs. The framework is evaluated using a robotic setup with a Panda Robot, a parallel-jaw gripper, and a Photoneo Motioncam3D, and it successfully manipulates ropes on different surfaces. The results highlight the adaptability and efficiency of the proposed method, with the NN model outperforming other architectures in terms of prediction accuracy and generalization.