We present the SLiding-window Initially-truncated Dynamic-response Estimator SLIDE, a deep-learning based method for the estimation of output sequences, e.g. displacements, for mechanical and multibody systems with forced excitation, e.g. control inputs, forces, or torques. The sliding of input and output windows enables the processing of longer sequences with feedforward networks, by moving both windows by the length of the output window, followed by concatenation of the solutions. The method focuses on damped systems and the truncation of the output window is chosen according to the decay of the initial conditions. Therefore the initial conditions do not need to be fully known, which is a major advantage for flexible systems, where the full system state is complex to measure. Due to the damping properties, each input-output sequence can be considered independently, hence the sliding is only applied in testing. The damping is approximated for general multibody systems by the complex eigenvalues of the system’s linearized equations. The application of SLIDE to different mechanical and multibody systems is shown, where a surrogate network estimates the dynamic response and a second error estimator network provides estimates for a logarithmically scaled error of the surrogate network to improve applicability. The deep-learning based method SLIDE enables estimation for the dynamic response, while offering speedups due to the utilization of modern deep-learning techniques and hardware like GPUs - especially for complex applications, e.g. flexible robotics, where peak speedups of 20 million compared to conventional simulation have been observed.