Recent advances in aerial robotics have enabled the use of multirotor vehicles for autonomous payload transportation. Resorting only to classical methods to reliably model a quadrotor carrying a cable-slung load poses significant challenges. On the other hand, purely data-driven learning methods do not comply by design with the problem’s physical constraints, especially in states that are not densely represented in training data. In this work, we explore the use of physics-informed neural networks to learn an end-to-end model of the multirotor-slung-load system and, at a given time, estimate a sequence of the future system states. An LSTM encoder-decoder with an attention mechanism is used to capture the dynamics of the system. To guarantee the cohesiveness between the multiple predicted states of the system, we propose the use of a physics-based term in the loss function, which includes a discretized physical model derived from first principles together with slack variables that allow for a small mismatch between expected and predicted values. To train the model, a dataset using a real-world quadrotor carrying a slung load was curated and is made available. Prediction results are presented and corroborate the feasibility of the approach. The proposed method outperforms both the first principles physical model and a comparable neural network model trained without the physics regularization proposed.