A machine learning system for training a dynamics model to learn dynamics of a physical system, in particular forward dynamics of a robotic arm, vehicle, domestic appliances, power tool or a manufacturing machine, by learning to infer a future state of the physical system based on a current state of the physical system, the machine learning system comprising: - an input interface for accessing: - training data comprising a time-series of states ( x t) of the physical system; - model data defining a machine learnable dynamics model ( f ( x t)) which comprises a machine learnable Lyapunov function ( V ( x t)); - a processor subsystem configured to learn the dynamics model based on the training data time-sequential pairs of states ( x t) so as to learn to infer a future state ( x t +1 = f ( x t)) of the physical system based on the current state ( x t), wherein said learning is constrained to provide a globally stable modelling of the dynamics of the physical system by jointly learning the dynamics model and the Lyapunov function so that values of the learned Lyapunov function decrease ( V ( x t +1) < V ( x t)) along all trajectories of states ( x 0, x 1,..., x T) inferred by the learned dynamics model, wherein the processor subsystem is further configured to jointly learn the dynamics model and the Lyapunov function by learning as the dynamics model ( f ( x t)) a projection (Proj) of nominal dynamics ( f̂ ( x t)) of the physical system, which are learned based on the time-series of states ( x t), onto a function that fulfills the Lyapunov condition as defined by the Lyapunov function ( V ( x t)), wherein the projection (Proj) is an orthogonal projection onto a halfspace. - an input interface for accessing: - training data comprising a time-series of states ( x t) of the physical system; - model data defining a machine learnable dynamics model ( f ( x t)) which comprises a machine learnable Lyapunov function ( V ( x t)); - training data comprising a time-series of states ( x t) of the physical system; - model data defining a machine learnable dynamics model ( f ( x t)) which comprises a machine learnable Lyapunov function ( V ( x t)); - a processor subsystem configured to learn the dynamics model based on the training data time-sequential pairs of states ( x t) so as to learn to infer a future state ( x t +1 = f ( x t)) of the physical system based on the current state ( x t), wherein said learning is constrained to provide a globally stable modelling of the dynamics of the physical system by jointly learning the dynamics model and the Lyapunov function so that values of the learned Lyapunov function decrease ( V ( x t +1) < V ( x t)) along all trajectories of states ( x 0, x 1,..., x T) inferred by the learned dynamics model, wherein the processor subsystem is further configured to jointly learn the dynamics model and the Lyapunov function by learning as the dynamics model ( f ( x t)) a projection (Proj) of nominal dynamics ( f̂ ( x t)) of the physical system, which are learned based on the time-series of states ( x t), onto a function that fulfills the Lyapunov condition as defined by the Lyapunov function ( V ( x t)), wherein the projection (Proj) is an orthogonal projection onto a halfspace.