Dynamics model for globally stable modeling of system dynamics

A machine learning system for training a dynamics model to learn dynamics of a physical system by learning to infer a future state of the physical system and/or its environment based on a current state of the physical system and/or its environment, the machine learning system comprising:

• an input interface configured for accessing:
• training data representing a time-series of states of the physical system and/or its environment;
• and
• model data defining a machine learnable dynamics model which includes a machine learnable Lyapunov function;
• and
• a processor subsystem configured to learn the dynamics model based on time-sequential pairs of states so as to learn to infer a future state of the physical system and/or its environment based on the current state, wherein the learning is constrained to provide a globally stable modelling of dynamics of the physical system by jointly learning the dynamics model and the Lyapunov function so that values of the learned Lyapunov function decrease along all trajectories of states inferred by the learned dynamics model;
• wherein the machine learnable Lyapunov function is represented at least in part by an input-convex neural network.

A computer-implemented method for training a dynamics model to learn dynamics of a physical system by learning to infer a future state of the physical system and/or its environment based on a current state of the physical system and/or its environment, the method comprising the following steps:

• accessing training data representing a time-series of states of the physical system and/or its environment, and model data defining a machine learnable dynamics model which includes a machine learnable Lyapunov function;
• learning the dynamics model based on time-sequential pairs of states so as to learn to infer a future state of the physical system and/or its environment based on the current state, wherein the learning includes:
• constraining the learning 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 along all trajectories of states inferred by the learned dynamics model;
• wherein the machine learnable Lyapunov function is represented at least in part by an input-convex neural network.

A computer-implemented method for controlling or monitoring a physical system using a machine learned modelling of dynamics of the physical system, the method comprising the following steps:

• accessing:
• sensor data representing an observation of a current state of the physical system;
• and
• model data defining a machine learned dynamics model which includes a machine learnable Lyapunov function, wherein the dynamics model is learned to infer a future state of the physical system and/or its environment based on the current state, wherein the learning of the dynamics model has been constrained to provide a globally stable modelling of the dynamics of the physical system by the dynamics model and the Lyapunov function having been jointly learned so that values of the learned Lyapunov function decrease along all trajectories of states inferred by the learned dynamics model;
• inferring the future state of the physical system based on the observation of the current state of the physical system as obtained from the sensor data;
• and
• using an output interface to an output device which is used in the control or monitoring of the physical system, to provide output data to the output device to enable the control or monitoring of the physical system based on the inferred future state,
• wherein the machine learnable Lyapunov function is represented at least in part by an input-convex neural network.

A non-transitory computer-readable medium on which is stored data representing instructions for training a dynamics model to learn dynamics of a physical system by learning to infer a future state of the physical system and/or its environment based on a current state of the physical system and/or its environment, the instructions, when executed by a processor system, causing the processor system to perform the following steps:

• accessing training data representing a time-series of states of the physical system and/or its environment, and model data defining a machine learnable dynamics model which includes a machine learnable Lyapunov function;
• learning the dynamics model based on time-sequential pairs of states so as to learn to infer a future state of the physical system and/or its environment based on the current state, wherein the learning includes:
• constraining the learning 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 along all trajectories of states inferred by the learned dynamics model;
• wherein the machine learnable Lyapunov function is represented at least in part by an input-convex neural network.

A control or monitoring system for controlling or monitoring a physical system using a machine learned modelling of dynamics of the physical system, the control or monitoring system comprising:

• an input interface for accessing:
• sensor data representing an observation of a current state of the physical system;
• and
• model data defining a machine learned dynamics model which includes a machine learnable Lyapunov function, wherein the dynamics model is learned to infer a future state of the physical system and/or its environment based on the current state, wherein the learning of the dynamics model has been constrained to provide a globally stable modelling of dynamics of the physical system by the dynamics model and the Lyapunov function having been jointly learned so that values of the learned Lyapunov function decrease along all trajectories of states inferred by the learned dynamics model;
• an output interface to an output device which is used in the control or monitoring of the physical system;
• and
• a processor subsystem configured to:
• infer the future state of the physical system based on the observation of the current state of the physical system as obtained from the sensor data;
• and
• using the output interface, provide output data to the output device to enable the control or monitoring of the physical system based on the inferred future state;
• wherein the machine learnable Lyapunov function is represented at least in part by an input-convex neural network.