Predicting a state of a computer-controlled entity

A computer-implemented method for training a machine learnable model for use in controlling or monitoring a computer-controlled entity in an environment, wherein the machine learnable model is trained to predict a future state of the computer-controlled entity or the environment based on sensor data which is indicative of a current state of the computer-controlled entity or the environment, the machine learnable model including a first neural network for approximating a drift component of a stochastic differential equation and a second neural network for approximating a diffusion component of the stochastic differential equation, the method comprising:

• obtaining a set of N observations, each observation comprising a time step and a variable indicating a state of the computer-controlled entity or the environment at the time step;
• obtaining a discretization of the stochastic differential equation;
• obtaining a time-evolving mean function and a time-evolving covariance function based on the discretization of the stochastic differential equation;
• obtaining the first neural network, the second neural network and a set of weights for each of the first neural network and the second neural network;
• determining an optimized set of weights for each of the first neural network and the second neural network using maximum likelihood estimation to maximize a probability of the set of N observations given the set of weights,
• wherein the maximum likelihood estimation includes iteratively performing:
• approximating a probability distribution of the variable corresponding to the state of the computer-controlled entity or the environment at each time step n of the set of N observations;
• for each time step n:
• estimating a mean for a time step n+1 using a mean for the time step n;
• estimating a covariance for the time step n+1 using the mean for the time step n+1 and a covariance estimated for the time step n;
• calculating a transition probability distribution of the variable corresponding to the state at the time step n+1 based on the estimated mean for the time step n+1 and the estimated covariance for the time step n+1;
• and
• determining a probability of the variable corresponding to the state at the time step n+1 from the set of N observations according to the calculated transition probability distribution, wherein the calculated transition probability distribution is configured to be sampled to obtain a prediction for the state of the computer-controlled entity at the time step n+1, wherein an uncertainty of the prediction is determined based on the covariance for the time step n+1;
• providing a controller that is configured to generate control data based on the prediction for the state of the computer-controlled entity at the time step n+1 and the uncertainty, wherein the computer-controlled entity includes a vehicle, a robot, a drone, a power tool, or a manufacturing machine;
• and
• providing an actuator of the vehicle, the robot, the drone, the power tool, or the manufacturing machine that is configured to control, based on the control data, a physical action of the vehicle, the robot, the drone, the power tool, or the manufacturing machine.

A non-transitory computer-readable medium on which is stored data representing instructions for enabling control or monitoring of a computer-controlled entity operating in an environment by predicting a future state of the computer-controlled entity or the environment using sensor data which is indicative of a current state of the computer-controlled entity or the environment, the instruction, when executed by a computer, causing the computer to perform:

• receiving the sensor data indicative of the current state of the computer-controlled entity or the environment;
• accessing a first trained neural network for approximating a drift component of a stochastic differential equation and a second trained neural network for approximating a diffusion component of the stochastic differential equation;
• discretizing the stochastic differential equation into time steps, wherein the discretized stochastic differential equation defines a second state of the computer-controlled entity or the environment as being dependent on the current state of the computer-controlled entity or the environment and a time interval between a time step k of the current state and a time step k+1 of the second state;
• obtaining a time-evolving mean function and a time-evolving covariance function based on the discretization, wherein at any time t, a state of the computer-controlled entity or the environment is expressed as a distribution defined by a mean at the time t and a covariance at the time t;
• obtaining a probability distribution of the current state of the computer-controlled entity or the environment, the probability distribution being defined by a current mean and a current covariance;
• determining a transition probability distribution of the second state of the computer-controlled entity or the environment by:
• estimating a mean for the second state by expanding the time-evolving mean function, using the current mean,
• estimating a covariance for the second state using the estimated mean for the second state and the current covariance;
• sampling from the determined transition probability distribution to obtain a prediction for the second state, wherein the computer-controlled entity includes a vehicle, a robot, a drone, a power tool, or a manufacturing machine, wherein an uncertainty of the prediction for the second state is determined based on the covariance for the second state;
• generating control data based on the prediction for the second state and the uncertainty;
• and
• controlling a physical action of the vehicle, the robot, the drone, the power tool, or the manufacturing machine by supplying the control data to an actuator of the vehicle, the robot, the drone, the power tool, or the manufacturing machine.

A prediction system for enabling control or monitoring of a computer-controlled entity operating in an environment by predicting a future state of the computer-controlled entity or the environment using sensor data which is indicative of a current state of the computer-controlled entity or the environment, the prediction system comprising:

• a data interface configured to:
• receive the sensor data indicative of the current state of the computer-controlled entity or the environment;
• and
• access a first trained neural network for approximating a drift component of a stochastic differential equation and a second trained neural network for approximating a diffusion component of the stochastic differential equation;
• a processor subsystem configured to:
• discretize the stochastic differential equation into time steps, wherein the discretized stochastic differential equation defines a second state of the computer controlled entity or the environment as being dependent on the current state of the computer-controlled entity or the environment and a time interval between a time step k of the current state and a time step k+1 of the second state;
• obtain a time-evolving mean function and a time-evolving covariance function based on the discretization, wherein at any time t, a state of the computer-controlled entity or the environment is expressed as a distribution defined by a mean at the time t and a covariance at the time t;
• obtain a probability distribution of the current state of the computer-controlled entity or the environment, the probability distribution being defined by a current mean and a current covariance;
• determine a transition probability distribution of the second state of the computer-controlled entity or the environment by:
• estimating a mean for the second state by expanding the time-evolving mean function, using the current mean,
• estimating a covariance for the second state using the estimated mean for the second state and the current covariance;
• sampling from the determined transition probability distribution to obtain a prediction for the second state, wherein the computer-controlled entity includes a vehicle, a robot, a drone, a power tool, or a manufacturing machine, wherein an uncertainty of the prediction for the second state is determined based on the covariance for the second state;
• generating control data based on the prediction for the second state and the uncertainty;
• and
• controlling a physical action of the vehicle, the robot, the drone, the power tool, or the manufacturing machine by supplying the control data to an actuator of the vehicle, the robot, the drone, the power tool, or the manufacturing machine.

A training system for training a machine-learnable model to predict a future state of a computer-controlled entity or an environment, wherein the machine-learnable model is trained to predict a future state of the computer-controlled entity or the environment based on sensor data which is indicative of a current state of the computer-controlled entity or the environment, the machine-learnable model including a first neural network for approximating a drift component of a stochastic differential equation and a second neural network for approximating a diffusion component of the stochastic differential equation, the training system comprising:

• a data interface configured to:
• obtain a set of N observations, each observation comprising a time step and a variable indicating a state of the computer-controlled entity or the environment at the time step;
• obtain a set of weights for each of the first neural network and the second neural network;
• and
• a processor subsystem configured to:
• obtain a discretization of the stochastic differential equation;
• obtain a time-evolving mean function and a time-evolving covariance function based on the discretization of the stochastic differential equation;
• determine an optimal set of weights for each of the first neural network and the second neural network using maximum likelihood estimation to maximize a probability of the set of N observations given the set of weights,
• wherein the maximum likelihood estimation includes iteratively performing:
• defining a probability distribution of the variable corresponding to the state of the computer-controlled entity or the environment at each time step n of the set of N observations;
• for each time step n:
• estimating a mean for a time step n+1 using a mean for the time step n;
• estimating a covariance for the time step n+1 using the mean for the time step n+1 and a covariance estimated for the time step n;
• calculating a transition probability distribution of the variable corresponding to the state at the time step n+1 based on the estimated mean for the time step n+1 and the estimated covariance for the time step n+1;
• and
• determining a probability of the variable corresponding to the state at the time step n+1 from the set of N observations according to the calculated transition probability distribution,
• wherein the calculated transition probability distribution is configured to be sampled to obtain a prediction for the state of the computer-controlled entity at the time step n+1 in order for control data to be generated based on the prediction for the state of the computer-controlled entity at the time step n+1, wherein an uncertainty of the prediction is determined based on the covariance for the time step n+1, and wherein the control data is further based on the uncertainty,
• wherein the computer-controlled entity includes a vehicle, a robot, a drone, a power tool, or a manufacturing machine, and wherein an actuator of the vehicle, the robot, the drone, the power tool, or the manufacturing machine is configured to control, based on the control data, a physical action of the vehicle, the robot, the drone, the power tool, or the manufacturing machine.