Abstract: A method and system for modelling industrial processes, including closed loop feedback processes. The system includes a sensor for measuring an input for the industrial process; and a processor configured to receive a measurement of the input from the sensor at an input time. The processor is also configured to implement a hybrid neural network model to output a derivative of the output at the input time, wherein the neural network model incorporates at least one neural network block and a first-principle block incorporating dynamic model having an ordinary differential equation defining the rate of change over time of the output as a function of the or each associated input; to input the derivative to an ordinary differential equation solver to predict the output at a subsequent time; and to output the prediction of the output at the subsequent time using the measured input.

Abstract: A method and system for modelling industrial processes, including closed loop feedback processes. The system includes a sensor for measuring an input for the industrial process; and a processor configured to receive a measurement of the input from the sensor at an input time. The processor is also configured to implement a hybrid neural network model to output a derivative of the output at the input time, wherein the neural network model incorporates at least one neural network block and a first-principle block incorporating dynamic model having an ordinary differential equation defining the rate of change over time of the output as a function of the or each associated input; to input the derivative to an ordinary differential equation solver to predict the output at a subsequent time; and to output the prediction of the output at the subsequent time using the measured input.