Reduced order modeling and control of high dimensional physical systems using neural network model

Abstract

A system and method are provided for training neural network for controlling operation of system having non-linear dynamics represented by partial differential equations (PDEs). The method comprises collecting digital representation of time series data indicative of instances of function space of the system and measurements of state of the operation of the system. Collocation points corresponding to solutions of the PDE are generated. The neural network is trained using training data including the collected time series data and the collocation points to train parameters of non-linear operator. The neural network has autoencoder architecture including encoder to encode each instance of the training data into latent space, the non-linear operator to propagate the encoded instances into the latent space with transformation determined by parameters of the non-linear operator, and decoder to decode the transformed encoded instances of the training data to minimize a hybrid loss function.