In this talk we present a neural network-based architecture for modeling time-evolution governed by unknown partial differential equations. We propose a Pade approximation based exponential neural operator scheme for efficiently learning the map between a given initial condition and activities at a later time. A multiwavelet basis is used for space discretization. By explicitly embedding the exponential operators in the model, we reduce the training parameters and make it more data-efficient which is essential in dealing with scarce real-world datasets. We perform experiments on non-linear systems such as Korteweg-de Vries (KdV) and Kuramoto–Sivashinsky (KS) equations to show that the proposed approach achieves the best performance and at the same time is data-efficient. We also show that urgent real-world problems like Epidemic forecasting (for example, COVID-19) can be formulated as a 2D time-varying operator problem. Time permitting, we discuss a second problem, namely of normalizing flows using vector quantization auto encoders (VQAE) and conformal mapping neural networks.

This talk is based on a joint work with Gaurav Gupta, Xiong Ye Xiao, Paul Bogdan (all from USC), accepted at ICLR 2022.