Title: Data Driven Modeling of Unknown Systems with Deep Neural Networks
Speaker: Dongbin Xiu
Abstract:
We present a framework of predictive modeling of unknown system from measurement
data. The method is designed to discover/approximate the unknown evolution operator
behind the data. Deep neural network (DNN) is employed to construct such an
approximation. Once an accurate DNN model for evolution operator is constructed, it
serves as a predictive model for the unknown system and enables us to conduct system
analysis. We demonstrate that residual network (ResNet) is particularly suitable for
modeling autonomous dynamical systems. Extensions to other types of systems will be
discussed, including non-autonomous systems, systems with uncertain parameters, and
more importantly, systems with missing variables, as well as partial differential equations
(PDEs).
