ABSTRACT

Quantifying uncertainty of numerical simulation due to the uncertainties in physical parameters has been of great interest due to its relevance to many engineering applications. While most of the uncertainty quantification methods assume prior knowledge on the physical equations or the probability distribution of the uncertainties, detailed physics models are not readily available in many real-world problems. In this study, we propose a deep learning approach for data-driven simulations of a dynamical system with random parameters without prior knowledge on the dynamical system or the random parameters. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of the random parameters from a training dataset, which consists of an ensemble of trajectories of randomly sampled parameters, and to perform a stochastic simulation by making an inference on a short-length sequence of a new trajectory. The learning task is formulated as a variational inference problem, in which an approximate posterior distribution makes an inference on the trajectory and a recurrent neural network makes a prediction by using the outcome of the inference. In the numerical experiments, it is shown that the proposed variational inference model makes a much more accurate simulation compared to the standard recurrent neural networks. It is found that the proposed deep learning model is capable of correctly identifying the dimensions of the random parameters and learning a representation of complex time series data.

BRIEF ACADEMIC/EMPLOYMENT HISTORY:

MOST RECENT RESEARCH INTERESTS:

Deep learning, Mathematical modeling, Statistical modeling, Time series analysis