Experience suggests that uncertainties often play an important role in quantifying the performance of complex systems. Therefore, uncertainty needs to be treated as a core element in the modeling, simulation, and optimization of complex systems. In this talk, I will first present a review of the novel UQ techniques I developed to conduct stochastic simulations for very large-scale complex systems.

A robust data-driven discovery of physical laws with confidence will be introduced. Discovering governing physical laws from noisy data is a grand challenge in many science and engineering research areas. I will present a new Bayesian approach to data-driven discovery of ODEs and PDEs. The new approach will be demonstrated through a wide range of problems, including shallow water equations and Navier–Stokes equations. In addition, solving PDEs and predicting material fracture in a fundamentally different way will be discussed. I will present a new paradigm in solving linear and nonlinear PDEs on varied domains without the use of the classical numerical discretization. Instead, we infer the solution of PDEs using a convolutional neural network with quantified uncertainty. The proposed neural network can predict the solution and its uncertainty simultaneously on-the-fly. Finally, I will introduce a new convolutional neural network named Peri-Net we developed to predict and analyze fracture patterns on a disk in real time. I will present and validate the results using the molecular dynamic collision simulations.