Abstract: This talk aims to close the gap by developing new theories and scalable numerical algorithms for complex dynamical systems that can be realistically predicted and validated. We are creating new technologies that can be translated into more secure and reliable new trustworthy artificial intelligence (AI) systems that can be deployed for real-time complex dynamical system prediction, surveillance, and defense applications to improve the stability and efficiency of complex dynamical systems and national security of the United States. We will present a novel neural homogenization-based physics-informed neural network (NN) for multiscale problems. We will also introduce new NNs that learn functionals and nonlinear operators from functions with simultaneous uncertainty estimates. In particular, we present a probabilistic neural operator network training procedure for solving partial differential equations with inhomogeneous boundary conditions. Using a light-weight extension of deep operator network (DeepONet) architecture, the trained networks are designed to provide rapid predictions along with simultaneous uncertainty estimates to help identify potential inaccuracies in the network predictions. DeepONet consists of a NN for encoding the discrete input function space (branch net) and another NN for encoding the domain of the output functions (trunk net). In particular, the predictive uncertainty of the network is calibrated to anticipate network errors by implementing a loss function that interprets the network prediction as a probability distribution as opposed to a single-point estimate. The proposed technique is also capable of solving problems on irregular, non-rectangular domains, and a series of experiments are presented to evaluate the network accuracy, as well as the quality of the predictive uncertainty estimates. We demonstrate that the novel probabilistic DeepONet can learn various explicit operators with predictive uncertainties.
Speaker’s Bio: Guang Lin is a Full Professor in the School of Mechanical Engineering and Department of Mathematics at Purdue University. Prof. Guang Lin is the Director of Data Science Consulting Service which performs cutting-edge research on data science and provides hands-on consulting support for data analysis and business analytics. He is also the Chair of the Initiative for Data Science and Engineering Applications at the College of Engineering. Lin received his Ph.D. from Brown University in 2007 and worked as a Research Scientist at the Department of Energy Pacific Northwest National Laboratory before joining Purdue in 2014. Prof. Lin has received various awards, such as the National Science Foundation CAREER Award, Mid-Career Sigma Xi Award, University Faculty Scholar, Mathematical Biosciences Institute Early Career Award, and Ronald L. Brodzinski Award for Early Career Exception Achievement.
Last Updated: December 9, 2022 - 3:16 pm