CCE Seminar: Deep Neural Networks for Inverse Modeling/Eric Darve
November 21, 2019, 12:00 PM
Professor of Mechanical Engineering and Computational Mathematics
Machine Learning has had tremendous success in various fields of computer science, including image and speech recognition, natural language processing, and reinforcement learning. We review recent efforts to apply some of these methods to computational engineering problems, including inverse modeling and stochastic inversing. We discuss numerical approximation properties of deep neural networks and compare them with spectral approximation schemes. Some of the applications focus on physics-informed machine learning, where we combine deep neural networks with knowledge of physical laws in the form of partial differential equations. This approach increases the accuracy of the predictions and reduces the need for extensive training data. We discuss applications to stochastic problems where the unknown is the probability density function of some random variable, which we learn from indirect observations.
Professor Darve received his Ph.D. in Applied Mathematics at the Jacques-Louis Lions Laboratory, in the Pierre et Marie Curie University, Paris, France. His advisor was Prof. Olivier Pironneau, and his Ph.D. thesis was entitled “Fast Multipole Methods for Integral Equations in Acoustics and Electromagnetics.” He was previously a student at the Ecole Normale Supérieure, rue d’Ulm, Paris, in Mathematics and Computer Science. Prof. Darve became a postdoctoral scholar with Profs. Moin and Pohorille at Stanford and NASA Ames in 1999 and joined the faculty at Stanford University in 2001. He is a member of the faculty in the Mechanical Engineering Department and the Institute for Computational and Mathematical Engineering. His current research interests include numerical linear algebra, fast linear solvers, parallel and high-performance computing, and machine learning.
Deep Neural Networks for Inverse Modeling
Eric Darve, Professor of Mechanical Engineering and Computational Mathematics