Paris Perdikaris with Georgios Kissas & Jacob Seidman: Supervised learning in function spaces
Abstract: While the great success of modern deep learning lies in its ability to approximate maps between finite-dimensional vector spaces, many tasks in science and engineering involve continuous measurements that are functional in nature. For example, in climate modeling one might wish to predict the pressure field over the earth from measurements of the surface air temperature field. The goal is then to learn an operator, between the space of temperature functions to the space of pressure functions. In recent years, operator learning techniques have emerged as a powerful tool for supervised learning in infinite-dimensional function spaces. In this practicum we will provide an introduction to this topic, discuss the formulation of existing methods (DeepONets and Neural Operators), and demonstrate how fundamental building blocks such as multi-layer perceptrons, convolutional networks and attention-based architectures can be used to construct deep learning models that can handle functional data. Our presentation will be accompanied by hands-on tutorials to elucidate key implementation aspects, as well as applications in scientific computing, climate modeling and optimal control.
Bios:
Paris Perdikaris is an Assistant Professor in the Department of Mechanical Engineering and Applied Mechanics at the University of Pennsylvania. His current research interests include physics-informed machine learning, uncertainty quantification, and engineering design optimization.
Georgios Kissas is a fourth year doctoral candidate in the department of Mechanical Engineering and Applied Mechanics at the University of Pennsylvania. His work focuses on developing methods for operator learning, physics-informed deep learning and data-driven medical diagnostics.
Jacob Seidman is a sixth year PhD student at the University of Pennsylvania in the program for Applied Mathematics and Computational Science. His research interests include optimization, optimal control, and machine learning for functional data.