OAC Core: Toward a Rigorous and Reliable Scientific Deep Learning Framework for Forward, Inverse, and UQ Problems

University Of Texas At Austin, Austin TX

Investigators

Abstract

While Deep Learning, a subset of machine learning, has proved to be state-of-the-art approach in many fields of computer sciences, it is still in its infancy in computational science and engineering communities. Unlike computational applied math methods in which solution accuracy and reliability are guaranteed, deep learning---in its present state---is often far from providing accurate predictions for engineering and science applications. For machine learning methods that serve as a basis for design,control, discovery, and decision-making, their solutions must be equipped with the degree of confidence. However, quantifying the uncertainty in machine learning solution remains challenging and an open problem. Thus, there is a critical need to develop reliable, robust, and model-aware deep learning methods to tackle complex, natural, engineered, and science systems in order to continue the pace of scientific discoveries and to promote the progress of science. This project is of immediate practical utility in both machine learning and computational engineering and sciences communities. It aims at solving real-world data-driven problems, which can lead to original scientific discoveries and promote the progress of science. The project open-sourced software developed on top of TensorFlow, Jax, and FEniCS/FireDrake is accessible to a diverse community of computer and computational science and engineering researchers, scientists, faculty, and students. Proposed research will be directly incorporated into the Introduction to machine learning course offered by the PI annually at the University of Texas at Austin. Students from the project contributes to the pipeline of advanced scientists to maintain US competitiveness and leadership in sciences and technologies. The long-term goal of the PI's research program is to develop scalable uncertainty quantification, optimization, mathematical, and parallel computational methods for scientific machine learning. The objective of this project is to: 1) equip deep learning with the underlying mathematical models to improve generalization error, especially for low data regime, 2) achieve comparable accuracy with traditional forward/inverse computational methods while taking a fraction of the cost; and 3) quantify the uncertainty in deep learning for forward/inverse solutions. To that end, the project develops 1) rigorous adaptive architecture design methods, 2) interpretable model-constrained methods to encode mathematical models into deep neural networks for solving forward and inverse problems and science and engineering, and 3) model-constrained statistical approaches for quantifying the uncertainty in neural network predictions. Practical forward and inverse seismic wave propagation---a problem in NSF portfolio---is chosen as the demanding testbed for the developments. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.