CSE Distinguished Seminar | Michael Mueller

Abstract

Integrating machine learning algorithms into computational simulations of turbulent multi-physics flows has the potential to improve these simulations in every sense of the word. Three distinct use cases for machine learning within computational simulations are presented and example applications drawn from combustion, plasmas, and offshore wind. First, machine learning algorithms can be used to accelerate computational simulations by reducing redundant computations. In solving a set of governing PDEs, one often must repeatedly evaluate algebraic auxiliary relationships (e.g., equations of state, constitutive laws, models for unresolved physics, etc.). These repetitive evaluations limit the computational intensity of these auxiliary relationships and/or the number of inputs. Adaptive binary trees are leveraged to learn these auxiliary relationships ‘on-the-fly’ and reuse prior evaluations with strict error control. Second, machine learning algorithms can be used to generalize these auxiliary relationships, with an emphasis on models for unresolved physics. These adaptive binary trees enable the use of more general auxiliary relationships that might otherwise be too computationally or memory intensive. However, as the complexity increases, the binary trees can themselves become too memory intensive. One advantage of machine learning algorithms such as neural networks is their compact storage, albeit at the cost of often considerable training time. A neural adaptive binary tree approach is developed in which regions of the adaptive binary tree are periodically pruned and the constituent data used to train a shallow neural network to replace this region of the tree, substantially reducing memory requirements. Strategies have also been developed for error control. Third, machine learning algorithms can be used to develop hybridized physics-based and data-based models. Rather than an either/or paradigm, hybridization leverages a both/and paradigm. While physics-based modeling frameworks are preferred due to their explicit satisfaction of fundamental physical laws, physics-based approaches often rely on sometimes invalid assumptions with no clear pathway forward (e.g., closure modeling). In a weak sense, data-based approaches can be used to provide new insights for missing physics and physics-based model improvement. In a strong sense, a data-based model can be trained to replace the hardest-to-model terms in an otherwise physics-based framework, retaining its attractive physical features.

Bio

Michael E. Mueller is the Acting Chair and Donald R. Dixon ’69 and Elizabeth W. Dixon Professor of Mechanical and Aerospace Engineering and the Interim Director of the Princeton Institute for Computational Science and Engineering at Princeton University. Since 2020, he is also jointly appointed as a Faculty Researcher at the National Laboratory of the Rockies. He currently serves as Editor of the Proceedings of The Combustion Institute. He received a BS degree in mechanical engineering from The University of Texas at Austin in 2007, a MS degree in mechanical engineering from Stanford University in 2009, and a PhD degree in mechanical engineering from Stanford University in 2012. His research interests encompass computational modeling of multi-physics turbulent flows with applications to energy, propulsion, and the environment, including combustion, offshore wind, aerosols, and plasmas, as well as broader areas of computational and data sciences including uncertainty quantification, algorithms for heterogeneous computational architectures, and data-based modeling and ML/AI algorithms. He is a Fellow of the American Society of Mechanical Engineers and an Associate Fellow of the American Institute of Aeronautics and Astronautics. Among other awards and recognitions for his research, he has been recognized with the Hiroshi Tsuji Early Career Research Award from The Combustion Institution and the Young Investigator Program (YIP) Award from the Army Research Office. He has also received the Princeton University Graduate Mentoring Award and the School of Engineering and Applied Science Distinguished Teacher Award.