DDPS | “Multi-fidelity linear regression for scientific machine learning from scarce data”

DDPS Talk date: August 2nd, 2024
Speaker: Elizabeth Qian (Georgia Tech, https://www.elizabethqian.com/)
Description: Machine learning (ML) methods have garnered significant interest as potential methods for learning surrogate models for complex engineering systems for which traditional simulation is expensive. However, in many scientific and engineering settings, training data are scarce due to the cost of generating data from traditional high-fidelity simulations. ML models trained on scarce data have high variance and are sensitive to vagaries of the training data set. We propose a new multifidelity training approach for scientific machine learning that exploits the scientific context where data of varying fidelities and costs are available; for example high-fidelity data may be generated by an expensive fully resolved physics simulation whereas lower-fidelity data may arise from a cheaper model based on simplifying assumptions. We use the multifidelity data to define new multifidelity control variate estimators for the unknown parameters of linear regression models, and provide theoretical analyses that guarantee accuracy and improved robustness to small training budgets. Numerical results show that multifidelity learned models achieve order-of-magnitude lower expected error than standard training approaches when high-fidelity data are scarce.

Bio: Elizabeth Qian is an Assistant Professor at Georgia Tech jointly appointed in the School of Aerospace Engineering and the School of Computational Science and Engineering. Her interdisciplinary research develops new computational methods to enable engineering design and decision-making for complex systems, with special expertise in model reduction, scientific machine learning, and multifidelity methods. Recent awards include a 2024 Air Force Young Investigator award and a 2023 Hans Fischer visiting fellowship at the Technical University of Munich. Prior to joining Georgia Tech, she was a von Karman Instructor at Caltech in the Department of Computing and Mathematical Sciences. She earned her SB, SM, and PhD degrees from MIT.

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IM release number is: LLNL-VIDEO-868128