Speaker: Yiping Lu, Courant Institute

Title: Simulation-Calibrated Scientific Machine Learning  

Abstract: Machine learning (ML) has achieved great success in a variety of applications suggesting a new way to build flexible, universal, and efficient approximators for complex high-dimensional data.  These successes have inspired many researchers to apply ML to other scientific applications such as industrial engineering, scientific computing, and operational research, where similar challenges often occur. However, the luminous success of ML is overshadowed by persistent concerns that the mathematical theory of large-scale machine learning, especially deep learning, is still lacking and the trained ML predictor is always biased. In this talk, I’ll introduce a novel framework of (S)imulation-(Ca)librated (S)cientific (M)achine (L)earning (SCaSML), which can leverage the structure of physical models to achieve the following goals: 1) make unbiased predictions even based on biased machine learning predictors; 2) beat the curse of dimensionality with an estimator suffers from it. The SCASML paradigm combines a (possibly) biased machine learning algorithm with a de-biasing step design using rigorous numerical analysis and stochastic simulation. Theoretically, I’ll try to understand whether the SCaSML algorithms are optimal and what factors (e.g., smoothness, dimension, and boundness) determine the improvement of the convergence rate. Empirically, I’ll introduce different estimators that enable unbiased and trustworthy estimation for physical quantities with a biased machine learning estimator. Applications include but are not limited to estimating the moment of a function, simulating high-dimensional stochastic processes, uncertainty quantification using bootstrap methods, and randomized linear algebra.
 
Bio: Yiping Lu is an instructor at the Courant Institute of Mathematical Sciences, New York University, and an incoming tenure-track assistant professor in the department of Industrial Engineering & Management Science at Northwestern University. He received his Ph.D. degree in applied math from Stanford University in 2023 and his Bachelor’s degree in applied math from Peking University in 2019.

This talk will be offered in a hybrid format. If you wish to participate remotely, please send an email to [email protected].