Georgia Tech SCL Georgia Tech SCL Georgia Tech SCL

Title: 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: Dr.Yiping Lu is  Courant instructor at Courant Institute of Mathematical Sciences, New York University, and an incoming tenure-track assistant professor at Industrial Engineering & Management Science, Northwestern University. I received my Ph.D. degree in applied math from Stanford University in 2023 and my Bachelor’s degree in applied math from Peking University in 2019.  The long-term goal of my research is to develop a hybrid scientific research discipline that combines domain knowledge (differential equation, stochastic process, control,…), machine learning and (randomized) experiments. To this end, I’m working on an interdisciplinary research approach across probability and statistics, machine learning, numerical algorithms, control theory, signal processing/inverse problem, and operations research. Yiping was a recipient of the Conference on Parsimony and Learning (CPAL) Rising Star Award in 2024, the Rising Star in Data Science from the University of Chicago in 2022, the Stanford Interdisciplinary Graduate Fellowship and the SenseTime Scholarship in 2021 for undergraduates in AI in 2019. He also serves as an area chair/senior PC member for NeurIPS and AISTATS. Homepage: https://2prime.github.io/