Title: Two Tales, One Resolution: Physics-Informed Test Time Scaling and Precondition

Speaker: Yiping Lu, Northwestern University

Abstract: In this talk, I will introduce a novel framework for physics-informed debiasing of machine learning estimators, which we call Simulation-Calibrated Scientific Machine Learning (SCaSML). This approach leverages the structure of physical models to achieve two key objectives:

Unbiased Predictions: It produces unbiased predictions even when the underlying machine learning predictor is biased.

Overcoming Dimensionality Challenges: It mitigates the curse of dimensionality that often affects high-dimensional estimators.

The SCaSML paradigm integrates a (potentially) biased machine learning algorithm with a de-biasing procedure that is rigorously designed using numerical analysis and stochastic simulation. Our methodology aligns with recent advances in inference-time computation--similar to those seen in the large language model literature--demonstrating that additional computation can enhance ML estimates. Furthermore, we establish a surprising equivalence between our framework and another research direction that utilizes approximate (linearized) solvers to precondition iterative methods. This connection not only bridges two distinct areas of study but also offers new insights into improving estimation accuracy in complex, high-dimensional (PDE) settings.

Zoom: https://northwestern.zoom.us/j/94570889326

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