Computational Math and Statistics Seminar by Alexei Sorokin: Scientific Machine Learning for Exact Recovery of Nonlinear PDEs
Speaker: , ÐÓ°ÉÂÛ̳
Title: Scientific Machine Learning for Exact Recovery of Nonlinear PDEs
Abstract:
Nonlinear partial differential equations (PDEs) with random coefficients arise in a number of scientific domains including fluid mechanics, geophysics, and medical imaging among others. Existing scientific machine learning (sciML) methods for solving nonlinear PDEs incur an accuracy ceiling, even when scaling to larger models. This talk will present CHONKNORIS, a novel sciML methods capable of machine precision recovery of nonlinear PDEs which is enabled through a close coupling with traditional numerical solvers. Specifically, CHONKNORIS is a learning-to-learn method which predicts the approximate Hessian operator in a Levenberg-Marquardt algorithm. We will cover applications to forward problems, foundation modeling, and an inverse problem from seismic imaging.
Computational Mathematics