Youngjoon Hong : Machine learning in numerical PDEs

Posted by David Nicholls , part of the Analysis and Applied Mathematics Seminar.

At

July 6, 2022, 3 p.m.

In

712 SEO

Abstract

As artificial intelligence makes progress, deep neural nets are being applied to increasingly complex problem setups. In response to the emerging difficulties of these new setups, deep learning research explores new modeling tools to enhance the predictive power of neural nets. Differential equations are among the new tools that are being incorporated into deep neural net models in various ways. In particular, neural networks and deep-learning have shown promise in speeding up scientific simulations. For solving PDEs, the goal is often to produce a model which can be used to quickly generate sample data for statistical analysis; this is often applied in the inverse problem of trying to determine a system's initial conditions, given later observations. The result is now an exciting new research field known as scientific machine learning, where techniques such as deep neural networks and statistical learning are applied to classical problems of applied mathematics. In this tutorial, our intention is to provide an accessible introduction to recent developments in the field of numerical solution of linear and nonlinear partial differential equations using techniques from machine learning and artificial intelligence.