Machine Learning in PDE - Discovering New, Unstable Solutions

Explore the innovative intersection of machine learning and partial differential equations in this 55-minute conference talk that demonstrates how modern ML techniques can be combined with traditional mathematical methods to discover new solutions of PDEs with remarkably low numerical error. Learn about groundbreaking approaches for identifying unstable solutions that were previously difficult to detect, and discover how numerical approximate solutions can be transformed into rigorous mathematical proofs through computer-assisted methods. Examine applications that lead to singularity formation and the existence of special solutions such as traveling waves, with particular focus on fluid mechanics equations including Euler and Navier-Stokes equations. Understand how these methodologies can be adapted and applied to other types of partial differential equations beyond fluid mechanics, opening new avenues for mathematical discovery and computational analysis.