High-Dimensional PDEs, Tensor Networks, and Convex Optimization

Overview

Explore innovative computational approaches for solving high-dimensional partial differential equations (PDEs) in this 53-minute lecture presented by Yuehaw Khoo from the University of Chicago at IPAM's Tensor Networks Workshop. Delve into the application of tensor networks and convex relaxations to construct inner and outer approximations of PDE solutions using low-order statistics. Discover how these techniques effectively combat the curse of dimensionality, offering new perspectives on tackling complex mathematical challenges in high-dimensional spaces.

Syllabus

Yuehaw Khoo - High-dimensional PDEs, tensor-network, and convex optimization - IPAM at UCLA

Taught by

Institute for Pure & Applied Mathematics (IPAM)

Reviews

Start your review of High-Dimensional PDEs, Tensor Networks, and Convex Optimization

Taught by

New Approaches in Simulation of Transition Paths - IPAM at UCLA

Tensor Networks vs. PCA and PLS for High Dimensional Medical Datasets

Solving High-Dimensional Partial Differential Equations Using Deep Learning

Deep Learning and Computations of PDEs by Siddhartha Mishra

Tensor Networks for High-Dimensional Integration and Optimization

Solving High-Dimensional Optimal Control Problems with Empirical Tensor Train Approximation

Never Stop Learning.