Poster

Solving high-dimensional parabolic PDEs using the tensor train format

Lorenz Richter · Leon Sallandt · Nikolas Nüsken

Keywords: [ Monte Carlo Methods ]

award Outstanding Paper Honorable Mention
[ Abstract ]
[ Paper ] [ Visit Poster at Spot D3 in Virtual World ]
Thu 22 Jul 9 p.m. PDT — 11 p.m. PDT
 
Oral presentation: Probabilistic Methods 5
Thu 22 Jul 6 p.m. PDT — 7 p.m. PDT

Abstract:

High-dimensional partial differential equations (PDEs) are ubiquitous in economics, science and engineering. However, their numerical treatment poses formidable challenges since traditional grid-based methods tend to be frustrated by the curse of dimensionality. In this paper, we argue that tensor trains provide an appealing approximation framework for parabolic PDEs: the combination of reformulations in terms of backward stochastic differential equations and regression-type methods in the tensor format holds the promise of leveraging latent low-rank structures enabling both compression and efficient computation. Following this paradigm, we develop novel iterative schemes, involving either explicit and fast or implicit and accurate updates. We demonstrate in a number of examples that our methods achieve a favorable trade-off between accuracy and computational efficiency in comparison with state-of-the-art neural network based approaches.

Chat is not available.