## UC Berkeley / Lawrence Berkeley Laboratory

#### Coordinate-adaptive tensor methods for PDEs

**Alec Dektor, LBNL**

Recently there has been a growing interest in efficient numerical algorithms based on tensor networks and low-rank techniques to approximate high-dimensional functions and solutions to PDEs. We present two new tensor approximation algorithms that compute coordinate systems in which the tensor of interest is low-rank. The first algorithm relies on a non-convex relaxation of the rank minimization problem and identifies a quasi-optimal low-rank coordinate system. The second algorithm is based on a sequence of time-dependent convex optimization problems and identifies an optimal time-dependent coordinate system for controlling tensor rank during time integration of PDEs.