Goal-Oriented Low-Rank Tensor Decompositions for Numerical Simulation Data

TL;DR

This paper presents a novel low-rank tensor decomposition method for high-dimensional simulation data that preserves quantities of interest and invariants, enabling more accurate analysis without full data access.

Contribution

It introduces a new low-dimensional model based on low-rank tensor decompositions that incorporates conservation principles directly into the dimensionality reduction process.

Findings

Effective in combustion and plasma physics simulations

Preserves invariants and quantities of interest

Improves analysis accuracy without full data access

Abstract

We introduce a new low-dimensional model of high-dimensional numerical simulation data based on low-rank tensor decompositions. Our new model aims to minimize differences between the model data and simulation data as well as functions of the model data and functions of the simulation data. This novel approach to dimensionality reduction of simulation data provides a means of directly incorporating quantities of interests and invariants associated with conservation principles associated with the simulation data into the low-dimensional model, thus enabling more accurate analysis of the simulation without requiring access to the full set of high-dimensional data. Computational results of applying this approach to two standard low-rank tensor decompositions of data arising from simulation of combustion and plasma physics are presented.