Maximum Entropy Snapshot Sampling for Reduced Basis Generation

TL;DR

This paper introduces a novel maximum entropy snapshot sampling method for reduced basis generation in dynamical systems, which efficiently selects essential snapshots based on dynamical stability, reducing computational effort and simplifying implementation.

Contribution

It develops a new basis generation framework using maximum entropy sampling that directly reduces snapshot numbers and is mathematically grounded, efficient, and easy to implement.

Findings

Supports reduced basis generation with fewer snapshots

Mathematically rigorous and computationally efficient

Automated and easy to implement

Abstract

Snapshot back-ended reduced basis methods for dynamical systems commonly rely on the singular value decomposition of a matrix whose columns are high-fidelity solution vectors. An alternative basis generation framework is developed here. The advocated maximum entropy snapshot sampling (MESS) identifies the snapshots that encode essential information regarding the system's evolution, by exploiting quantities that are suitable for quantifying a notion of dynamical stability. The maximum entropy snapshot sampling enables a direct reduction of the number of snapshots. A reduced basis is then obtained with any orthonormalization process on the resulting reduced sample of snapshots. The maximum entropy sampling strategy is supported by rigid mathematical foundations, it is computationally efficient, and it is inherently automated and easy to implement.