Tensor-networks for High-order Polynomial Approximation: A Many-body Physics Perspective

TL;DR

This paper explores high-order polynomial approximation through tensor networks from a many-body physics perspective, highlighting entanglement entropy as a measure of model capacity and demonstrating advantages in nonlinear dynamics modeling.

Contribution

It introduces a novel connection between quantum information concepts and functional approximation, applying tensor networks to high-order polynomial problems.

Findings

Tensor networks effectively model high-order nonlinear dynamics.

Entanglement entropy correlates with model capacity and complexity.

Promising advantages over traditional methods in specific applications.

Abstract

We analyze the problem of high-order polynomial approximation from a many-body physics perspective, and demonstrate the descriptive power of entanglement entropy in capturing model capacity and task complexity. Instantiated with a high-order nonlinear dynamics modeling problem, tensor-network models are investigated and exhibit promising modeling advantages. This novel perspective establish a connection between quantum information and functional approximation, which worth further exploration in future research.