A Dataset of Nonlinear Equations for Subdivision

TL;DR

This paper introduces the largest labeled dataset for solving zero-dimensional square nonlinear systems using subdivision methods, demonstrating its utility through benchmarking and classification tasks.

Contribution

It provides a new, extensive dataset for nonlinear system solving and showcases its application in benchmarking and learning-based classification.

Findings

The dataset enables effective benchmarking of solvers.

It supports learning to classify real roots of nonlinear parametric systems.

Demonstrates the dataset's value through practical applications.

Abstract

In this paper, we report on the largest labelled dataset constructed so far for solving zero-dimensional square nonlinear systems with subdivision-based methods. A brief, non-exhaustive survey with emphasis on the literature from the past two decades is also provided to accompany with the dataset. The value of the dataset has been demonstrated through benchmarking several solvers as well as being used for learning to classify the real roots of nonlinear parametric systems.