A Dataset of Nonlinear Equations for Subdivision

2026-03-28

AI Summary

This work addresses the long-standing scarcity of large-scale annotated datasets in the domain of solving zero-dimensional nonlinear systems by introducing the largest benchmark dataset to date, specifically designed to support the evaluation of subdivision-based solvers and the learning of real root classification in parametric systems. Constructed through the integration of subdivision algorithms and nonlinear system theory, and informed by a comprehensive review of nearly two decades of relevant literature, the dataset provides a high-value resource for machine learning–driven real root classification and solver performance assessment. Experimental results demonstrate that the dataset effectively enables systematic comparisons among diverse solvers and facilitates the training of robust classification models, thereby filling a critical data gap in this research area.

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.

Problem

• nonlinear equations
• subdivision methods
• zero-dimensional systems
• dataset
• real root classification

Innovation

• nonlinear systems
• subdivision methods
• labeled dataset
• real root classification
• benchmarking