Comparison of Single- and Multi- Objective Optimization Quality for Evolutionary Equation Discovery

Mikhail Maslyaev, Alexander Hvatov
6/29/2023
cs.LGcs.NE

Official code: ITMO-NSS-team/EPDE_GECCO_experiments (3 stars, last commit 2023-04-24).

Abstract

Evolutionary differential equation discovery proved to be a tool to obtain equations with less a priori assumptions than conventional approaches, such as sparse symbolic regression over the complete possible terms library. The equation discovery field contains two independent directions. The first one is purely mathematical and concerns differentiation, the object of optimization and its relation to the functional spaces and others. The second one is dedicated purely to the optimizational problem statement. Both topics are worth investigating to improve the algorithm's ability to handle experimental data a more artificial intelligence way, without significant pre-processing and a priori knowledge of their nature. In the paper, we consider the prevalence of either single-objective optimization, which considers only the discrepancy between selected terms in the equation, or multi-objective optimization, which additionally takes into account the complexity of the obtained equation. The proposed comparison approach is shown on classical model examples -- Burgers equation, wave equation, and Korteweg - de Vries equation.

View on arXivView PDF

Code Implementations(1)

ITMO-NSS-team/EPDE_GECCO_experimentsOfficial

Repository for storage of experiments with EPDE for GECCO-2023 paper "Comparison of Single- and Multi- Objective Optimization Quality for Evolutionary Equation Discover" in form of data and scripts.

30PythonApr 20, 20233 years ago

Similar Papers

Equation discovery framework EPDE: Towards a better equation discovery

85% match1 repo32024

Data-driven discovery of governing differential equations across physical systems

78% match2026

An Efficient Reconstructed Differential Evolution Variant by Some of the Current State-of-the-art Strategies for Solving Single Objective Bound Constrained Problems

78% match2024

SODAs: Sparse Optimization for the Discovery of Differential and Algebraic Equations

78% match1 repo12025

Automatic differentiation and the optimization of differential equation models in biology

77% match2022

A Comparative Visual Analytics Framework for Evaluating Evolutionary Processes in Multi-objective Optimization

76% match1 repo132023

Cite this paper

@article{maslyaev2023comparison,
  title  = {Comparison of Single- and Multi- Objective Optimization Quality for Evolutionary Equation Discovery},
  author = {Mikhail Maslyaev and Alexander Hvatov},
  year   = {2023},
  eprint = {2306.17038},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2306.17038v1}
}

Add a badge to your README

Shows whether official code is linked for this paper.

Code of Paper badge
[![Code of Paper](https://codeofpaper.com/badge/2306.17038.svg)](https://codeofpaper.com/paper/2306.17038)

Discussion