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Equation discovery framework EPDE: Towards a better equation discovery

Mikhail Maslyaev, Alexander Hvatov

TL;DR

This paper enhances the EPDE algorithm -- an evolutionary optimization-based discovery framework that generates terms using fundamental building blocks such as elementary functions and individual differentials, and incorporates multi-objective optimization.

Abstract

Equation discovery methods hold promise for extracting knowledge from physics-related data. However, existing approaches often require substantial prior information that significantly reduces the amount of knowledge extracted. In this paper, we enhance the EPDE algorithm -- an evolutionary optimization-based discovery framework. In contrast to methods like SINDy, which rely on pre-defined libraries of terms and linearities, our approach generates terms using fundamental building blocks such as elementary functions and individual differentials. Within evolutionary optimization, we may improve the computation of the fitness function as is done in gradient methods and enhance the optimization algorithm itself. By incorporating multi-objective optimization, we effectively explore the search space, yielding more robust equation extraction, even when dealing with complex experimental data. We validate our algorithm's noise resilience and overall performance by comparing its results with those from the state-of-the-art equation discovery framework SINDy.

Equation discovery framework EPDE: Towards a better equation discovery

TL;DR

This paper enhances the EPDE algorithm -- an evolutionary optimization-based discovery framework that generates terms using fundamental building blocks such as elementary functions and individual differentials, and incorporates multi-objective optimization.

Abstract

Equation discovery methods hold promise for extracting knowledge from physics-related data. However, existing approaches often require substantial prior information that significantly reduces the amount of knowledge extracted. In this paper, we enhance the EPDE algorithm -- an evolutionary optimization-based discovery framework. In contrast to methods like SINDy, which rely on pre-defined libraries of terms and linearities, our approach generates terms using fundamental building blocks such as elementary functions and individual differentials. Within evolutionary optimization, we may improve the computation of the fitness function as is done in gradient methods and enhance the optimization algorithm itself. By incorporating multi-objective optimization, we effectively explore the search space, yielding more robust equation extraction, even when dealing with complex experimental data. We validate our algorithm's noise resilience and overall performance by comparing its results with those from the state-of-the-art equation discovery framework SINDy.
Paper Structure (14 sections, 18 equations, 4 figures, 8 tables, 1 algorithm)

This paper contains 14 sections, 18 equations, 4 figures, 8 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Overview of the proposed method
  3. Representation of differential equations
  4. Optimization criteria
  5. Evolutionary optimization
  6. Validation of the algorithm
  7. Partial differential equations
  8. Burgers' equation
  9. Korteweg-de Vries equation
  10. Ordinary differential equations
  11. Systems of differential equations
  12. Experimental summary
  13. Conclusion
  14. Experiment parameters

Figures (4)

  • Figure 1: The workflow of the proposed approach for the evolutionary-based data-driven algorithm of differential equations discovery.
  • Figure 2: Scheme of the cross-over operator.
  • Figure 3: Scheme of the mutation operator.
  • Figure 4: Example of Van der Pol oscillator state predictions, based on obtained differential equations. a) Equation with misidentified structure; b) Equation with correct terms but deviating coefficients; c) Predictions with the correct data-driven equation.