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<p>This paper introduces the Evolutionary Extended Processed Method (EEPM), which is a hybrid numerical solver with evolutionary algorithms and machine learning be used to efficiently solve ordinary differential equation (ODE). Existing methods have difficulties solving large-scale, linear, nonlinear and stiff equations because of the high preprocessing costs and limited flexibility. EEPM deals with these problems by updating transformation matrices with evolutionary algorithms and dynamically selecting step sizes with a machine learning aided controller. Benchmark tests, such as harmonic oscillators, exponential growth and logistic models, indicate than EEPM is more accurate, more stable and has a lower computational cost than traditional solvers, such as Strang-Marchuk, Leapfrog, Adams–Bashforth and the Trapezoidal Rule. This method is also competitive against the state of the art learning-based solvers, and demonstrates the potential for real world problems. Despite the challenges to implement correctly, such as machine learning training and computational overhead, EEPM is adaptable and efficient, thus it can be used in complex systems, in engineering simulations, climate modeling and nonlinear dynamics.</p>

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EEPM a hybrid evolutionary and machine learning-based approach for efficient ODE integration

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年1月2日

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  • V. Murugesh,
  • M. Priyadharshini,
  • Getahun Fikadu Tilaye

摘要

This paper introduces the Evolutionary Extended Processed Method (EEPM), which is a hybrid numerical solver with evolutionary algorithms and machine learning be used to efficiently solve ordinary differential equation (ODE). Existing methods have difficulties solving large-scale, linear, nonlinear and stiff equations because of the high preprocessing costs and limited flexibility. EEPM deals with these problems by updating transformation matrices with evolutionary algorithms and dynamically selecting step sizes with a machine learning aided controller. Benchmark tests, such as harmonic oscillators, exponential growth and logistic models, indicate than EEPM is more accurate, more stable and has a lower computational cost than traditional solvers, such as Strang-Marchuk, Leapfrog, Adams–Bashforth and the Trapezoidal Rule. This method is also competitive against the state of the art learning-based solvers, and demonstrates the potential for real world problems. Despite the challenges to implement correctly, such as machine learning training and computational overhead, EEPM is adaptable and efficient, thus it can be used in complex systems, in engineering simulations, climate modeling and nonlinear dynamics.