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

Murugesh V. Priyadharshini M. Tilaye G.F.
December 2026 Springer Science and Business Media B.V.

Discover Computing
2026 #29 Issue 1

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.

Evolutionary algorithms , Evolutionary algorithms combined with machine learning , Evolutionary extended processed method (EEPM) , High-accuracy integration and computational efficiency , Machine learning-assisted integration , Numerical stability of stiff systems , Operator splitting , Ordinary differential equations (ODEs)

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School of Computer Science, Coventry University Kazakhstan, 3A, Korgalzhyn Highway, Astana, Kazakhstan
Department of Computer Science & Engineering, Faculty of Science and Technology (IcfaiTech), ICFAI Foundation for Higher Education, Hyderabad, 501203, India
Department of Software Engineering, Bule Hora University, Bule Hora, Ethiopia

School of Computer Science
Department of Computer Science & Engineering
Department of Software Engineering

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Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026