Optimizing the neural network and iterated function system parameters for fractal approximation using a modified evolutionary algorithm

Fractal interpolation has gained significant attention due to its ability to model complex, self-similar structures with high precision. However, optimizing the parameters of Iterated Function System (IFS)-based fractal interpolants remains a challenging task, particularly for Rational Fractal Cubic...

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Vydané v:Scientific reports Ročník 15; číslo 1; s. 13720 - 24
Hlavní autori: Abdulla, Sana, Mahipal Reddy, K.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: London Nature Publishing Group UK 21.04.2025
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Adaptability
Algorithms
Artificial neural network
Computer applications
Differential evolution
Evolution
Fractal interpolation function
Fractals
Grid search algorithm
Humanities and Social Sciences
Image processing
Iterated function system
Machine learning
multidisciplinary
Neural networks
Prediction models
Rational fractal
Science
Science (multidisciplinary)
Iterated function system
Differential evolution
Rational fractal
Artificial neural network
Grid search algorithm
Fractal interpolation function
ISSN:2045-2322, 2045-2322
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Shrnutí:Fractal interpolation has gained significant attention due to its ability to model complex, self-similar structures with high precision. However, optimizing the parameters of Iterated Function System (IFS)-based fractal interpolants remains a challenging task, particularly for Rational Fractal Cubic (RFC) splines, which offer greater flexibility in shape control. In this study, we propose an evolutionary optimization strategy to enhance the accuracy and adaptability of RFC splines by optimizing their scaling factor and shape parameters using our novel Fractal Differential Evolution (FDE) algorithm. The FDE method iteratively refines the parameter space to achieve an optimal fit to the target data, demonstrating improved convergence and computational efficiency compared to traditional approaches. To validate the effectiveness of our method, we present a detailed numerical example showcasing the impact of optimized parameters on RFC spline interpolation. Furthermore, as a practical application, we develop a predictive model by approximating the FDE-optimized RFC spline using an Artificial Neural Network (ANN). The ANN is fine-tuned through the FDE algorithm to minimize the Euclidean distance between the RFC spline and the network’s predictions, ensuring high accuracy. This neural network model is subsequently used for extrapolation, enabling robust predictions beyond the observed data. Our results highlight the potential of integrating fractal-based interpolation with machine learning techniques, paving the way for applications in computational geometry, image processing, and time series forecasting.
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ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-025-94821-5