What question did this study set out to answer?

The study aims to enhance the forecasting accuracy of agricultural production in India using fractal interpolation techniques combined with deep learning models.

June 9, 2026Open Access

A fractal-enhanced deep learning framework for forecasting agricultural production in India

Key Points

The study aims to enhance the forecasting accuracy of agricultural production in India using fractal interpolation techniques combined with deep learning models.
Utilized fractal interpolation function with variable and constant scaling factors as data augmentation techniques.
Employed long short-term memory (LSTM) and bidirectional LSTM (Bi-LSTM) models to predict annual crop production from 1961 to 2023.
Evaluated model performance using MAPE and statistical tests including Wilcoxon and Diebold–Mariano tests.
LSTM with variable-scaling FIF achieved MAPE values of 5.06% for Millet, 1.95% for Maize, and 1.70% for Wheat.
Bi-LSTM with variable-scaling FIF obtained the best performance for Rice, yielding MAPE of 1.39%.
The choice of scaling approach was more influential on performance than the choice between LSTM and Bi-LSTM.

Abstract

Forecasting agricultural production in India is highly challenging due to non-stationary dynamics driven by policy factors and climate volatility. This study investigates the effectiveness of the fractal interpolation function (FIF) (with both variable and constant scaling factors) as a data augmentation technique to improve the prediction accuracy of long short-term memory (LSTM) and bidirectional LSTM (Bi-LSTM) models. These models were used to predict the annual production of four major crops in India (Millet, Maize (corn), Wheat, and Rice) from 1961 to 2023. The FIF with a variable scaling factor produced a lower Hurst exponent (ranging from 0. 777 to 0. 875) and a correspondingly higher fractal dimension (ranging from 1. 153 to 1. 574) than the FIF with a constant scaling factor. This resulted in a rougher interpolation that more effectively captured the non-smooth features and local volatility of the time series. The experimental results demonstrate that models trained on fractal-interpolated data significantly outperformed those trained on the original data. The LSTM integrated with variable-scaling FIF achieved the best overall performance for three crops, recording the highest R^2 values and the lowest error metrics. Notably, it achieved MAPE values of 5. 06\% (Millet), 1. 95\% (Maize), and 1. 70\% (Wheat). However, for Rice, the Bi-LSTM integrated with variable-scaling FIF delivered the best performance, yielding MAPE = 1. 39\% on the test set (2011–2023). These improvements were further confirmed by the Wilcoxon and Diebold–Mariano tests. The findings of this study highlight that capturing the long-memory and self-similar characteristics of agricultural time series through fractal interpolation substantially improves the learning capabilities of recurrent neural networks. The choice of scaling approach proved to be a more dominant factor for performance than the choice between LSTM and Bi-LSTM. This framework underscores the importance of adaptive fractal interpolation for handling irregular agricultural time series and offers a promising tool for enhanced yield forecasting, especially for rain-dependent and climate-sensitive crops in India.

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