LefNet: Lightweight Explainable Fast-trained Network for wheat growth prediction and mechanism resolving

Purpose: Investigating mechanisms of crop growth through neural networks presents significant challenges in AI-for-agriculture, since end-to-end deep learning models usually considered as “black-box” and lack interpretability. Method: To solve this issue, we propose LefNet, a Lightweight, Explainable and Fast-trained neural Network for crop growth prediction and mechanism resolving. The core improvement of LefNet is to replace neural connections between layers with Taylor polynomials, whose coefficients are learned during the training of crop growth prediction. Leveraging the parallel-friendly nature of polynomials, LefNet improves computational efficiency by avoiding computationally expensive recursive operations, while also recovering symbolic relationships among variables through finite polynomial expressions. This design both reduces model complexity and generates interpretable symbolic formulas that contains insights of the underlying growth mechanisms. Such polynomials are not the actual mechanism, but they consist unique understandings for further mechanism verification. Results: For the experiment, considering diverse fertilization strategies and sowing dates, we collected a simulated time-series data set reflecting multiyear wheat growth in northeast China to verify the performance of LefNet in both time series forecasting and mechanistic resolving. The performance of LefNet in crop growth forecasting surpasses existing state-of-the-art methods, decreasing 7.5% of mean square error (MSE) with 26.8% improvement of training efficiency, and its recovery of relationships is also validated by the existing literature. Conclusion: These results indicated that our interpretable model achieves accurate crop growth prediction while providing interpretable symbolic expressions that may offer insights into the underlying growth mechanisms, suggesting a promising direction for developing lightweight and explainable crop growth prediction models. The code is publicly available at https://github.com/lsl3/LefNet.