Lv et al. (2026) Hybrid PSO-SVM and symbolic regression model for agricultural water demand prediction

Identification

• Journal: Scientific Reports
• Year: 2026
• Date: 2026-01-13
• Authors: Hong Lv, Yuting Zhao, Wei Wang, Kai Hou, Xiaokang Zheng
• DOI: 10.1038/s41598-026-34995-8

Research Groups

• Yellow River Engineering Consulting Co., Ltd., Zhengzhou 450003, China
• School of Water Conservancy and Transportation, Zhengzhou University, Zhengzhou 450001, China

Short Summary

This study developed a hybrid Particle Swarm Optimization–Support Vector Machine (PSO-SVM) and symbolic regression model to identify key factors influencing agricultural water demand in Bayannur City, China, and forecast future trends, predicting that demand will stabilize above 5 billion cubic meters annually, peaking at 5.156 billion cubic meters in 2028.

Objective

• To identify the core determinants of agricultural water demand, distinguishing between driving and restraining factors, by integrating machine learning with interpretable modeling.
• To construct an explicit and interpretable mathematical equation for agricultural water demand prediction using symbolic regression.
• To forecast future agricultural water demand trends in Bayannur City to support regional water resource management and policy-making.

Study Configuration

• Spatial Scale: Bayannur City, Inner Mongolia Autonomous Region, China.
• Temporal Scale: Historical data from 1990–2022 (33 years); future demand forecast for 2023–2035.

Methodology and Data

• Models used: Particle Swarm Optimization–Support Vector Machine (PSO-SVM) for factor identification and parameter optimization, and Symbolic Regression (SR) for constructing the predictive equation.
• Data sources: Agricultural water use data from Bayannur City and Inner Mongolia Autonomous Region Water Resources Bulletins (1990–2022). Socio-economic indicator data from various governmental statistical yearbooks and bulletins (e.g., "Statistical Yearbook of Bayannur City and Inner Mongolia Autonomous Region," "China Rural Statistical Yearbook"). The dataset includes 16 variables covering regional water resource endowment, rural population characteristics, agricultural production models, agricultural modernization level, and agricultural economic development.

Main Results

• Agricultural water use in Bayannur City is influenced by a bidirectional mechanism: driven by factors such as Grain Yield (effect size: 0.069) and Effective Irrigated Area (effect size: 0.064), and inhibited by Per Capita Disposable Income of Rural Residents (effect size: -0.061) and High-Efficiency Irrigation Rate (effect size: -0.061).
• The symbolic regression model achieved a Mean Squared Error (MSE) of 1.1557 and a Coefficient of Determination (R²) of 0.877, with a 95% prediction interval of approximately ±0.2083 billion cubic meters.
• The forecast indicates that Bayannur’s agricultural water demand will remain above 5 billion cubic meters annually from 2023 to 2035, peaking at 5.156 billion cubic meters in 2028 before gradually stabilizing.
• Sensitivity analysis revealed that a 20% increase in grain yield or effective irrigated area leads to a 2.86% and 2.93% increase in water demand, respectively. Conversely, a 20% increase in high-efficiency irrigation rate results in a 3.58% reduction, and a 20% increase in rural per capita disposable income leads to a 3.26% reduction in agricultural water usage.

Contributions

• Developed a novel hybrid modeling framework integrating PSO-SVM for quantitative identification of primary driving and restraining factors of agricultural water demand.
• Constructed the first symbolic-regression-derived explicit mathematical equation for Bayannur's agricultural water system, enhancing interpretability and verifiability for policy analysis.
• Bridged the gap between high predictive accuracy (from machine learning) and structural interpretability (from symbolic regression), offering a practical and transparent tool for regional water resource policy-making.

Funding

• National Key Research and Development Program of China (No. 2023YFC3206800)
• National Natural Science Foundation of China (52209038, and 52109038)
• Henan Province Youth Talent Support Project (2023HYP017)

Citation

@article{Lv2026Hybrid,
  author = {Lv, Hong and Zhao, Yuting and Wang, Wei and Hou, Kai and Zheng, Xiaokang},
  title = {Hybrid PSO-SVM and symbolic regression model for agricultural water demand prediction},
  journal = {Scientific Reports},
  year = {2026},
  doi = {10.1038/s41598-026-34995-8},
  url = {https://doi.org/10.1038/s41598-026-34995-8}
}