Wang et al. (2026) High-accuracy groundwater flow modeling in pumping aquifer via physics-informed neural network improved with Fourier feature

Identification

• Journal: Advances in Water Resources
• Year: 2026
• Date: 2026-07-02
• Authors: Jinxin Wang, Zhenjiao Jiang, Chao Song, Ruifeng Wang, Zhiqiang Yin
• DOI: 10.1016/j.advwatres.2026.105402

Research Groups

• Key Laboratory of Groundwater Resources and Environment, Ministry of Education, College of Environment and Resources, Jilin University, China
• State Key Laboratory of Deep Earth Exploration and Imaging, College of Geo Exploration Science and Technology, Jilin University, China
• The 4th Geological Team of Hebei Geology and Mining Bureau (Water Source Conservation Research Center of Hebei Province), China
• National Center of Comprehensive Natural Resources Survey, China Geological Survey, China

Short Summary

This study proposes a novel physics-informed neural network (PINN) model enhanced by incorporating Fourier feature layer and well function for accurate groundwater flow modeling in pumping aquifers. The results demonstrate that the accuracy of F-PINN is highly improved compared to classical PINN models.

Objective

• Investigate the feasibility of using physics-informed neural networks with Fourier feature encoding and well function for predicting groundwater levels and flow velocities in pumping aquifers.

Study Configuration

• Spatial Scale: Aquifer system with a single pumping well or five-spot wells.
• Temporal Scale: Short-term to long-term groundwater flow dynamics.

Methodology and Data

• Models used: Physics-informed neural network (PINN) with Fourier feature layer and well function.
• Data sources: Synthetic aquifers, numerical simulations, and theoretical analysis.

Main Results

• The proposed F-PINN model exhibits improved accuracy in predicting groundwater levels and flow velocities at near-well and far-well regions compared to classical PINN models.
• The Fourier feature layer enables robust learning of groundwater flow with extremely high and low hydraulic gradients.
• The well function method overcomes the subjectivity and physical inconsistency of conventional Gaussian kernel functions in handling well flow conditions.

Contributions

• This study contributes a novel F-PINN model that leverages the spatiotemporal Fourier feature to capture high- and low-gradient components in groundwater level evolution, enhancing model robustness.
• The proposed well function method provides a physically consistent approach for defining pumping rates in PINN models.

Funding

• This research was supported by the National Natural Science Foundation of China (Grant No. 52109223) and the Key Laboratory of Groundwater Resources and Environment, Ministry of Education, China.

Citation

@article{Wang2026Highaccuracy,
  author = {Wang, Jinxin and Jiang, Zhenjiao and Song, Chao and Wang, Ruifeng and Yin, Zhiqiang},
  title = {High-accuracy groundwater flow modeling in pumping aquifer via physics-informed neural network improved with Fourier feature},
  journal = {Advances in Water Resources},
  year = {2026},
  doi = {10.1016/j.advwatres.2026.105402},
  url = {https://doi.org/10.1016/j.advwatres.2026.105402}
}