# Developing a cost-effective emulator for groundwater flow modeling using deep neural operators

arXiv: https://arxiv.org/abs/2304.12299 · HTML: https://mlsanity.com/paper/2304.12299/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2023.

## Built on by (most cited first, 8 of 8)

- [Neural Chaos: A Spectral Stochastic Neural Operator](https://mlsanity.com/paper/2502.11835/) (2025)
- [Synergistic Learning with Multi-Task DeepONet for Efficient PDE Problem Solving](https://mlsanity.com/paper/2408.02198/) (2024)
- [Physics-Informed Latent Neural Operator for Real-time Predictions of time-dependent parametric PDEs](https://mlsanity.com/paper/2501.08428/) (2025)
- [TANTE: Time-Adaptive Operator Learning via Neural Taylor Expansion](https://mlsanity.com/paper/2502.08574/) (2025)
- [Time Series Predictions in Unmonitored Sites: A Survey of Machine Learning Techniques in Water Resources](https://mlsanity.com/paper/2308.09766/) (2023)
- [Efficient Training of Deep Neural Operator Networks via Randomized Sampling](https://mlsanity.com/paper/2409.13280/) (2024)
- [Leveraging Deep Operator Networks (DeepONet) for Acoustic Full Waveform Inversion (FWI)](https://mlsanity.com/paper/2504.10720/) (2025)
- [A Resolution Independent Neural Operator](https://mlsanity.com/paper/2407.13010/) (2024)

## Abstract (arXiv)

Current groundwater models face a significant challenge in their implementation due to heavy computational burdens. To overcome this, our work proposes a cost-effective emulator that efficiently and accurately forecasts the impact of abstraction in an aquifer. Our approach uses a deep neural operator (DeepONet) to learn operators that map between infinite-dimensional function spaces via deep neural networks. The goal is to infer the distribution of hydraulic head in a confined aquifer in the presence of a pumping well. We successfully tested the DeepONet on four problems, including two forward problems, an inverse analysis, and a nonlinear system. Additionally, we propose a novel extension of the DeepONet-based architecture to generate accurate predictions for varied hydraulic conductivity fields and pumping well locations that are unseen during training. Our emulator's predictions match the target data with excellent performance, demonstrating that the proposed model can act as an efficient and fast tool to support a range of tasks that require repetitive forward numerical simulations or inverse simulations of groundwater flow problems. Overall, our work provides a promising avenue for developing cost-effective and accurate groundwater models.