Physics-informed deep learning for groundwater contamination sources identification under sparse monitoring

• A physics-informed deep learning framework was developed for source identification. • Sparse multi-temporal head and concentration data were integrated with physical priors. • Simulation and field-based cases demonstrated accurate source localization (∼20 m). • Robustness analysis showed resilience to strong monitoring noise (∼30 m). • The framework supports sustainable groundwater risk assessment and remediation planning. Groundwater contamination poses persistent risks to environmental and public health, especially in industrial regions where monitoring networks are sparse and uncertain. Source identification is critical for effective remediation and risk management but is hindered by aquifer heterogeneity and limited observations. A physics-informed deep learning framework is proposed that integrates spatial encoding, recurrent temporal modules, and probabilistic outputs to reconstruct source location, release timing, and release intensity from sparse multi-temporal data. Hydraulic and concentration gradients were explicitly embedded as physical features, improving interpretability and stability of the inversion. In simulation cases, the framework localized sources with mean spatial errors of ∼20 m and yielded reliable estimates of release parameters (release time R 2 = 0.94, RMSE = 3.84–3.87 days; concentration R 2 = 0.95, RMSE = 0.61 mg/L). Field-based cases which adopted actual facility layouts and monitoring networks further demonstrated its applicability under realistic hydrogeological settings (spatial error 0.64 grids, 20.09 m; release time R 2 = 0.91, RMSE = 4.64 days; concentration R 2 = 0.82, RMSE = 1.11 mg/L). Robustness analyses confirmed resilience to observational noise and irregular sampling, with combined perturbations (σ h = 0.5–1 m, σ c = 1–2 mg/L) keeping spatial error 20–22 m, release time R 2 > 0.92 and concentration R 2 > 0.76. These results show that physics-informed learning can enable rapid and reliable groundwater contamination source identification even with sparse monitoring. The proposed framework offers a practical tool to support environmental management and remediation planning in complex contaminated sites.