Authors: Henok Teklu, Norman L Jones, Gustavious P Williams – Brigham Young University
Title: Liquid Neural Network–Based Imputation of Missing Groundwater Time Series Under Sparse Observations
Presentation Type: Poster Presentation
Abstract: Missing data in groundwater monitoring records is a pervasive barrier to reliable basin-scale hydrological analysis. Public databases contain millions of water-level measurements, yet most wells are sampled infrequently over their period of record, with multi-year gaps that render standard interpolation methods ineffective. Existing imputation approaches often operate in either the spatial domain (donor regression, geostatistical interpolation) or the temporal domain (Extreme Learning Machines, LSTM, GRU), but not both simultaneously. We present a hybrid framework coupling Matrix Completion (MC) with Liquid Neural Networks (LNN) to fill temporal gaps in groundwater-level time series by jointly exploiting spatial cross-well correlations and continuous-time temporal dynamics. The method operates in two stages: first, Piecewise Cubic Hermite Interpolating Polynomials (PCHIP) fill short gaps (up to 24 months) to densify the monitoring network; second, large gaps are addressed through donor-based initialization using correlated reference wells, iterative Singular Value Decomposition-based matrix completion across a composite matrix of donor wells, and globally available GLDAS soil moisture auxiliary variables, followed by Liquid Neural Network refinement using closed-form continuous-time dynamics. The MC predictions serve as reservoir input for the LNN during gap periods, while the LNN readout is trained exclusively on real observations, ensuring fidelity to ground truth while benefiting from spatial context. Cross-validation on 592 wells in the Great Salt Lake Basin under random missing-data scenarios (5-50% removal) yields Kling-Gupta Efficiency (KGE) of 0.84-0.85 with RMSE below 3 ft, while consecutive-gap scenarios (2-5 years) yield KGE of 0.78-0.82 — demonstrating robust performance even for the multi-year gaps where prior methods degrade substantially. The framework requires only well locations, irregular observations, and globally available auxiliary data, with all hyperparameters auto-optimized per well, making it applicable to any groundwater monitoring network worldwide.