Neural State Estimation for a Water Distribution Network: An Ablation Study and Gradient-Based Explainability

ArtinisLabs SA, Greece

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Abstract

We benchmark four families of neural state estimators for a non-linear water distribution network (WDN) when only past and current actuation signals are available, i.e. without feeding back any measurement of the network state. Using a simulation of a three-conduit network with five exogenous inputs and ten internal states, we compare a memoryless MLP, a windowed MLP, an LSTM, a GRU, and a regularized Temporal Fusion Transformer (TFT) under an identical chronological split. The GRU with a 20-step input window reaches the best validation RMSE of 7.59 × 10⁻² (validation R² = 0.976) with only 14,410 parameters, outperforming the LSTM, the windowed MLP and the TFT. We then probe the best GRU with permutation importance and gradient × input attribution; both methods agree that the upstream reservoir head u₁ dominates the prediction, in line with the physics of the network. Compact recurrent estimators thus appear to be a strong default for input-driven WDN state estimation, and gradient-based attribution is a cheap, model-agnostic way to add explain-ability to an already-trained estimator.