Estimating transient vertical hyporheic exchange fluxes from streambed temperatures using LSTM-autoencoder-enhanced physics-informed neural networks

Abstract

Accurately quantifying hyporheic exchange fluxes is crucial for understanding the transport and fate of contaminants and nutrients in the hyporheic zone. Over the past two decades, both physics-based analytical and numerical models, as well as data-driven models have been widely employed to infer these fluxes from streambed temperatures. However, each model type has notable limitations: physics-based models can suffer from structural errors that diminish inversion accuracy, while data-driven models often create input–output relationships without adequately considering the constraints imposed by established physical processes. To address these limitations, this study introduces a novel inversion framework termed LSTM-AE-PINN that integrates the physics-informed neural network (PINN) with the long short-term memory-based autoencoder (LSTM-AE) to estimate transient vertical hyporheic exchange fluxes (VHEFs). This framework leverages PINN to merge observational data with scientific principles and uses LSTM-AE to derive a low-dimensional representation of the VHEF time series, thereby streamlining parameter identification. The efficacy of LSTM-AE-PINN is evaluated through two synthetic case studies and one real-world application, demonstrating consistent superiority over PINN. It improves Kling-Gupta Efficiency (KGE) scores for VHEF estimations by 2.31 % to 88.62 %, with greater advantages in sparse or highly uncertain observational scenarios. This advancement not only refines VHEF estimation but also establishes a transferable template for inferring time-dependent parameters in broader hydrological contexts.