Using physics‐informed neural networks to quantify submarine groundwater discharge under high‐frequency tidal dynamics using heat as a tracer

Estimating exchange rates of submarine groundwater discharge (SGD) at high temporal resolution over extended periods remains challenging, particularly when using heat as a tracer in highly dynamic environments such as tidal systems. Currently available heat transport models struggle to accurately quantify SGD exchange rates in these settings, where sharp transitions and high‐frequency fluctuations in hydrodynamic forcings cannot be reproduced with current inverse optimization methods. This study evaluates the ability of Physics‐Informed Neural Networks (PINNs) to overcome these limitations through inverse modeling of temperature derived Darcy fluxes. Three case studies—a synthetic step‐function transition, a synthetic tidal pumping scenario, both published datasets, and measurements from a field‐scale tidal creek (Texel, Netherlands)—were used to test and validate the PINN approach. Unlike conventional methods such as VFLUX and 1DTEMPRO, which exhibited delays and inaccuracies when tidal cycles influence groundwater fluxes on sub‐daily to daily frequencies, the PINN successfully predicted exchange fluxes driven by the K1 (24‐h) and M2 (12‐h) tidal cycles with a high degree of accuracy. Spectral analysis confirmed the PINNs ability to precisely estimate the impact of multi‐scale tidal signals on SGD dynamics at a sub‐daily resolution. This work highlight PINN as a powerful inversion method when using heat as a tracer in highly dynamic environments, offering new insights into the complex interplay between tidal signals and SGD in coastal systems.