Abstract Extreme geomagnetic storms, such as the May 2024 Gannon event, pose significant risks to technological infrastructure, requiring robust forecasting models. Here, we apply Physics‐Informed Neural Networks (PINNs) to the Burton equation to model the storm’s ring current dynamics by studying the temporal evolution of the SuperMAG SMR index during the Gannon storm. By solving the inverse problem, we determine optimal parameters for multiple solar wind‐magnetosphere coupling functions while enforcing physical consistency. We use an ensemble PINN approach with Random Fourier Features to capture high‐frequency fluctuations in the SMR $SMR$ index and quantify epistemic uncertainties. Our comparative analysis reveals that physically motivated merging functions best describe the main phase energy injection, whereas electric field proxies maximize the global fit. These findings demonstrate that PINNs effectively automate model discovery and validate physical hypotheses crucial for the development of next‐generation for operational space weather forecasting tools.

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