Abstract: Computationally efficient and differentiable weather models promote the discovery of previously unknown extreme weather systems through deep searches using gradient descent. Here we search for gray swan extreme events that have not yet happened, and lie at the limit of a physically constrained optimization problem. Having the ability to determine these limits is important because the short observational record provides little guidance beyond extrapolation into tails of uncertain distributions. This approach is useful for dynamical studies, synthetic training data for ML models, emergency planning, infrastructure design, and insurance hazard assessment. Introducing small perturbations to ERA5 in order to achieve a short-term extreme-event objective, we find cyclones along the East Coast of North America that are more intense than any previously observed. The question of physical plausibility of such storms is addressed using a tradition physics model to validate the simulated gray swan events.