The assimilation and prediction of phase-resolved surface gravity waves are critical challenges in ocean science and engineering. Potential flow theory (PFT) has been widely employed to develop wave models and numerical techniques for wave prediction. However, traditional wave prediction methods are often limited. For example, most simplified wave models have a limited ability to capture strong wave nonlinearity, while fully nonlinear PFT solvers often fail to meet the speed requirements of engineering applications. This computational inefficiency also hinders the development of effective data assimilation techniques, which are required to reconstruct spatial wave information from sparse measurements to initialize the wave prediction. To address these challenges, we propose a novel solver method that leverages physics-informed neural networks (PINNs) that parameterize PFT solutions as neural networks. This provides a computationally inexpensive way to assimilate and predict wave data. The proposed PINN framework is validated through comparisons with analytical linear PFT solutions and experimental data collected in a laboratory wave flume. The results demonstrate that our approach accurately captures and predicts irregular, nonlinear, and dispersive wave surface dynamics. Moreover, the PINN can infer the fully nonlinear velocity potential throughout the entire fluid volume solely from surface elevation measurements, enabling the calculation of fluid velocities that are difficult to measure experimentally.

Extreme events are evolving as a direct consequence of climate change, leading to the emergence of new, previously unobserved phenomena [1, 2]. In remote regions like the Arctic, where in-situ measurements are sparse, scientists must increasingly depend on analytical and numerical models to explore these events. However, modeling in such regions presents significant challenges due to the uncertainties in the data required to calibrate and validate these models [3]. Consequently, large simplifications are often necessary, resulting in substantial discrepancies between observed and modeled phenomena. The mysterious 10.88 mHz very-long-period (VLP) seismic signal, which appeared following a tsunamigenic landslide in the Dickson Fjord, Greenland, on September 16th, 2023, and the subsequent interdisciplinary scientific efforts to determine its origin, underscore these challenges. Two independent studies [4, 5] have hypothesized that the signal was driven by a standing wave, or seiche, which formed in the aftermath of the tsunami. While it is well-documented that seiches can form in resonant enclosed and semi-enclosed basins [6], the loading-induced tilt they produce has only been observed locally (< 30 km) and for short durations (< 1 hour)[5, 7]. Moreover, no prior evidence exists of persistent fluid sloshing (lasting several days) without an external driver.