Physics-Informed Neural Networks for Offshore Tsunami Data Assimilation

In recent years, offshore tsunami observation networks equipped with ocean bottom pressure gauges (OBPGs), such as S-net, DONET, and N-net, have been deployed around Japan, enabling real-time collection of high-quality tsunami data near the source. These networks make it possible to estimate the spatiotemporal variation of the tsunami wavefield using a data assimilation approach, and to predict coastal tsunamis from the initial or current tsunami wavefield. This study proposes a novel tsunami data assimilation method that uses physics-informed neural networks (PINNs) to estimate tsunami wavefields from the observed OBPG data. The neural network was optimised by minimising the sum of the data loss, which quantifies discrepancies from the tsunami data, and the physical loss, which quantifies the satisfaction of the linear long wave equation. This was performed to ensure that the estimated results are consistent with both the observed data and the physics of tsunami propagation, even when there is limited observational data and significant noise.  We first validated the effectiveness of the proposed method using synthetic S-net OBPG data from the 2011 Tohoku-oki earthquake (Mw 9.0) tsunami. The results confirmed that by using both data and physical constraints in the PINN optimisation, the PINN could adequately assimilate the spatiotemporal distribution of the tsunami wavefield from OBPG data, even outside the network coverage area. The predicted tsunami waveforms at the coastal stations, computed from the estimated initial wavefield, showed good agreement with the actual waveforms. Next, we conducted an experiment using actual S-net OBPG data from the 2016 Fukushima-oki earthquake (Mw 6.9) tsunami. The initial tsunami source estimated by PINN was in good agreement with other studies based on waveform inversion, although the maximum source amplitude and maximum coastal tsunami heights were slightly underestimated. We also conducted an experiment using N-net OBPG data from the 2024 Hyuganada earthquake (Mw 7.0) tsunami. The PINN could accurately estimate the initial tsunami source, even though the tsunami source of this event was located outside the N-net coverage area. Finally, we have shown that incorporating tsunami observations over time into the iterative optimisation of the PINN model allows for accurate and efficient tsunami data assimilation.