Surrogate Modeling of Tsunami Simulation using Neural Operator: Application to Rapid Source Inversion

In this study, we developed an efficient framework for tsunami source inversion based on the Neural Operator (NO). Tsunami simulations calculate the spatio-temporal evolution of sea surface height, using vertical seafloor displacement as the initial condition. However, high-resolution simulation over large computational domains involves significant computational costs. Furthermore, inverse analysis to estimate fault parameters from observed waveforms requires repeated forward simulations, making computational efficiency a critical challenge. To address these issues, we developed a surrogate tsunami simulation model based on the NO framework. Unlike conventional numerical solvers, the trained NO model can instantly predict the spatio-temporal wavefield from a given initial seafloor displacement.

We employed the U-shaped Neural Operator (U-NO), which combines a U-Net-like encoder-decoder structure with the efficient Fourier-space convolutions. The training dataset was generated using the open-source tsunami simulation code JAGURS: we first simulated 2000 seafloor displacement patterns derived from randomly selected fault parameters. Then JAGURS was used to calculate the subsequent tsunami wavefields, and the NO model learned the relationship between the initial conditions and the wavefields. Validation using unseen test cases confirmed that the NO model successfully reproduces the spatio-temporal propagation patterns of the tsunamis, although spectral analysis revealed a tendency to underestimate short-wavelength components.

A significant advantage of our PyTorch-based NO model is its compatibility with automatic differentiation, enabling direct computation of gradients of the output wavefield with respect to the input parameters. Leveraging this capability, we performed gradient-based source inversion by minimizing the misfit between observed and predicted waveforms. To address the underdetermined nature of estimating parameters over tens of thousands of grid points, spatial smoothing via Laplacian regularization was introduced.

Furthermore, we developed an integrated model by connecting the NO model with Okada (1985)’s crustal deformation formulas implemented in PyTorch. This integrated model enables direct prediction of tsunami wavefield from fault parameters (e.g., location, slip amount). This approach also enables efficient exploration of nonlinear parameter space using gradient-based optimization, offering a significant computational advantage over traditional grid-search approaches. While challenges remain, such as sensitivity to initial parameter selection and the presence of local minima due to strong nonlinearity, the proposed framework demonstrates great potential for rapid source estimation. Future work will focus on (1) improving the representation of short-wavelength components, (2) extending this framework to more complex governing equations such as dispersive tsunami models, and (3) application to real observation data.