the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 22 May 2026
A Factorized Fourier Neural Operator Surrogate for Basin-Scale Tsunami Propagation
Abstract. Tsunami models have been developed for several decades, and many have shown good agreement with observations from real world events. The model solves wave equations, but simulation is usually computationally expensive in a large-scale basin. To assess potential tsunami impacts, ensemble analysis is standard for sampling source uncertainties, but computational costs constrain the number of scenarios that can be evaluated. Machine‑learning approaches have been developed to reduce the computational burden and accelerate typical tsunami‑ensemble analyses. However, these surrogate models are usually task-specific; they emulate buoy signals, sensor inputs, and maximum water level maps. Recent advances in machine learning techniques, such as neural operators, allow learning full wave evolution from physics-based simulations. Here, we introduce a data-driven tsunami surrogate model based on a Factorized Fourier Neural Operator (F-FNO). Memory-efficient F-FNO supports higher Fourier mode capacity, enabling the tsunami surrogate model to learn scenario-based COMCOT simulations and generalize to unseen epicenter locations/extrapolated magnitudes. We designed logic tree-based COMCOT simulations for the East Sea (Sea of Japan) to construct a surrogate operator. The F-FNO learns tsunami propagation through a short sequence of wavefield states and creates a general operator function that generates future wave and velocity fields. From the logic tree, we hold out the largest magnitude (8.0) and one specific source location for model evaluation and to test the scalability of the neural operator. As a result, the surrogate predicted tsunami waves with root mean square errors in surface elevation of 2–8 cm and first-arrival timing errors of approximately 8–12 min. Running the F-FNO surrogate requires approximately 8.5–12 s per scenario on a single GPU, compared to 87.9–95.7 s of COMCOT simulation time. The computational efficiency of the operator and its potential to scale to larger scenario ensembles support more timely tsunami scenario analysis and can complement physics-based solvers in offshore applications.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-1909', Anonymous Referee #1, 24 Jun 2026
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RC2: 'Comment on egusphere-2026-1909', Erlend Storrøsten, 07 Jul 2026
The manuscript presents an emulator for offshore tsunami wave propagation, which is a useful and relatively less explored direction compared with the larger body of emulator studies focused on inundation. The authors approximate the numerical propagation model using a Fourier Neural Operator in an iterative prediction framework, with the aim of reproducing the full simulation output rather than only selected quantities. This is a meaningful contribution, and the manuscript is overall well written. Although the dataset is somewhat limited, the evaluation is systematic and gives a useful first assessment of the method’s potential. That said, some important aspects of the method’s applicability and limitations should be clarified more explicitly.
Comments
The efficiency comparison is currently made against a relatively traditional CPU-based solver. This is informative, but it does not fully establish the computational advantage of the emulator relative to modern high-performance tsunami codes. I would therefore encourage the authors to discuss how the reported efficiency compares with highly optimized GPU-accelerated implementations, even if only qualitatively (see https://link.springer.com/chapter/10.1007/978-3-319-55480-8_16). In this respect, the inclusion of PCOMCOT in Table 4 is interesting, since it highlights that dispersive models are substantially more computationally demanding; this broader context may deserve slightly more attention.
The manuscript leaves some uncertainty regarding how site specific the model is. While bathymetry is included as an input (L61), the model appears to be trained on a fixed grid. If so, does the model need to be retrained for a different bathymetry or site? More generally, the extent to which the method generalizes with respect to bathymetry and resolution should be clarified. This is particularly relevant because the iterative prediction strategy may involve both error accumulation and higher cost than direct prediction.
Figures 11 and 13 suggest a possible bias toward underprediction, especially for sharp peaks. If such a bias is present, it is not well captured by the current metrics. A scatterplot of predicted versus simulated maximum amplitude could help clarify this point. It may also be worth discussing whether the use of RMSE contributes to smoother, slightly damped predictions. In a related study, similar issues were mitigated using an asymmetric loss function (https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2025JH001100).
In Figure 11, the time series appear to show some spurious predictions prior to wave arrival that are not present in the simulations. Since preserving the sea at rest is an important property in tsunami modeling, it would be useful to comment on whether the F-FNO approach introduces spurious oscillations, and whether this could also help explain the outliers in Figure 12a.
Minor comments:
L9: COMCOT has not been introduced.
L12: "From the logic tree, we hold out...". It sounds like you construct a single test set, however in reality you explore multiple different train-test splits.
L35: Due to the large number of potential sources PTHAs are often based on several thousand simulations. See "Selva et al. Quantification of source uncertainties in Seismic Probabilistic Tsunami Hazard Analysis (SPTHA)".
L48: "...learn wavefields as function spaces rather than vectors.". It is not entirely clear to me what is meant here.
L75: "The simulation inputs are normalized with wet-cell masking..". What does it mean?
Figure 1: I like the figure, however it contains several notions that has not yet been defined such as Y_t, ATE, Context length,.. This is valuable when looking back at the figure after reading a bit more, but may bee confusing at first.
L122: "All dynamic variables are normalized channel-wise...". Normalization is often based on some kind of invariance, is this the case here?
L136: Are the variables H, W and d_v defined? What are the dimensions?
Equation 6: The circle with a dot (\odot) operator has not been defined.
L179: The training parametere are stated both in the text and in the table caption below.
Figure 7: p-values are reported here and before (L284). Could you briefly mention the underlying hypothesis associated with this p-value?
Figure 11: Are the y-axes aligned in both columns of the plots? Markers seems to be placed differently.
Figure 14: Looks like allot is happening in the interval 0-10. Perhaps a log transform could make the details of the plot somewhat more visible?Citation: https://doi.org/10.5194/egusphere-2026-1909-RC2
Data sets
Test-EM Evaluation Dataset Jinyoung Kim et al. https://doi.org/10.5281/zenodo.19198928
Model code and software
F-FNO Tsunami Surrogate Code Jinyoung Kim et al. https://doi.org/10.5281/zenodo.19198928
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General comments:
The paper creates a new type of tsunami surrogate model. It is based on a Factorized Fourier Neural Operator (F-FNO) a good choice due for NO due to the ability of F-FNO to capture higher Fourier modes -- as shown in the comparison with regular FNOs. The application to the sea of Japan tsunami sources shows excellent timing but the amplitudes are underestimated by some margin.
The method is underperforming against more established emulation approaches cited in the context of peaks for hazard assessments. However the F-FNO benefits are more about its ability to emulate wave propagation between function spaces: inputs and outputs can be fields. The impulsive source forcing is interesting as well as physics-guided learning strategies. Nice implementation and extension of FNO, with lots of care in the accumulation of errors over hundreds of steps, and loss tailored to the problem, with efficient implementation. The design of experiments is unfortunately substandard.
I suggest major revisions (or reject and resubmit if more time is needed) as there is lots of potential but the current version suffers from a few issues that need to be addressed:
Specific comments:
The main attraction of NOs as explained, is the ability to take as inputs fields v GPs and other approaches. What can we learn about the dynamics and patterns with an F-FNO emulator v GPs?
The logic tree lines 202-211 is not a good design to train the F-FNO, unable to explore enough across 3-4 values only, compared to say a Latin Hybercube or a sequential design. It is also very large with 486 values despite for only 6 parameters (for each scaling law type). A GP would need less than 100 samples to be trained on 6 parameters. The training needs to be redone and discussed. I expect a big improvement in the quality of the emulation.
For validation, the authors hold out the largest magnitude (8.0) and one specific source location for model evaluation and to test the scalability of the neural operator.
This is too small for validation, I suggest a Leave-one-out strategy.
There is no comparison with other techniques on the example case. In the discussion some mention of the possibly higher accuracy of other methods due to focus on specific outputs, but some illustrations of shortcomings/strength of the method would be good.
The introduction is good, the motivation explicit with the aim to go beyond "predicting a fixed set of outputs such as maximum water level and inundation maps": explain the benefits obtained from that? Dynamics are mentioned and nice motivation but what can potentially be learned from this approach?
Fig 8 there is an obvious issue of extrapolation as outside the range of training.
Fig 10 and 11 very interesting. Often underestimated of peak wave height discussed in section 3.3
Speed-up is interesting 10x but COMCOT is fast model, PCOMCOT is discussed as more relevant extension 50-75x but also higher resolution near the coastline (as discussed but not performed) would be more expensive and more accurate?
Usually surrogates allow gains of multiple orders of magnitude. Ideally a higher resolution model than a fast coarse resoution COMCOT should be the simulator that will then be emulated.
The whole paragraph in the Conclusions "The surrogate functions as a rapid offshore boundary condition generator, facilitating the creation of nested grids that enhance the resolution of site-specific hazard studies. By accelerating the outer grid propagation.." is not fit for purpose. Indeed the main simulation costs are local not propagation in seconds but local high resolution coastal modelling. I suggest to remove this paragraph and ideally run the model at higher resolution -- including near the coastline -- to train te F-FNO. It should actually boost the quality of the F-FNO (using the right design) and provide a stronger statement of success in terms of impact on hazard assessements and warning and in terms of computational efficiency.