The paper by Ryan Love et al. presents (to my knowledge) the first study of machine learning on GIA models. They do an extensive analysis and find very interesting results, which can be used in future studies. The structure of the paper is very good and only a few references are missing. The paper fits nicely into GMD.  I have provided detailed comments in the attached pdf.

Review of "A Fast Surrogate Model for 3D-Earth Glacial Isostatic Adjustment using Tensorflow (v2.8.10) Artificial Neural Networks"

by Wouter van der Wal

The paper presents the first development and application (“proof of concept”) of a neural network to ‘replace’ a GIA model with 3D Earth structure. 3D GIA models use a more accurate representation of the Earth than 1D Earth model but because of their long computation times several applications, such as inversion for global ice history based on a 3D Earth structure, are currently out of reach. The paper shows that sufficient accuracy can be reached with an emulator based on a neural network with a limited training data set consisting of runs of a full 3D GIA model. The authors find that training an emulator on a residual signal between a model with 3D and 1D earth structure improved results. Important tests such as more ice models will have to be done in the future but this paper is a great first step in what is clearly an important research goal for the field of GIA modelling. The comparisons with a full 3D model are well chosen and clearly shown in the figures and the results support the conclusions. I recommend publication after taking into account the comments below, especially comment 3 which focuses on the description of the method. The attached pdf contains textual comments which probably do not need an individual reply in a rebuttal.

Main comments

1. The first application of neural network to emulate a GIA model as far as I know is Lin et al. (2023), which has been published since September 2023 and presented at AGU Fall meeting in 2022. That does not take away any of the scientific value of the current manuscript but Lin et al. (2023) should be discussed in some detail, e.g. , in terms of type of neural network selected, time steps, loss function, but also because it uses many different ice histories which the current manuscript states as important future work (of course Lin et al did not use 3D GIA models).
2. 335-355: this part of the paper is separate from the main goal of the paper and the emulator does not seem necessary for it. I think it can be removed without any loss for the main objective. If the authors have a strong wish to keep this part, the results and conclusions need to be placed in context with a long list of earlier studies that have reached similar conclusions as in line 338, 348 and 353. The extra research goal should be introduced in more detail compared to what is now in line 70-72, including previous work and what the current paper adds to it, and the conclusion in line 389 should also state that the conclusions are in agreement with many earlier studies.
3. I found the description of the method sometimes lacking in detail. As the first application of neural networks to a 3D GIA model the it will be followed up by other studies. For that reason it is important know what has been tried and why certain choices are made. Especially I would say in a journal such as GMD. Below are specific comments. I think none of them requires extra modelling.

104: this difference should be quantified because it is a source of error that will contribute to the difference between emulated and explicit results, since the emulation is based on the 3D model but the result is added to the NMSS model.

134 and further: The text here is hard to grasp. Testing and comparison is not specific enough, and the proxy-data: model comparison is not explained yet. With neural networks it is good to be clear about what tests and validation are done. In line 232 it is now not clear what the validation subensemble is.

145-147: This is an important finding, and for future development of ANN it is very useful to know why RSL itself can not be accurately emulated, and whether this is worthy of further research or not. Other questions: How is the ROC computed, the difference between two consecutive timesteps? How is RSL later reconstructed from this, by integrating the emulated ROC over time? It would be helpful to provide an indication of some of the preliminary results.

154: It is not clear to me how the probability density function is created, could you clarify this? Should this be seen as a histogram of all ROC for all timesteps or per timestep?

164: Can you provide some insight on why you selected this library?

165: “we train separately”. Doesn’t this result in a different ANN (different weights) for each ice history, viscosity, lithosphere thickness? I might miss something obvious but it would be good to clarify.

169: Can you explain why 4 time steps is a good choice? It is not intuitive as the “memory” of GIA would go back further than that, and the paper later concludes that it could be a reason for the worse performance for present-day uplift rates.

174: Can you specify it here? This is now done in line 214. From my experience the choice of stopping condition can be important. Please explain if you have tried other stopping criteria, for example averaging only over locations with significant signal (and compare to Lin et al).

183: Because the training expense and performance are the main results of the paper, can you give some insight in how these vary?

224: This is the first time the weights are mentioned. It would be good to mention these weights already in section 2.1 as I think these are the ‘output’ of the training.

324: Could you add a conclusion or implication from the result in this paragraph? Do you think the ANN should not be used for intermediate field, or should N be increased?

328: “within 2 parameter value increments” In table 1 this does not appear to be the case for delta_total for USGC: 0.05 for EMU and 0.8 for EXP. Can you check this?

Miscellaneous comments

Caption figure 1. The lithosphere values shown are scaled, but the values in North America are above 200 km which is thick compared to other GIA studies. It would be good to comment on that in the text

Figure 2: There are a few apparent outliers for LT = 96 km, could you comment on those?

262: If this is correct, does that mean that the RSL anomaly is also relatively large for present? If you have these results it would be good to report on that to support your tentative conclusion

332: It is a nice idea to use the emulator to find a larger area in the parameter space that can be searched with the explicit method, but what do you mean exactly by the “parameter space that provides the optimal fits”. Is it the best fit parameters with a confidence region? How does it differ between EMU and EXP?

References

Lin, Y., Whitehouse, P.L., Valentine, A.P. and Woodroffe, S.A., 2023. GEORGIA: A graph neural network based EmulatOR for glacial isostatic adjustmentGeophysical Research Letters, 50(18), p.e2023GL103672.