Scientific comments

1. In many machine-learning contexts (e.g., VAEs or standard autoencoders), the forward (decoder) and inverse (encoder) are trained jointly with a single objective. Clarify why two-step training is chosen over a single integrated approach, and discuss potential pros/cons.
2. In the proposed method, the training of the forward operator is deterministic. Have you considered a probabilistic (or noisy) surrogate as well?
3. Equation 9 needs to be clarified. What are the assumptions for the prior p(z)?
4. “Substituting Eq 9 in Eq 12 gives Eq 13”. This part needs more detailed explanation or derivation steps for better comprehension.
5. What are the features used for the measurements? Statistics of the time series, properties of the PSD?
6. What are the architecture and training parameters of the deterministic counterpart?
7. Does the provided uncertainty represent aleatory, epistemic components or mixed? In the latter case, how to decompose it?
8. The study focuses on two specific damage types within a single mooring line. This constraint simplifies the problem but may not represent the diversity of real-world conditions, where multiple damage types may occur at various locations.
9. Damage data and measurement data will be needed to train the forward operator in a supervised manner. Similar to the above comment, it works in the case study because the same damage mode is simulated for both training and testing. But in reality, it wil not be the case. In this context, how would you address the following barriers for practical application:
   1. Damage data can be rarely collected from the real structure and therefore, simulations will be required to train the model. The difference between the simulated response and the real turbine response will affect the model robustness.
   2. The simulated dataset will not cover all possible damage scenarios.

Technical comments

Literature review should be more structured.

Citation style should be proper and consistent throughout the manuscript. Cite in parentheses wherever is relevant.

The manuscript still needs careful and thorough proof-reading.

1. The authors combine a GMM with Autoencoders (using a deterministic encoder) to leverage the strengths of both methods, particularly for capturing multimodal latent representations. However, the paper should include a comparison between the proposed GMM-AE approach and a standard Variational Autoencoder for at least one case scenario. This would allow for evaluating reconstruction accuracy, clustering performance, and trade-offs such as increased model complexity while exploring whether the VAE's inherent stochasticity in the encoder provides comparable benefits.

2. The number of Gaussian components in a GMM is typically a hyperparameter that must be set before training. The authors set it equal to 5; why? there is no comment about this. Choosing the wrong number of components can lead to underfitting or overfitting.

3. The authors need to properly discuss the limitations of using GMM. 

- GMM suffers in the context of high-dimensional data. In this case, the damaged feature space is pretty small, which is convenient. How would this scale up?

GMM assumes that the data can be modeled as a combination of Gaussians. What if this assumption is not met? 

- the EM algorithm behind GMM is sensitive to initialization - how is it initialized here?

4. The authors also use the operational loading conditions as input. You are never specific about which one you are using. You mention wave height, wind speed, and peak period for the simulations. Are those the input as well? How sensitive is your solution to having/not having those inputs to the encoder and then back to the decoder?

5. They should consider extending their analysis to scenarios involving simultaneous damage to two mooring lines. This will allow them to test the methodology's capability to capture the coupled dynamics between the lines and their impact on the floating platform's overall response.