General comments

The preprint deals with the analysis of the performance of different machine learning methods in inverse modelling of groundwater system. It compares the TNNA method described in previous papers by the authors' collective (J. Chen et al., 2021) with other machine learning methods and shows significantly better performance of the TNNA method compared to several other methods.

The scientific contribution of the preprint is fair, but not very good. The paper does not introduce a new method, but presents on two selected academic problems the good performance of a previously described method. It uses appropriate procedures and criteria for comparison and the results are presented in a very clear, lucid and convincing manner.

The study is well constructed and executed; its scientific quality is very good but I have one reservation about the chosen methodology that I will describe in the following paragraph.

Specific comments

My only comment on the methodology used in the preprint, which I consider to be significant, is the failure to include measurement error in the test problems used. The optimization problems are well chosen, but the measurements used to calibrate the parameters (inverse modeling) were not burdened with any random error emulating measurement error.

This may have a significant impact on the applicability of the method. In inverse modelling, in practice, we face two types of problems - the lack of ability to fit the measured data and the so-called overfitting of the data consisting in their too accurate replication by the model (by including the measurement error in the model parameters, i.e. damaging them in terms of the ability of further prediction). If the aim of the study was to show possible applicability of TNNA to solution of inverse models of groundwater problems, this feature of the study does not allow to fulfil the intended objective.

Technical corrections

The language of the preprint is clear, I did not notice any specific errors or typos.

While the topic covered could be of interest, using a Gaussian covariance (or double exponential, as it is called in the paper) without any nugget effect renders the comparison exercise a purely academic exercise with little or no practical bearing. Besides the fact that the underlying random function model behind the K-L expansion is the multiGaussian one, another decision that is far from reality.

In summary, for this paper to have any practical interest, the comparison exercise should be performed using a clearly non-multiGaussian random function with the kind of spatial variability one is expected to find in the field, not the unrealistic smooth spatial variability induced by a Gaussian covariance function.