the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
AutoQS v1: Automatic parameterization of QuickSampling based on training images analysis
Grégoire Mariethoz
Abstract. Multiple‐point geostatistics are widely used to simulate complex spatial structures based on a training image. The use of these methods relies on the possibility of finding optimal training images and parametrization of the simulation algorithms. While methods for selecting training images are available, parametrization can be cumbersome. Here, we propose finding an optimal set of parameters using only the training image as input. The difference between this and previous work that used parametrization optimization is that it does not require the definition of an objective function. It is based on the analysis of the errors that occur when filling artificially constructed patterns that have been borrowed from the training image. The main advantage of our approach is to remove the risk of overfitting an objective function, which may result in underestimating the variance or in a verbatim copy of the training image. Since it is not based on optimization, our approach finds a set of acceptable parameters in a predictable manner by using the knowledge and understanding of how the algorithms work. The technique is explored in the context of the recently developed QuickSampling algorithm, but it can be easily adapted to other pixel-based multiple-point statistics algorithms using pattern matching, such as Direct Sampling or Single Normal Equation Simulation (SNESIM).
Mathieu Gravey and Grégoire Mariethoz
Status: final response (author comments only)
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RC1: 'Comment on gmd-2022-229', Anonymous Referee #1, 17 Oct 2022
This very interesting paper would ease the use of multiple-point statistical simulation by optimizing the parameters that generally require manual tuning before acceptable results are obtained.
The main problem with the current version is that it has been written in a hurry, it contains too many typos, and, more importantly, the explanations are unclear, sometimes because of brevity, sometimes because of improper English usage, sometimes because the author presumes that the reader knows much more than he should.
The paper needs a thorough review of the text to make it understandable to someone who is not an expert in MPS simulations and might not have worked with either QS or DS. A few more sentences or paragraphs explaining some of the parameters or some of the technicisms used would provide a better understanding. A rearrangement of some of the sentences is also necessary to ensure that the flow of information is logical.
Many sentences with interesting statements are thrown out in the middle of paragraphs with which they are unrelated without supporting evidence.
And most importantly, the authors must emphasize that their approach is valid for a specific training image. When new simulations are to be generated, a new optimization must be carried out.
An annotated manuscript is attached with detailed comments.
- AC1: 'Reply on RC1', Mathieu Gravey, 25 Feb 2023
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CEC1: 'Comment on gmd-2022-229', Juan Antonio Añel, 12 Dec 2022
Dear authors,
Unfortunately, after checking your manuscript, it has come to our attention that it does not comply with our "Code and Data Policy".
https://www.geoscientific-model-development.net/policies/code_and_data_policy.html
You have archived your code on GitHub. However, GitHub is not a suitable repository. GitHub itself instructs authors to use other long-term archival and publishing alternatives, such as Zenodo. Therefore, please, publish your code in one of the appropriate repositories, and reply to this comment with the relevant information (link and DOI) as soon as possible, as it should be available for the Discussions stage. In this way, you must include in a potentially reviewed version of your manuscript the modified 'Code and Data Availability' section, the DOI of the code.Juan A. AñelGeosci. Model Dev. Exec. EditorCitation: https://doi.org/10.5194/gmd-2022-229-CEC1 -
AC3: 'Reply on CEC1', Mathieu Gravey, 25 Feb 2023
We will upload the code to Zenodo as a new package version release.
Citation: https://doi.org/10.5194/gmd-2022-229-AC3
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AC3: 'Reply on CEC1', Mathieu Gravey, 25 Feb 2023
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RC2: 'Comment on gmd-2022-229', Ute Mueller, 01 Jan 2023
The paper by Gravey and Mariethoz provides an interesting approach to determining a suitable parameter set for geostatistical multiple point simulation. The method is based on simulating individual pixels and using the prediction error as the sole metric to find optimal parameters.The approach is sufficiently novel to warrant publication ultimately, but at present it lacks clarity and the quality of the scientific writing needs to be improved.
Comments on the Introduction
1. You state that the parameterisation depends on the specifics of the algorithm. This is undoubtedly true, but it would help the reader to have a quick synopsis of the two algorithms and associated parameters before going into details of selection of parameters.
2. Line 45: I would not talk about philosophies but rather about approaches here.
3. Lines 47 to 49: It would help if you explained what kind of metrics were computed and I assume you mean that the corresponding metrics computed for the simulation matched as closely as possible. But this is not stated clearly.
4. Line 60: You say “If both approaches show good results, then they are both related to optimization methods, and therefore the user has no control over the duration of the optimization process”. It is not at all clear to me what you are trying to say here. Both approaches rely on optimization of some kind, irrespective of the quality of the results. So can you please be more precise?
5. Lines 70-71: I am not sure what you mean when you say “the underlying principle of our approach is that a sequence of well-simulated pixels converges to a good simulation overall”. Please clarify! (what does well-simulated mean? How can a sequence of pixels converge to a good simulation? Good in what sense?)
Comments on “Challenges related to inappropriate parameters”
Most of this section is about verbatim copy, should you maybe change the title of the section to a title that highlights this? Also, it seems the issue of “verbatim copy” is one of DS and QS only? It is also not clear how constraining the conditional probability distribution of Z(x) given an MPS algorithm is related to the issue of verbatim copy, (for ENESIM, SNESIM and IMAPLA this justifies the need of a large enough training image)
6. Line 90-91: it would be useful to introduce the abbreviation for the threshold here
7. Line 92 The definition of “verbatim copy” should be provided here rather than in lines 98 following.
Comments on Method
8. Line 125 : The sentence “Binary variables are a particular case of continuous and categorical variables.” seems a throw-away comment whose purpose is entirely obscure.
9. In the pseudocode for the QS algorithm it would help to have a definition of the entire parameter set
10. line 138: What do you mean by “find a candidate in T those matches N(x) using \theta?
11. line 144: What do you mean by “ A perfectly simulated pixel is a pixel that respects the conditional probability distribution” what probability distribution do you mean here? Presumably this is related to formula (1)?
12. line 159: please define the discretised parameter space \theta (it is not really defined in line 1 of algorithm 2)
13. line 161: you need to define what “th” stands for ( I do realise you mean threshold, …..)
14. in line 162 you talk about representative stages D of the simulation, but then in line 164 you say that D represents the density of a neighbourhood. What do you mean by density of a neighborhood? Also, is D part of the parametrerisation theta? If not, why not?
15. Should algorithm 2 not have as a first step “randomly generate a set “V”
16. What do you mean when you say sample a neighborhood N(v) from T respecting D???, see also line 180
Comments on “An efficient implementation”
Section 3.1 needs to be proofread carefully. You really should adhere to principles of good scientific writing and avoid starting sentences with symbols and also check word-order.
17. Line 198 The variables \theta_h and \theta_S represent sets. Sets cannot be added, but you can define their union. Thus \theta_h \cup \theta_S would be more appropriate than \theta_h + \theta_S, alternatively write \theta=(\theta_h, \theta_S)
18. the criterion you list in formula (4) needs further explanation and the sentence “… a given parameterisation is only further explored if the error is a range of a \sigma” does not make sense. To me the top line in 203 would make more sense written as
\epsilon(\theta,D,T)-\epsilon(\theta_{min}, D,T) > \frac{1}{2} (\sigma(\theta,D,T)-\sigma(\theta_{min}, D,T))
Comments on Results
19. Line 213 the term “uniform” has specific connotations. I would suggest the term “fixed” might better capture what you mean here. Also, does the kernel you consider here also have radial shape and why do you use \omega, when later on you use w?
In figure 3 you introduce the term “ignorance treshold” without provision of a definition.
20. Lines 227-228: “we also note that even if the parameterisation is logical it is diffifult to predict” what do you mean?
21. I believe Figure 4 warrants more discussion. Also, in the discussion n line 238 you use the term “two stage process” but that seems ill chosen for the behaviour you describe
22. line 252: It is the neighbours furthest from the location considered that are allocated the negligible weights with large values of the shape parameter \alpha, and the sensitivity of n decreases, but n doesn’t become insensitive
23. in line 270 the word adaptative needs to be inserted
Figure 8: the title of the figure in row 3 column 1 needs to be corrected.
In the appendix, please provide a reference for each of the training images. It is interesting to note that the variogram reproduction for Delta Lena shows the “right” shape, but the sill are too low and connectivity is not as good as one would hope. Any thoughts on why this happens?
It would also be good to see some results for multivariable images. You allude to the algorithms working in this case also, but being slow
Citation: https://doi.org/10.5194/gmd-2022-229-RC2 - AC2: 'Reply on RC2', Mathieu Gravey, 25 Feb 2023
Mathieu Gravey and Grégoire Mariethoz
Mathieu Gravey and Grégoire Mariethoz
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