Review Reports

Round 1

Reviewer 1 Report

The subject treated in this work is of high interest for the community of reactor physics. Indeed, to apply and accept the BEPU approach for reactor transient calculations, some challenges have to be overcomed. The work presented in this paper is an important step towards  a significant acceleration of this approach. The future work on a spatial reactor core models will be most significant.  

The article is structured clearly, the introduction gives a good overview of the recent advances in this domain. The application of the methods on the point-kinetic transient demonstrates clearly the obtained results.

The topic is very relevant, and this work contributes to go towards a more precise estimation of safety parameters which might contribute to improve the nuclear safety demonstration in the future.

Several references are missing (lines: 42, 108, 228)

In section 3.2, the FIgure 2 is not mentioned. If it presents something interisting, it should be commented in the text. 

In section 3.2, The figures use the notation Tc and Tf, without definition of those variables. 

In section 3.3, the matrix A dimensions described in Figure 3, are not clear. Please define precisly what those variables are, espacially: Fuel (fuel temperature ?), coolant (coolant temperature?) and Source ?  You can add those information in the Appendix A.

Section 3.3, it's unclear why the dimension 9 is mentioned, and a dimneion 10 appears in Figure 3. Please clarify or correct.

A general comment, you analyse specifically the temperatures of fuel and coolant, but what about the power. There also some safety concerns on this observable. The Figure 1, is in log-log representation, so it impossible to see the effects of the input parameter uncertainties on the power.

Typos present in lines: 

53: stadies

64: uncertainty

153: comprehensive

170: analysis

259: Appendix A

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Please can you explain the below-what does it mean?

The lowest precision level has been evaluated at which 10 the round-off error lays within the uncertainty of the model output. The calculations showed that the 11 total gain in the bit-complexity of about 24 times can potentially be actualized by running the reactor 12 core model on a field-programmable gate array

 

Please briefly discuss the methodology employed and its limitations for wider readership.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Reviewer report:

Applied Sciences (MDPI) - Manuscript ID: applsci-2072880

Acceleration of the Nuclear Reactor Uncertainty Quantification using Low Precision Hardware

Alexey Cherezov, Alexander Vasiliev and Hakim Ferroukhi

 

The authors performed nuclear reactor core uncertainty analysis using low-precision arithmetic. They determined that the lowest precision level that produces acceptable results involves 13 significand bits and found for that case that bit complexity is reduced by about a factor of 24 compared to full-precision calculations that involve 52 significand bits. My comments are as follows:

1. I believe that the title of the paper may be inappropriate/misleading, since low-precision (FPGA) hardware only provided motivation for the presented work and it was not actually used therein. My suggestion would be to replace "using Low Precision Hardware" with "by using Low-Precision Arithmetic" in the title.

2. On line 40 (p.2) it is not clear to me how reducing precision of the calculations can enable "improved physical and numerical approximations". I would suggest removal of that phrase.

3. Figure 5 does not seem to convey the intended message in the best possible way. I would strongly suggest that the authors use the same scales for the graphs in each column. I would recommend using x(-15,15),  y(-2,5) for the left column and x(-5,5), y(-1,1) for the column on the right and make sure that the legend in each graph is placed in the area with the lowest point-density. Also, it may be sufficient to place the legend only in the top left graph instead of having 8 copies of it.

4. Some references seem to be missing, as indicated by the question marks on lines 42 (p.2), 108 (p.3), 228 (p.6).

5. Figure 2 as well as Tables A1, A2, and A4 are not referenced in the text. Also, I would suggest insertion of "(see Table 1)" on line 247 (p.2) between "algorithm" and "required", in order to improve readability.

6. While the language used can be properly understood, some improvements in style may be in order.  For example, I assume that "one-fold boost of speed " (line 106, p.2) means that the speed was doubled and that "inherent chaotic behavior of a mathematical model" (line 38, p.2) means that the model (which does not behave chaotically) involves randomized variables or produces a distribution of results. On line 62/63 (p.2) it is not clear what "runs out on" means and perhaps the whole sentence should be rephrased, to start with "In the nuclear...". On line 39 (p.2) "reinvest" should probably be replaced by "redirect", and "perform more executions" should probably be replaced by "improve statistics in simulations". On line 47 (p.2) and in other similar instances (line 49 on p.2, line 93 on p.3, line 301 on p.9) "in" should be removed. On line 55 (p.2) "2 times decrease" should be replaced with "decrease by a factor of 2". On line 55 (p.2) "that" should be replaced with "which is". On line 53 (p.2) "stadies" should be replaced with "studies". On line 57 (p.2) "which deficiency" should be replaced with "deficiency of which". On line 303 (p.9) "times of that" should be replaced with "times that". On line 64 (p.2) "uncertfchereainty" should be replaced with "uncertainty" and "meant" should be replaced with "meaning that". On line 73 (p.2) the first "the" should be omitted. This list is not complete and additional corrections may be needed as well.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

I am completely satisfied with the author’s

response to my criticism.  I believe that the

paper now deserves to be published in this

revised form.