reviews: 
Comments: The article presents a study on the optimal design of a neutrinoless double-beta decay detector, a Rare Event Design. The authors introduce a surrogate model, RESuM, to solve this optimization problem and gain computational cost. This algorithm is based on Conditional Neural Process, incorporating prior information. The authors applied their work to the LEGEND experiment, a physics detector for neutrinoless double-beta decay.

The Rare event Design problem is mainly well stated and very clear.  The Large and Small N scenarios provide a very good understanding of the problem.

Bayesian prior knowledge with Conditional Neural Process (CNP) is clear in the text. CNP is explained in Appendix 11. The details shows the CNP is rich : by the use of surrogate modelling it generates data as fast simulator. It is more efficient for exploration of parameter space, uncertainty quantification and model validation.

The simulations, results and validation of RESuM are well explained.

RESuM reduces LEGEND neutron background by (66.5 \pm 3.5)% using only 3.3% of the computational power of traditional methods. This is a very good achievement.

All in all, this is a very good paper.
Strengths: The study is well conducted, very clear and concise, very interesting. The stated results are also very impressive and I hope this will lead to a larger breakthrough regarding neutrinoless double-beta decay community. The code is well presented and commented.

The work can be applied to Astronomy or Material Science. There are many other application possibilities in physics.

The work is motivated by the experimental discovery of neutrinoless double-beta decay (NLDBD), leading to answering the question ‘Why is there more matter than antimatter in our universe?’. Which makes a link with one of the opening questions of Javier Duarte talks at ICML24 ‘What is our universe made of?'. Thus, this work is very relevant for the community, and source of enthusiasm since the potential discovery of NLDBD would  lead to a Nobel-Prize-level breakthrough in physics.
Weaknesses: The authors indicates in the limitations and applications part that due to limitation of ressources available they computed only 100 High Fidelity simulation, maybe the publication of the article will help to convince to gain more ressources.

The authors also add that the active learning functions used un RESuM are simplistic, they will consider more sophisticated one in future work.

Minor comments that do not impact the score :

They are many inconsistencies in the notations, here are what I noted while reading, some might be redundant

Line 95, independent of the other events

Line 97, \mathbf{Phi} is not defined. Is it for conciseness?

Line 97,  dollar i dollar-th

Line 133, dollar { y \in  blablabla } dollar should make it appear on the same line

Line 153-154, Why highlight +1 and +0? Should be in dollar 1 dollar, same for dollar 0 dollar

Line 186, \mathbf{\phi}

Line 187, the same

Line 188,  \mathbf for theta

Line 172, The use of the nuisance parameters is unclear to me. The vertical bar followed by X_ki, phi_ki, theta_k means conditionally, if possible this should be improved.

Line 183, Figure 1 title is ‘Overview of the RESuM framework’ which is not the case of Figure 3. I assume the authors mean Figure 1 then.

In Figure 1, if the MFGP combines prediction from LF and HF simulations, why are the arrows pointing at them and not starting from them?

In the section 3, the vector of design parameters is \mathbf{\theta} thus it should be the same in all the study.

In the introduction, line 49, 51, 52. According to section 4 it should be in \mathbf?

In the section 3,

Line 92-93, is it in \mathbf?

Line 96, in \mathbf

Line 108-109, the same

Line 113-114, the same for \theta and \phi

Line 120,  the same for \theta, N should be in  dollar N dollar

Line 124-125, the same for \theta

Line 126, the same for \theta twice in the eq

Line 126-127, \infty should be used and same for \theta

In the section 4,

Line 140, mathbf for \theta

Line 151, the same for \theta_k the k-th simulation trial

Line 152, the same for \theta_k and \phi_ki

Line 153, it should be  dollar N dollar,  dollar y dollar also

Line 160-161, \mathbf for \theta_k and \phi_ki

Line 187-188, \mathbf for \phi and \theta

Line 204, the same for \theta

Line 209, the same for \theta_k and \phi_ki

Line 212-213, the same for \theta and \phi_ki

In the section 5,

Line 261-263, the parameters of design should be the same as in the figure 2 (\varphi in particular). Figure 2 represents explicitly 4 parameters, n is missing

Line 265, \mathbf for the design parameters and the corresponding space

Line 289-290, \mathbf for \phi

Line 298, the same for \phi

Line 360, I suggest ‘plotted against the five parameters in Fig3.’ Since you only present five.

Line 370-371, the same for \theta

Line 395-400, parameters should be consistent with line 261-263

Line 404-405, parameters should be consistent with line 261-263

Line 409, also

Figure 4 and Table 1, should be consistent with line 261-263

Line 441-446, the same for \theta and the corresponding space

In section 6,

Line 491 and 492, the same for \theta and \phi

In section 2,

Line 93-93, I would have introduced the stochastic process X_1, …, X_N and specify after that

Line 213, \mathbf for theta and phi

Line 222, ^{HF} is necessary for y_CNP

Line 224, ^{LF} is necessary for y_CNP

In the supplementary materials

Line 738, \mathcal{L}_k appears two times

A.9 must be improved:

Are \theta and \theta’ vectors as in the manuscript?

What kind of matrix is K? What are K_LL, K_\delta?

Could you give a reference or improve the theory, please?

A.10 \Theta must be in bold

Is \theta a scalar or a vector?

Could you give a ref or a proof for the approximation of I(\theta) for GP model? It seems simple, but I would like to be convinced this is right.
Recommendation: 10
Reviewer confidence: 5
Soundness/correctness: 4
Clarity: 4