A Versatile Deposition Model for Natural and Processed Surfaces

Round 1

Reviewer 1 Report

This article essentially generalizes the Kardar-Parisi-Zhang approach describing the evolution of the roughness of a growing surface. The article uses a larger number of parameters, which are also probabilistic in nature. Modelling has been carried out for a very large number of combinations of parameters, and the simulation results are collected into a single database, which allows you to correctly select probabilistic parameters in order to obtain the desired simulation result.

I liked the article, it is quite clearly written, examines the most important parameters and contains a comparison with various types of real growth surfaces. I think this approach is a real improvement on the KKardar-Parisi-Zhang approach, which was very popular in the 20th century.

In principle, I have no comments on the substance of the article, so I believe that it can be published in current form.

Author Response

This article essentially generalizes the Kardar-Parisi-Zhang approach describing the evolution of the roughness of a growing surface. The article uses a larger number of parameters, which are also probabilistic in nature. Modelling has been carried out for a very large number of combinations of parameters, and the simulation results are collected into a single database, which allows you to correctly select probabilistic parameters in order to obtain the desired simulation result. I liked the article, it is quite clearly written, examines the most important parameters and contains a comparison with various types of real growth surfaces. I think this approach is a real improvement on the KKardar-Parisi-Zhang approach, which was very popular in the 20th century.  In principle, I have no comments on the substance of the article, so I believe that it can be published in current form.

Thank you for your positive feedback and thorough review of our manuscript. We appreciate your recognition of our model's clarity and its potential as an improvement upon the KPZ approach. Your positive remarks on our examination of key parameters and comparison with real growth surfaces are appreciated, as they enhance the practical relevance of our model.  We thank you once again for your time and insightful comments.

Reviewer 2 Report

The paper is devoted to the development and analysis of a robust deposition model, which allows for simulating the dynamics of the growth process across a broad range of possible growth regimes. The generative approach proposed by the authors is notably simple, as it has only a few hyperparameters that describe certain physics-based phenomena on the surface (nucleation, smoothing, diffusion, etc.). This combination still enables the description of various morphologies, which, in my opinion, is a significant advantage of the model. It contains many illustrations in the Supplementary Materials, proving its robustness. This paper aligns with the journal's scope and serves as a useful example for readers on using modern approaches to describe complex systems through modeling. I believe it might interest the readers of Dynamics.

The following questions and suggestions arose during the review:

1)  I have not found Supplementary Materials 1 attached to the paper during the review, so I was not able to analyze or attempt to use the code. Certainly, its availability to readers, along with a description enabling its use, would strengthen the article.

2) I suggest adding a more detailed description of how the model's hyperparameters are connected to the macroscopic conditions of growth. For instance, the number of nucleation events is not directly controlled by experimenters, whereas supersaturation is. However, nucleation probability is determined by supersaturation according to nucleation theory, which shows an extremely nonlinear dependence. The same applies to surface diffusion (e.g., temperature), smoothing factor (the surface energy, which depends on the solvent of the solution from which the crystal grows, etc.). This could be beneficial for experimenters using the code to simulate and/or reproduce experimental morphologies, or even for determining in which direction the conditions need to be changed to obtain, for example, a smoother or less porous morphology, etc.

Considering these points, I believe the article is suitable for publication after addressing these comments and undergoing minor revision.

Author Response

The paper is devoted to the development and analysis of a robust deposition model, which allows for simulating the dynamics of the growth process across a broad range of possible growth regimes. The generative approach proposed by the authors is notably simple, as it has only a few hyperparameters that describe certain physics-based phenomena on the surface (nucleation, smoothing, diffusion, etc.). This combination still enables the description of various morphologies, which, in my opinion, is a significant advantage of the model. It contains many illustrations in the Supplementary Materials, proving its robustness. This paper aligns with the journal's scope and serves as a useful example for readers on using modern approaches to describe complex systems through modeling. I believe it might interest the readers of Dynamics.

Thank you for your evaluation of our paper. We appreciate your recognition of our robust deposition model, designed to simulate growth dynamics across a broad range of regimes. Your acknowledgment of the simplicity of our generative approach, despite incorporating key physics-based phenomena, is encouraging. We are pleased that you found the model's ability to describe various morphologies to be a significant advantage. Below you can find our responses to your comments and remarks.

1)  I have not found Supplementary Materials 1 attached to the paper during the review, so I was not able to analyze or attempt to use the code. Certainly, its availability to readers, along with a description enabling its use, would strengthen the article.

We thank the reviewer for the feedback. The source code has been shared with the publisher, together with a read me file, to facilitate its usage by the curious readers.

2) I suggest adding a more detailed description of how the model's hyperparameters are connected to the macroscopic conditions of growth. For instance, the number of nucleation events is not directly controlled by experimenters, whereas supersaturation is. However, nucleation probability is determined by supersaturation according to nucleation theory, which shows an extremely nonlinear dependence. The same applies to surface diffusion (e.g., temperature), smoothing factor (the surface energy, which depends on the solvent of the solution from which the crystal grows, etc.). This could be beneficial for experimenters using the code to simulate and/or reproduce experimental morphologies, or even for determining in which direction the conditions need to be changed to obtain, for example, a smoother or less porous morphology, etc.

We thank the reviewer for the valuable feedback. We added a discussion at the end of the “Proof-of-Concept: Urea Deposit Formation Section”, and explained how domain expertise, such as what triggers the deposit nucleation process for a given application can be taken advantage of to use the model better.

Reviewer 3 Report

This work presents a comprehensive deposition model aimed to investigate the growth dynamics of deposits on surfaces under practical situations. Furthermore, it addresses the difficulty of characterizing the complex morphology of deposits with large visual fluctuations. tackles important problems about deposition initiation, nucleation point behavior, spatial scaling, deposit growth rates, spread dynamics, and surface mobility. The model uses a top-down methodology and a small set of hyperparameters to generate various surface morphologies, thereby reverse engineering the sub-physics of the deposit generation process. The debate included a full explanation of all the various preposition factors; thus, I recommend that this work be considered for publishing in this Journal in the style described.

Author Response

This work presents a comprehensive deposition model aimed to investigate the growth dynamics of deposits on surfaces under practical situations. Furthermore, it addresses the difficulty of characterizing the complex morphology of deposits with large visual fluctuations. tackles important problems about deposition initiation, nucleation point behavior, spatial scaling, deposit growth rates, spread dynamics, and surface mobility. The model uses a top-down methodology and a small set of hyperparameters to generate various surface morphologies, thereby reverse engineering the sub-physics of the deposit generation process. The debate included a full explanation of all the various preposition factors; thus, I recommend that this work be considered for publishing in this Journal in the style described.

We thank the reviewer for his/her time, consideration and the positive evaluation of our work. We appreciate your recognition of our deposition model and its ability to address challenges in characterizing complex deposit morphologies. Your recommendation for publication is greatly appreciated.

Reviewer 4 Report

This work presents combination of top-down model simulation and machine learning about the deposition of powder-like substances.  The work is mainly focused on the porous materials, which is important in various applications.  The model and procedures are sound and the publication is beneficial to the readers.

My only concern is the usage of "hyperparameter".  By my understanding, this term is about the number of the parameters, choice of the model itself.   I think "parameters" is more suitable.  Please consider this point.

Author Response

This work presents combination of top-down model simulation and machine learning about the deposition of powder-like substances.  The work is mainly focused on the porous materials, which is important in various applications.  The model and procedures are sound and the publication is beneficial to the readers.

My only concern is the usage of "hyperparameter".  By my understanding, this term is about the number of the parameters, choice of the model itself.   I think "parameters" is more suitable.  Please consider this point.

We thank the reviewer for the feedback, and positive evaluation of our work. We updated the manuscript accordingly.

Round 2

Reviewer 2 Report

The authors addressed all the points, therefore I suppose that the paper may be accepted for publication.

Reviewer 4 Report

The revision has no problem.