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At the moment, the tag has the following usage guidance:

A field which employs computers to model and study chemical systems and chemical behavior, using various models, from approximations of the Schrödinger equation to Monte-Carlo simulations, to modeling with differential equations.

I am especially puzzled by the "modeling with differential equations" part. How is modeling computational? Isn't translating physical reality to mathematical models very much theoretical rather than computational?

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    $\begingroup$ Suppose you have a system that is well modeled by a set of differential equations. How do the equations get solved, if the analytical route is too difficult? Presumably, the equation solutions, whether analytical or numerical, are to be compared with experimental results. $\endgroup$
    – Ed V
    Commented Aug 12, 2022 at 13:06
  • $\begingroup$ @EdV I would use an ODE solver. Note that it's called solver, not modeler. $\endgroup$ Commented Aug 12, 2022 at 13:10
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    $\begingroup$ I consider modeling as "the wired frame" of model equations and "covering sheets/layers" of computations of numerical solutions. There is no model before the model image is computed. By other words, equations (+plus analytical/numerical algorithms to solve them ) are just instructions how to create the abstract model of particular reality aspect. // But I also see a domain overlap with mattermodeling.stackexchange.com $\endgroup$
    – Poutnik
    Commented Aug 12, 2022 at 14:30
  • $\begingroup$ @Poutnik I am not claiming that models are God-given. One creates a candidate model and then numerical methods can help validate the model. However, by the time a model is considered good enough, one can work with the ODEs in ways that are non-computational. And there is a whole field based on and devoted to extracting qualitative information from ODEs without ever solving them. $\endgroup$ Commented Aug 12, 2022 at 14:40
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    $\begingroup$ Well, supercomputers compute a model of atmosphere state every few hours. Is the model predicting the future state of atmosphere the set of Richardson's partial differential equations, the ways how they are solved, the way how additionaldata are involved, or the computed schema, describing the future atmosphere for given regions and time ? In a sense, all of them together. There are computational and non-computational parts in the modelling. Sometimes computational part is trivial, easy and fast, sometimes the exact opposite. $\endgroup$
    – Poutnik
    Commented Aug 12, 2022 at 15:02
  • $\begingroup$ @Poutnik Yes, but the point of this question is whether the tag's usage guidance needs improvement in order to promote better tagging. I am playing the librarian's role here. A rich library where nothing can be found due to lassitude and sloppiness is a very sad sight. $\endgroup$ Commented Aug 12, 2022 at 15:26
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    $\begingroup$ Sure, that is why I was just commenting. I do mean there is serious overlap with this tag and MMSE (which I guess is newer). Many comments in the main CH SE refer computation questions to this sister site. $\endgroup$
    – Poutnik
    Commented Aug 12, 2022 at 15:55
  • $\begingroup$ The usage guidance is a summary based on chemistry.stackexchange.com/tags/computational-chemistry/info The extended information is more useful and might have been chewed up in creating the summary. $\endgroup$
    – Buck Thorn Mod
    Commented Aug 13, 2022 at 8:02

3 Answers 3

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I am especially puzzled by the "modeling with differential equations" part. How is modeling computational? Isn't translating physical reality to mathematical models very much theoretical rather than computational?

I see reality modeling as kind of analogy to the IT TCP/IP protocol stack - a 4-layer model:

  • "Application layer" - Mathematical description(modeling) of reality, usually by equations, often partial differential ones
  • "Transport layer" - Mathematical description of analytical/numerical solving of equations above, applied on available data
  • "Internet layer" - Algorithms generating data for values of reality atributes, modeling particular aspects of reality
  • "Link layer" - Interpretation or application of computed reality model.

These steps may be trivial or complex, following complexity level of the modeled part of reality.

Some may consider only the top layer as scientific models of reality and in a narrower model meaning, they are true. But in broader meaning, it is the whole stack. One cannot be a great cook if all he has is a book of never tried great recipes. Equations are useless if not applied.


The summary info for the Matter modeling SE site, which may compete for focus with CH SE computational-chemistry tag:

Matter Modeling Stack Exchange is a question and answer site for Matter Modelers: computational chemists, material scientists, particle physicists, data scientists, and anyone else who uses computational methods to study molecules and materials.

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  • $\begingroup$ What if "to modeling with differential equations" were replaced with "to validation of mathematical models based on differential equations"? $\endgroup$ Commented Aug 14, 2022 at 17:07
  • $\begingroup$ I do not see much difference, those layers are abstract enough. lf you mean formal prove of internal consistence of mathematical model, that can be done solely in the top level, as it does not need input data. Otherwise all layers have to be involved. $\endgroup$
    – Poutnik
    Commented Aug 14, 2022 at 17:17
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The usage guidance is a summary based on https://chemistry.stackexchange.com/tags/computational-chemistry/info . The extended information is more useful and might have been chewed up in creating the summary.

How is modeling computational? Isn't translating physical reality to mathematical models very much theoretical rather than computational?

Yes, computational chemistry requires models (discrete ones often) but the reverse is not true. Models exist outside of computational chemistry, and those models are generated using theory. Computational methods often play an important part in testing models.

I am especially puzzled by the "modeling with differential equations" part.

I also find this could use editing. It presumably refers to finite element methods.

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"I am especially puzzled by the "modeling with differential equations" part. How is modeling computational? Isn't translating physical reality to mathematical models very much theoretical rather than computational?"

Often the word "modeling" includes not only constructing the model, but also solving it. "Modeling with differential equations" is computational because most differential equation need to be solved using "computations". I agree with you that the word "modeling" wasn't needed (or at least, wasn't the perfect word choice). If you were to suggest a tag edit, I would most likely click "approve" (assuming that I would agree with your edit). I also don't think this is in the top 50 most important things to work on at Chem.SE though :)

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    $\begingroup$ In some way, we can see mathematical description by equations as a reality model. In other way, we may see solving these equations for particular data as construction of an abstract model of reality, as equations themselves are not a reality model. Like the 3D CAD computer data of a house versus the 3D printed 1:N house model for client presentation. Which one is a model? Both are models, in different step levels of modelling realization. $\endgroup$
    – Poutnik
    Commented Aug 13, 2022 at 6:53

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