inverse problems · configuration space what the projection keeps · underdetermined experiments, collapsed configuration spaces, and the tools brought from outside · started October 2026

The brief

The brief

The founding note of 14 October 2026, organised into twelve theses, then kept verbatim below. The ideas are Iñigo González de Arrieta's, shared with Josu; Josu's brief is to think on them and develop them. Ids never change; theses added later are appended with the log entry that adds them.

The problem

  • T01 Inverse problems in which the theory is known — the model that governs the response of the system to the probe — but the values of the parameters that enter it are poorly known.
  • T02 The experiment itself is underdetermined: too many parameters are involved for what the measurement can tell apart.
    Named as a second key concept, next to the poor knowledge of the parameter values.
  • T03 Knowing the theory is therefore not enough to infer the actual behaviour of the system, nor to say why the observed response is what it is.

The picture

  • T04 The experiment is a kind of projection. In that projection many parameters are collapsed: the configuration space of the system is collapsed onto the space of what is measured.
  • T05 Extracting the values of the parameters from the projection is not evident, not easy, and perhaps not possible at all — unless something else, an external tool, is brought in.

The known case

  • T06 Powder diffraction: the result of a Rietveld refinement of a crystal structure is compatible with many combinations of atomic coordinates, when the coordinates are the degrees of freedom used.
  • T07 Mode crystallography is the external tool there: it explores the configuration space in another set of independent coordinates, the amplitudes of the symmetry-adapted modes. After the analysis the structure is again described by atomic coordinates, but many of their possible values have been discarded by the symmetry the mode analysis searched with.

The proposal

  • T08 In these highly underdetermined inverse problems, bring in other tools: machine learning over thorough, massive data sets.
  • T09 Those data sets are to be treated massively and automatically by scripts, not analysed by hand one experiment at a time.
  • T10 The valuable user knowledge is not applied by hand to each data set; it is used to write the scripts that treat the data — the symmetry in diffraction is the example of super-user knowledge put in a script.

Scope and method

  • T11 The paper in the project (Daun et al. 2019, Drude parameters of liquid germanium nanoparticles from extinction measurements) is another example of the same situation; it is not to become the whole subject.
  • T12 Method: analyse the ideas, put them in a sorted, coherent discourse, think and rethink them; then elaborate, propose, innovate; then discuss. The work follows the protocol of the FOCUS–difes and FullProf (diff-ref-struct) projects: a website holding everything, a repository, a log on the site, and the sources used.

The text, verbatim

As written, typing included, so that the organised list above can always be checked against it.

I am going to write down some ideas; for the moment, they are not mine, are Iñigo Gonzalez de Arrieta’s, he has shared them with me…I would to think on them, and to try to develop them a little bit further

the main point is the following: the inverse problems; even better, the poor knowledge on the actual values for the underlaying models governing the physics of some inverse problems, in the form of “I have the experimental data from an experiment, I kwno the theory that governs the theoretical response of the system to the probe used in the exepriment, but there are somany paramters involved, and the experiment itself is so undetermied (this is another key concept), that even if I know thigns, those are not enough to infere the actual behaviour of the system; or why the actual response is what I observe”…it something like that; Of course, the experiment is a kind of projection, and in that projection, many parameters are collapsed, the configuration space is collapsed, and the extraction of the values of those parameters from the projection is not evident, is not easy, perhaps even it can not be done, unless something else, another external tool is not used

for instance, in the case I know most, perhpas, the powder diffraction of materials, the refinement of the diffractograms, the final result of the refinement, in the case of the crystla structure, for instance, is compatible with many possible combinations of atomic cooridnates, if that is the set of degrees of freedom use; here it comes the mode crystallography, the external tool, to make some exploration of the configuration space, now described in another set of independent coordinates, the amplitudes of the mode adapted to the symmetry, so that the exploration of the configuration space (after the analysis, of course, we do describe the crystal structures by the atomic coorinates, whose many values have been discarded byt eh mode analysis, which searches suing symmetry…)

so the idea is that in thses highly indetermined inverse problems tray to use some other tools, machine learning over throughout data, massive data sets, already massively adn automatically trated using scrpts so that the crafting, the valuable user knowledge is not introduced by hand analyszing some experimental data one by one soo to ssay, but, that knowledge is used to create the scripts to massively treat the data (the symmetry in diffraction, the guidance by the super-user knowledge put in the scripts)

analyze the ideas, create a threat, a discourse, let’s try to put the feet on the floor

the paper in the project is another example (but I would not like to stuck there, it is another example)

so, the ideas, put them in a discourse, sorted, coherent, think and rethink on those, wisely then, let’s discuss, let’s elaborate them

but you also elaborate, propose, innovate, wisely report et’s follow the portocol we have been following in the case of FOCUS-DifFIT and the FullProf cases, a website which is going to hold everythng, a repository to save everythign the log in the website, the source we are using…