The programme
Seven proposals, from the cheapest to the largest, each with what it would show, what it needs and roughly what it costs; then six questions the discussion has to answer before any of them starts. Proposed 14 October 2026 (L006). Ids P1… and Q1… never change.
The diagnostic every fit should print
At the end of any refinement — Rietveld, dielectric, Drude — compute the singular value decomposition of the weighted Jacobian at the solution and print three things: the stiffness spectrum (the singular values, on a log scale, so that the decades show); the two or three sloppiest directions written out in the names of the parameters that compose them ("0.7 × occupancy(O2) − 0.7 × B_iso(O2)"); and the credible region of the one pair of parameters the user cares about, drawn, not tabulated. Programs already compute everything needed; nobody prints it this way.
Shows: which of the three kinds of underdetermination the fit is facing, at a glance. Needs: an engine that exposes the Jacobian; the diff-ref-struct core does, difes does. Cost: days. Theses: T02, T05.
The toy that makes the thesis visible
One synthetic displacive structure — a perovskite with a known octahedral-tilt distortion from a cubic parent — and one instrument model. Simulate the pattern with noise. Refine it from a few hundred starting points in atomic coordinates, and again in symmetry-mode amplitudes; map the tube of each in two dimensions; draw the valley in coordinates and show how it aligns with one axis in mode space. Then remove information (shorten the angular range, raise the noise, switch X-rays for neutrons) and watch the valley lengthen and turn.
Shows: the argument of §4 of the discourse as a figure series, with the script that made it. Needs: a scriptable Rietveld engine with mode-described phases (the diff-ref-struct core, or GSAS-II with ISODISTORT amplitudes) and AMPLIMODES for the decomposition. Cost: two weeks. Theses: T04, T06, T07.
The corpus: one family, treated whole by scripts, the tube kept
Take one structural family where the parent is unambiguous (the perovskites \(\mathrm{ABX_{3}}\) are the obvious one); pull every entry from a structure database; decompose each against its parent (the script carries the parent assignment as a recorded input, with its provenance); simulate patterns under a few instrument models and noise levels; run the scripted refinement in mode coordinates from several starting points; and store everything — solution, singular spectrum and vectors, alternative minima, amplitudes with uncertainties, residuals — in a queryable table. Not a structure per entry: a tube per entry per instrument.
Shows: what T09 and T10 produce when the output is the right one. Needs: P2's machinery, a database licence, compute for some tens of thousands of refinements. Cost: a quarter, one person. Theses: T08–T10.
Learn over the corpus what no single refinement shows
Three targets, in order of difficulty. Identifiability maps: for each mode of the family, as a function of radiation, range and noise, how well the corpus determines it — a property of the forward map, learned from the corpus, and true before any sample is measured. Amortised posteriors: a network trained on (amplitudes, simulated pattern) pairs that returns the posterior over amplitudes for a new pattern, with the branches of the fibre, in the time one refinement takes. Inadequacy flags: residual structure that recurs across the family, which is a wrong model and not noise.
Shows: §7 of the discourse, with the limits respected: distributions out, never points. Needs: P3. Cost: a quarter. Theses: T08.
The same scheme for infrared spectra, with difes
The configurations are the difes and FOCUS libraries of dielectric functions; the scripts are difes recipes extended to keep the tube; the simulated data are reflectance and emittance spectra on the group's real ranges with the group's real noise. The question to learn: which oscillator parameters a given range determines, and how the answer changes with the number of oscillators chosen. This is the case closest to Iñigo's work and the one on which the group has its own data to test against.
Shows: the move carried to a problem without space groups, where causality plays symmetry's part. Needs: difes, which exists, and its libraries. Cost: a quarter. Theses: T05, T08–T10.
Daun's problem, redone three ways
Reproduce Fig. 9 of Daun et al. from its stated model, priors and noise law; then replace the approximate Mie model and its model-error term by a forward surrogate trained once on the exact Mie sums; then compute, from the Jacobian over the prior range, the expected information gain per spectral band, and show that the ultraviolet source would have been chosen before the halogen lamp was tried. The paper's data are not public, so the reproduction is on synthetic spectra from its own parameters; the point is the method, not the numbers.
Shows: the three uses of learning in a problem Iñigo's community reads (JQSRT). Needs: a Mie code and an afternoon of MCMC. Cost: a month. Theses: T11.
A perspective, written with Iñigo
Not before the toy exists: a perspective article that states the three kinds, the projection picture, the generalisation of the mode-crystallography move, and the principle that the expert's knowledge belongs in the basis and in the scripts, with the P2 figure as its evidence and the three cases as its examples. Venue open; the argument is domain-independent and the examples are from two communities.
Theses: all.
Questions for the discussion
- Q1The name. "inverse-problems-configuration-space" is a folder name. What is the thing called — the collapsed configuration space, what the projection keeps, scripted expertise? The name decides what the perspective argues.
- Q2Which case leads. Diffraction has the exact tool and the clean toy (P2); infrared has the group's own data and Iñigo's expertise (P5). One of them is phase 1.
- Q3Which family for the corpus. Perovskites are proposed because the parent is unambiguous. Is there a family closer to the group's current work where the same holds?
- Q4The hypothesis as input. The discourse insists that the parent structure, the number of oscillators and the choice of Drude are recorded inputs with provenance, not hidden in the scripts. Agreed, and in what form?
- Q5What counts as a result. A value with an uncertainty, a region, a ranking of directions, a diagnosis that the model is wrong? Daun et al. ended with the last and it was the honest result. The programme proposes that the region and the ranking are always reported and the value only when the region is small.
- Q6Who writes the first script. T10 says the expert's knowledge goes into the scripts. The expert is Iñigo for the infrared case and Josu for the diffraction case; the script has to be written with them, not for them. In what sessions?