What a structural test cannot identify: degeneracy-aware Bayesian calibration of a multiscale material mode

Multiscale material models are calibrated against structural tests, and which parameterssuch a test can identify is asked less often than it should be. When the stiness operatordepends linearly on the constitutive tensor while the loading does not, so that the responseis homogeneous of degree one, and the unresolved architecture enters as a multiplicativeamplitude, the test identies exactly one scalar combination and the orthogonal direction isexactly at: no quantity of data removes it. We state this as a proposition, verify that twoparameter pairs related by the degeneracy generate identical data to 0, and measure it throughthe Fisher information, whose null direction is recovered as (0.7071, −0.7071). An independentroute conrms it: LevenbergMarquardt from 25 starting points returns the same mist to4.7 × 10−15 with the tensor scale ranging over 600 orders of magnitude, and the informationfrom its Jacobian reproduces the joint condition number to 2.7 × 10−10.Nanoindentation breaks the degeneracy, being homogeneous of degree one in the tensor veried to 8.88 × 10−16 and blind to the mesoscale. Both single-channel informationmatrices are singular, for complementary reasons; jointly they have rank two, with conditionnumber 196. Sweeping the indentation noise turns the analysis into experimental design: thearchitectural amplitude is determined to 0.70.9 % at realistic precision a Laplace gurethat the full posterior of the recovery study conrms at 1.2 % and the return saturates ata oor of 0.7 % set by the compression noise rather than by the indentation.Two methodological consequences follow. Freezing the strain eld of a single solve givesan emulator that is linear in the tensor and, by minimum potential energy, never below thesolved value: its error has a known sign over the whole admissible cone, reaching 1.205 % overthe prior, and a bias of known sign is what makes a mean-shift correction eective inside asampler. And the identiability analysis supplies the coordinates in which to sample: therotation that decouples the two channels brings the posterior correlation from 0.98 to 0.13and costs 4.0 fewer calls to the expensive model per eective sample. We separate that eectfrom the algorithm, because the two are easily confused where the ridge is straight anadaptive proposal learns it as well, and the rotation's advantage is only that it is known inadvance; where material parameters bend the ridge, adaptation fails at Rˆ = 15.0 and theanalytic decoupling is what remains. Identiability analysis is normally run as a diagnostic;we argue it should also be run as a change of basis.