Certified Monotone Probabilistic Networks for Recipe-to-Specification Modelling and Inverse Design of Knitted Fabric Areal Density

Surrogates fitted to observational records with co-selected settings can invert physically required signs. In a public table of 10,902 weft-knitting production records where the recorded characteristic is the booked areal density, loop length and areal density are positively associated, which is opposite to the sign required by the Munden relation, and the required sign reappears only when yarn linear density is held fixed. We present a recipe-to-specification surrogate, a gated network that is certified monotone by construction, with conformalised quantile heads, and prove that conformalisation preserves the network’s certificate and marginal coverage. In this table, unconstrained learners move against the required direction on 37.8–53.4% of finite-difference probes, and the constrained learners on none, and direct Munden models are 2.7 and 2.0 times less accurate than the certified network on random and temporal splits. At fixed yarn, the required sign appears in single jersey and LS/J, holds on balance in rib, and does not appear in pique or fleece terry. On a synthetic benchmark with known truth, the constrained models have a lower interventional-grid error in 18 out of 18 comparisons under Munden truth, and 17 out of 18 under non-Munden truth, but they are markedly worse on fleece terry, where the truth contradicts the constraint. Inverse design with the model produces candidate recipes for a booked specification; these recipes have not yet been knitted and measured.