Sign-Constrained Neural Processes for Transferring Probabilistic Fire Danger across Fujian, China

Danger ratings are built where fires have been recorded and used where they have not, so their value rests on how much of a fitted response survives a move to another landscape. We test that question on a benchmark assembled for Fujian province, southeast China, from 43,400 quality-filtered VIIRS and MODIS active-fire detections, daily reanalysis meteorology and terrain derivatives: 171 grid cells of 0.25°, 2922 days and 15,205 fire cell-days at a base rate of 3.04%. Models are fitted on the coastal belt and the lowland interior (2015–2019) and evaluated on the mountain interior in 2021–2022, a region absent from training. The model we propose keeps the response linear in standardized predictors, learns a prior over its coefficients from 24 source blocks, and constrains the humidity and wind coefficients by sign while training, which makes an increase of predicted probability with humidity, or a decrease with wind, unreachable for any input. On the held-out region it reaches an AUC-PR of 0.079 (95% interval 0.067–0.092), against 0.093 for logistic regression and 0.101 for a random forest, while its negative log-likelihood of 0.135 trails the best baseline at 0.123. Two consequences follow. Exact monotonicity is obtained at a measurable cost in sharpness, since every unconstrained model fails the wind test on 100.0% of matched pairs. Local labels do help as well: 256 labelled cell-days lift AUC-PR from 0.079 to 0.101, the same level a logistic regression reaches by refitting on those labels (0.103), so the closed-form update is a safe instrument, not a source of gain.