Which {Model} Should {We} {Trust} for {Sparse} {Spatial} {Prediction}? {Comparing} {Point} {Predictions} and {Uncertainty} in {3D} {Velocity} {Mapping} from {Sparse} {Borehole} {Observations}.

@inproceedings{Cilli2026RM,
 abstract = {Sparse borehole measurements are often combined with dense geological and geophysical predictors to populate three-dimensional subsurface models. Producing a spatial prediction is relatively straightforward; determining where predictions are reliable remains more difficult. We compare Random Forest (RF) with CV+ conformal prediction, an exact multitask Gaussian Process, TabPFN, and TabICLv2 for predicting shear and compressional wave velocities, Vs and Vp, in the Vierzon area. The predictors comprise depth, a relative geological time field computed from borehole and surface geological data, a kriged resistivity field obtained by inversion of airborne electromagnetic data, and three surface-geology text-embedding components derived from 1:50,000 geological-map descriptions. All methods are evaluated using Leave-One-Borehole-Out validation and spatial exclusion buffers ranging from 0 to 10 km. No model is uniformly superior. At zero buffer, TabPFN provides the highest Vp accuracy (R2 ≃ 0.81), whereas Random Forest performs best for Vs (R2 ≃ 0.72). The Vp prediction performance remains comparatively stable over several kilometres, while the Vs prediction performance degrades markedly 0when nearby boreholes are excluded. The uncertainty estimates have different statistical interpretations. For RF with CV+, the nominal 90% intervals contain approximately the intended proportion of velocity measurements at held-out boreholes, although their widths vary little across the prediction volume. The GP produces spatially structured posterior predictive intervals under its fitted covariance and noise model. TabPFN approximates a posterior predictive distribution induced by its synthetic pretraining prior, whereas TabICLv2 directly estimates conditional predictive quantiles. Their model-derived intervals are spatially heterogeneous, but they do not provide the same theoretical guarantee as CV+ concerning the proportion of future observations expected to fall within them. Despite comparable cross-validation scores, the methods produce different velocity fields and uncertainty patterns, particularly at depth. This disagreement reveals substantial sensitivity to model assumptions in regions that are weakly constrained by borehole observations. Model assessment should therefore consider not only point-prediction accuracy, but also how performance changes when nearby boreholes are excluded, the proportion of held-out observations contained within the predicted intervals, the corresponding interval widths, and their spatial variation. The four uncertainty representations provide complementary information and should not be interpreted as interchangeable estimates of subsurface uncertainty. These results show that model assessment should consider spatial transferability, empirical coverage, interval sharpness, and sensitivity to training-data support in addition to point-prediction accuracy. Different uncertainty methods provide complementary information and should not be interpreted as interchangeable estimates of subsurface uncertainty.},
 author = {Cilli, Roberto and Caumon, Guillaume and Clausel, Marianne and Kohboor, Behshad and Bourassi, Pierre-Alexandre and Peyrefitte, Aurélie},
 booktitle = {2026 {RING} meeting},
 language = {en},
 pages = {23--47},
 publisher = {ASGA},
 title = {Which {Model} Should {We} {Trust} for {Sparse} {Spatial} {Prediction}? {Comparing} {Point} {Predictions} and {Uncertainty} in {3D} {Velocity} {Mapping} from {Sparse} {Borehole} {Observations}.},
 year = {2026}
}