Dual-Representation Mondrian Conformal Assignment of Pressure-Transient GeoTypes: A Reproduction and Extension for Fractured-Reservoir Flow

Fractured reservoirs exhibit recurring fluid-flow behaviours hidden in the shape of their pressure-transient responses. A recent study clusters geologically consistent discrete-fracture-network (DFN) ensembles into flow-behaviour classes and attributes each class to fracture-network properties. This preprint first reproduces that pipeline, DFN pressure transients, Bourdet-derivative features, dynamic-time-warping (DTW) k-medoids clustering into a GeoType catalogue, and random-forest / TreeSHAP attribution, on the original open 4TU corpus and on analytic dual-porosity families, recovering clean clusters (silhouette up to 0.86 on the real transients, higher than on the analytic families) and the finding that fracture intensity (log I) is the top attributed control. It then extends the pipeline in two ways. First, it makes the assignment coverage-controlled, which the base random-forest attribution is not, with a class-conditional (Mondrian) split-conformal assigner on a DTW nonconformity score that emits per-class p-values, a prediction set, and an out-of-catalogue flag (empirical coverage 0.85-0.87 at target, out-of-catalogue rate 0.03-0.15, mean set size 1.5-1.7). Second, and the methodological contribution, it introduces a dual-representation Mondrian conformal assigner that conformalizes jointly across two nonconformity scores (the DTW shape distance and a physics-descriptor implausibility from the attribution forest) and accepts a GeoType only in the per-class conjunction of the two prediction sets. This excludes curves that are shape-close to the wrong physics, which single-score conformal accepts: the dual conjunction tightens the mean set size below one and flags right-shape-wrong-physics curves at an honest cost of coverage (e.g. 0.85 to 0.73, 0.87 to 0.75). The shape machinery is signal-agnostic and is exercised on hydrogeology pumping-test field data as well as reservoir transients. The contribution is a faithful reproduction plus a coverage-controlled assignment that fuses shape space and physics-descriptor space, with every number backed by a committed deterministic artifact. Code, committed artifacts, and the workbench (MIT): https://github.com/fsantibanezleal/CAOS_RES_Pulso . Reusable shape machinery (Apache-2.0): https://github.com/fsantibanezleal/CAOS_GeoTypes .