Korzhinskii-Net: Physics-Informed Neural Network for Sub-Surface Mineral Prospectivity Modelling

Mineral prospectivity modelling (MPM) underpins exploration economics, yet most operational pipelines reduce to data-driven classifiers trained on shallow surface proxies. Such models are blind to the subsurface physics that actually localises ore: heat advection, fluid flow, and lithology-dependent precipitation. We present Korzhinskii-Net, a 2-D radial physics-informed neural network (PINN) that couples Darcy flow, advective-diffusive heat transport, and a softplus-saturated reaction rate into a single differentiable forward model, weakly supervised by surface and remote-sensing proxies. The network is named after Dmitri S. Korzhinskii (1899-1985), whose theory of infiltration metasomatism provides the physical scaffold. We evaluate Korzhinskii-Net on six ore provinces spanning three commodity classes - Udokan (sandstone-hosted Cu), Sukhoi Log, Olimpiada, and Berezovskoye (orogenic Au), Vorontsovskoye (Carlin-type Au), and Dalnegorsk (skarn polymetallic) - under a fair, leakage-controlled 5-fold cross-validation protocol with hard ring-shaped negatives and baseline proxy features disabled. Korzhinskii-Net attains a mean PR-AUC of 0.708 versus 0.235 for the strongest classical baseline (support vector machine), and a mean fractional rank of 0.036 versus 0.475. The improvement is consistent across all six provinces and three commodity systems, suggesting that physics-informed differentiable simulators, even when constrained only by global open-data proxies, can recover localisation patterns that pure feature-based learners systematically miss. We release the full pipeline and evaluation harness as open source.