A Fast Random-Feature Surrogate for Geothermal Heat-Transport Prediction and Breakthrough Risk Screening

Repeated geothermal evaluation motivates inexpensive flow and heat-transport approximations. We combine proper orthogonal decomposition (POD) with extreme learning machine (ELM) regression to reconstruct temperature fields and predict production curves and horizon-capped breakthrough times from simulation data. A manufactured elliptic benchmark examines spectral residuals; a conditional one-dimensional bound distinguishes approximation, interpolation, and regularization under assumed discrete stability. In the synthetic early-time case, the mean relative field-trajectory reconstruction error is 7.506×10−4, with an online speedup of approximately 105×. These field evaluations reuse a database involved in fitting and do not establish independent parameter generalization. In the accelerated case, the direct production-curve model has a mean relative error of 2.150×10−2 on a parameter-held-out set, while direct capped-time queries are more than four orders of magnitude faster than the numerical reference solve. Non-crossing cases are right-censored; their capped-time errors do not measure unobserved event timing. Regression and sensitivity studies use a single-band, two-dimensional permeability model. The velocity-only diagnostic does not establish reference-solver stability, and the finest archived grid violates the diffusion part of a sufficient explicit time-step restriction. The results demonstrate a fast simulation-trained surrogate, while stable reference refinement, independent field validation, and more realistic fracture geometries remain necessary before reservoir-scale use.