Physics-Based Decline Curve Analysis and Machine Learning for Temperature Forecasting in Enhanced Geothermal Systems: Utah FORGE

Reliable temperature forecasting in Enhanced Geothermal Systems (EGS) is essential, yet petroleum-based decline curves and many machine-learning surrogates do not enforce geothermal heat transfer, while thermo-hydro-mechanical (THM) simulation remains computationally expensive. This study proposes a physics-consistent framework that advances both decline-curve analysis and surrogate modeling. The classical Arps decline family is generalized for geothermal use by introducing an equilibrium-temperature term motivated by Newton-type cooling, ensuring finite late-time temperature limits while reducing exactly to the conventional Arps forms when the equilibrium term is set to zero. The extended decline curves are validated against Utah FORGE downhole temperature measurements and then used to construct learning surrogates on a controlled THM dataset spanning fracture count, well spacing, fracture spacing, host-rock thermal conductivity, and circulation rate. An equation-informed neural network embeds the modified decline equations as differentiable internal computational layers to produce full 0-60 month temperature trajectories from design and operational inputs. A probabilistic Gaussian Process Regression surrogate is also developed for direct multi-horizon forecasting with calibrated uncertainty, while a direct XGBoost regression baseline provides a purely data-driven reference. Across the simulation dataset, the extended decline models reproduce temperature trajectories with near-perfect fidelity (median RMSE = 0.071 {\deg}C), and the equation-informed network achieves typical hold-out errors of MAE = 3.06 {\deg}C and RMSE = 4.49 {\deg}C. The Gaussian Process surrogate delivers the strongest predictive accuracy across 3-60 month horizons (RMSE = 3.39 {\deg}C; MAE = 2.34 {\deg}C) with well-calibrated uncertainty, whereas the XGBoost baseline exhibits higher errors.