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 °C), and the equation-informed network achieves typical hold-out errors of MAE = 3.06 °C and RMSE = 4.49 °C. The Gaussian Process surrogate delivers the strongest predictive accuracy across 3-60 month horizons (RMSE = 3.39 °C; MAE = 2.34 °C) with well-calibrated uncertainty, whereas the XGBoost baseline exhibits higher errors.

翻译：增强型地热系统（EGS）中的可靠温度预测至关重要，然而基于石油工业的递减曲线和许多机器学习代理模型并未强制满足地热传热约束，而热-水-力（THM）耦合模拟仍存在计算成本高昂的问题。本研究提出一个物理一致性框架，同步推进了递减曲线分析和代理建模技术。通过引入受牛顿型冷却启发的平衡温度项，将经典Arps递减曲线族推广至地热应用领域，该扩展模型在确保有限晚期温度极限的同时，当平衡项设为零时可精确退化为传统Arps形式。扩展递减曲线经犹他州FORGE井下温度测量数据验证后，被用于在涵盖裂缝数量、井距、裂缝间距、围岩热导率和循环流量的受控THM数据集上构建学习代理模型。方程感知神经网络将修正后的递减方程作为可微分内部计算层嵌入，能够根据设计和运行参数生成完整的0-60个月温度轨迹。同时开发了概率性高斯过程回归代理模型，用于实现具有校准不确定性的多时间尺度直接预测，而直接XGBoost回归基线则提供纯数据驱动的参照基准。在整个模拟数据集中，扩展递减模型以近乎完美的保真度复现了温度轨迹（中位数RMSE = 0.071 °C），方程感知神经网络在保留测试集上取得典型误差指标MAE = 3.06 °C和RMSE = 4.49 °C。高斯过程代理模型在3-60个月预测范围内展现出最优预测精度（RMSE = 3.39 °C；MAE = 2.34 °C）且具有良好校准的不确定性，而XGBoost基线模型则表现出更高的误差水平。