Forward Osmosis (FO) is a promising low-energy membrane separation technology, but challenges in accurately modelling its water flux (Jw) persist due to complex internal mass transfer phenomena. Traditional mechanistic models struggle with empirical parameter variability, while purely data-driven models lack physical consistency and rigorous uncertainty quantification (UQ). This study introduces a novel Robust Hybrid Physics-ML framework employing Gaussian Process Regression (GPR) for highly accurate, uncertainty-aware Jw prediction. The core innovation lies in training the GPR on the residual error between the detailed, non-linear FO physical model prediction (Jw_physical) and the experimental water flux (Jw_actual). Crucially, we implement a full UQ methodology by decomposing the total predictive variance (sigma2_total) into model uncertainty (epistemic, from GPR's posterior variance) and input uncertainty (aleatoric, analytically propagated via the Delta method for multi-variate correlated inputs). Leveraging the inherent strength of GPR in low-data regimes, the model, trained on a meagre 120 data points, achieved a state-of-the-art Mean Absolute Percentage Error (MAPE) of 0.26% and an R2 of 0.999 on the independent test data, validating a truly robust and reliable surrogate model for advanced FO process optimization and digital twin development.

翻译：正渗透（FO）是一种具有前景的低能耗膜分离技术，但由于其内部复杂的传质现象，准确模拟其水通量（Jw）仍面临挑战。传统的机理模型难以处理经验参数的可变性，而纯数据驱动模型则缺乏物理一致性及严格的不确定性量化（UQ）。本研究提出了一种新颖的鲁棒混合物理-机器学习框架，采用高斯过程回归（GPR）实现高精度、不确定性感知的Jw预测。其核心创新在于，基于详细非线性FO物理模型预测值（Jw_physical）与实验水通量（Jw_actual）之间的残差对GPR进行训练。关键的是，我们通过将总预测方差（sigma2_total）分解为模型不确定性（认知不确定性，源自GPR的后验方差）和输入不确定性（偶然不确定性，通过Delta方法对多变量相关输入进行解析传播），实现了一套完整的不确定性量化方法。利用GPR在数据稀缺场景下的固有优势，该模型仅使用120个数据点进行训练，即在独立测试数据上达到了0.26%的平均绝对百分比误差（MAPE）和0.999的R2，验证了其作为先进FO工艺优化和数字孪生开发的真正鲁棒且可靠的代理模型。