Hybrid Physics-ML Model for Forward Osmosis Flux with Complete Uncertainty Quantification

TL;DR

This paper presents a hybrid physics-ML model using Gaussian Process Regression for accurate, uncertainty-aware water flux prediction in forward osmosis, achieving high accuracy with limited data and enabling advanced process optimization.

Contribution

It introduces a novel hybrid physics-ML framework that combines physical models with GPR for uncertainty quantification in FO flux prediction, especially effective with small datasets.

Findings

Achieved 0.26% MAPE and 0.999 R2 on test data

Decomposed predictive variance into epistemic and aleatoric uncertainties

Validated the model's robustness and reliability for FO process optimization

Abstract

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.