<p>Physical sciences are essential to the predictive modeling of complex environmental systems, particularly environmental monitoring and sustainability applications, as they provide the deterministic foundation required to predict future ecological behaviours. Traditionally, AI deployment in environmental monitoring is hindered by data scarcity and qualities as well as poor drift phenomena (i.e., changes in data distribution or input–output connections over time). Integrating physical sciences with advanced Artificial Intelligence (AI), such as Long Short-Term Memory (LSTM), Random Forests (RF), and Multi-Layer Perceptrons (MLP), has recently emerged as an effective way to address the training data shortage, increase model generalizability, and provide a robust solution for predicting water pollution concentration and management. Motivated by these considerations, this research leverages the analytical solution of the Advection–Diffusion Equation (ADE) as a physics-based engine to generate a high-fidelity synthetic dataset of 50,000 spatiotemporal observations. This physics-derived data is then used to train a novel hybrid RF-MLP algorithm to profile pollutant concentration (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C\)</EquationSource> </InlineEquation>) across spatial coordinates (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(x\)</EquationSource> </InlineEquation>) under varying hydrodynamic flow speeds (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mu \)</EquationSource> </InlineEquation>). The proposed algorithm employs a three-stage sequential residual learning logic, utilizing RF for stable feature partitioning of spatial-hydrodynamic inputs and MLP for refined non-linear error correction of the physics-based residuals. The algorithm's performance was benchmarked against nine standalone AI models using a comprehensive suite of metrics. The experiments demonstrated exceptional precision with a Correlation Coefficient (CC) of 1.0, a Scattered Index (SI) of 0.0002, a Willmott’s Index (WI) of 1.0, a test RMSE of 0.0000295, and an R<sup>2</sup> of 1.0. Beyond accuracy, the hybrid algorithm achieved a training time of 67.53 s, significantly outperforming deep learning architectures like BiLSTM, which required 650.28 s while yielding lower precision. These results reveal that the physics-guided hybrid AI algorithm provides an optimal trade-off between computational efficiency and predictive fidelity, offering a scalable tool for real-time spatial mapping of river pollution.</p>

A new hybrid physics-guided AI algorithm for water quality prediction supported by variable coefficients advection-diffusion model

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2026年4月30日

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Hussein Karam Abd El-Sattar,
Mohammed Elshambakey,
Samar Antar,
Ahmed Saleh,
Nahla Mohamed Sakr,
Fayez Nassif Ibrahim,
Sahar Mohamed Ali Abou Bakr

摘要

Physical sciences are essential to the predictive modeling of complex environmental systems, particularly environmental monitoring and sustainability applications, as they provide the deterministic foundation required to predict future ecological behaviours. Traditionally, AI deployment in environmental monitoring is hindered by data scarcity and qualities as well as poor drift phenomena (i.e., changes in data distribution or input–output connections over time). Integrating physical sciences with advanced Artificial Intelligence (AI), such as Long Short-Term Memory (LSTM), Random Forests (RF), and Multi-Layer Perceptrons (MLP), has recently emerged as an effective way to address the training data shortage, increase model generalizability, and provide a robust solution for predicting water pollution concentration and management. Motivated by these considerations, this research leverages the analytical solution of the Advection–Diffusion Equation (ADE) as a physics-based engine to generate a high-fidelity synthetic dataset of 50,000 spatiotemporal observations. This physics-derived data is then used to train a novel hybrid RF-MLP algorithm to profile pollutant concentration ( \(C\) ) across spatial coordinates ( \(x\) ) under varying hydrodynamic flow speeds ( \(\mu \) ). The proposed algorithm employs a three-stage sequential residual learning logic, utilizing RF for stable feature partitioning of spatial-hydrodynamic inputs and MLP for refined non-linear error correction of the physics-based residuals. The algorithm's performance was benchmarked against nine standalone AI models using a comprehensive suite of metrics. The experiments demonstrated exceptional precision with a Correlation Coefficient (CC) of 1.0, a Scattered Index (SI) of 0.0002, a Willmott’s Index (WI) of 1.0, a test RMSE of 0.0000295, and an R² of 1.0. Beyond accuracy, the hybrid algorithm achieved a training time of 67.53 s, significantly outperforming deep learning architectures like BiLSTM, which required 650.28 s while yielding lower precision. These results reveal that the physics-guided hybrid AI algorithm provides an optimal trade-off between computational efficiency and predictive fidelity, offering a scalable tool for real-time spatial mapping of river pollution.