⚡ electrical engineering

A Visual Guided Physics Informed Neural Networks Framework for Real Time Coagulant Dose Optimization in Water Treatment Plants

This study proposes a Real-Time Sensing and Visual Information-Guided Physics-Informed Neural Networks (RTS-VG PINNs) framework that integrates deep visual perception with governing physical laws to overcome the inherent delays of traditional indicators and achieve robust, real-time optimization of coagulant dosage in water treatment plants.

Original authors: Galang Adira Prayoga, Emir Husni, Reza Darmakusuma, Herto Dwi Ariesyady

Published 2026-07-03

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Galang Adira Prayoga, Emir Husni, Reza Darmakusuma, Herto Dwi Ariesyady

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Problem: Waiting for the Water to Clear

Imagine you are trying to make muddy water clear by adding a special powder (a coagulant) that clumps the dirt together so it sinks. In a water treatment plant, operators usually have to wait until the dirt has settled to the bottom and the water on top looks clear before they know if they added the right amount of powder.

The paper calls this a "time lag." It's like trying to steer a giant ship by looking at the wake behind it rather than the water in front of you. By the time you see the water is still muddy, you've already wasted time and chemicals. Traditional sensors (like turbidity meters) only tell you what happened after the dirt has settled, not what is happening right now inside the mixing tank.

The Solution: Giving the Computer "Eyes" and "Common Sense"

The researchers created a new system called RTS-VG PINNs. Think of this system as a smart assistant that has two superpowers:

Super Vision (The "Eyes"): Instead of just waiting for the water to clear, the system uses a high-speed camera to watch the mud clumps (flocs) form in real-time. It uses advanced AI (specifically ResNet-50 and YOLOv8, which are like very sharp-eyed detectives) to spot tiny changes in how the mud clumps together before they sink. It can tell the difference between "just starting to clump," "clumping tightly," and "settling down" just by looking at a video.
Physics Common Sense (The "Brain"): The system doesn't just guess based on pictures; it also knows the laws of physics. It is programmed with the mathematical rules that govern how mud settles (the Kynch sedimentation equation) and how particles stick together (Langmuir–Smoluchowski kinetics).

How It Works: The "Hybrid" Approach

The researchers combined these two powers into one framework:

The Visual Guide: The camera watches the mud. If the AI sees the mud clumps getting bigger and denser, it tells the system, "Hey, the settling speed is increasing!" This gives the system a "heads up" before the water actually clears.
The Physics Check: The system takes that visual clue and runs it through the "laws of physics" to ensure the prediction makes sense. It's like a chef tasting a soup (data) but also knowing the recipe (physics) so they don't add too much salt just because the soup looks salty.
The Result: The system calculates the perfect amount of powder to add right now to get the best result, rather than reacting to what happened five minutes ago.

The Experiment: Training the AI

To teach this system, the researchers set up a lab experiment:

They used different types of water (some natural, some made with clay).
They added different amounts of powder (from a little bit to a lot).
They filmed the whole process with a high-speed camera and measured the water quality with sensors.
They taught the AI to recognize four stages: Dispersion (mud is scattered), Aggregation (mud starts sticking), Densification (mud gets heavy), and Settling (mud sinks).

The Results: Why It's Better

The researchers tested their new system against standard computer models (like Random Forest or Support Vector Machines) that only look at numbers without "seeing" the process or knowing the physics.

Accuracy: The new system was more accurate at predicting the best amount of powder. It achieved a higher score (R² = 0.498) compared to the other models.
Handling Noise: Real-world data is messy (like a shaky camera or a dirty sensor). The new system was better at ignoring the "noise" and finding the true signal because the laws of physics acted as a safety net.
Seeing the Invisible: The system could "see" inside the tank and map out where the mud was dense and where it was thin, even though no sensor was actually inside the tank. It reconstructed the invisible 3D movement of the mud using only the camera and the math.

The Bottom Line

This paper claims that by giving a computer eyes to watch the mud clump and common sense (physics) to understand how it moves, we can optimize water treatment in real-time. It stops the system from reacting to the past and allows it to predict the future, saving time and chemicals while making the water cleaner faster.

Note on Limitations: The paper admits this was tested in a small lab setting. The "ship" analogy works well in a small bucket, but the researchers note that scaling this up to a massive industrial tank with real-world issues like changing light or weather is a challenge for the future. They also suggest that while their "settling speed" variable works well, there might be other hidden factors in the mud that need to be studied later.

Technical Summary: A Visual Guided Physics Informed Neural Networks Framework for Real Time Coagulant Dose Optimization in Water Treatment Plants

1. Problem Statement

Coagulation is a critical unit process in water treatment for reducing turbidity and color, yet optimizing coagulant dosage remains challenging due to the complex, nonlinear physicochemical interactions involved. Conventional control strategies rely on real-time turbidity measurements or the degree of flocculation (DF) as process indicators. However, the authors identify a fundamental limitation: these metrics represent macroscopic outcomes of particle aggregation and sedimentation that exhibit inherent physical delays. Because changes initiated at the bottom of a thickener require time to propagate upward to the supernatant layer, turbidity and DF measurements provide reactive, lagged feedback rather than real-time insight into evolving floc dynamics. This temporal mismatch restricts traditional control strategies, leading to inefficient chemical usage and reduced operational efficiency. Furthermore, purely data-driven machine learning models often suffer from a lack of physical interpretability and poor generalization when faced with sparse, noisy, or out-of-distribution data.

2. Methodology

The study proposes a Real-Time Sensing and Visual Information-Guided Physics-Informed Neural Networks (RTS-VG PINNs) framework. This hybrid architecture integrates real-time sensor data, deep visual perception, and governing physical laws into a unified learning system. The methodology proceeds through three main stages:

A. Experimental Data Acquisition

Experiments were conducted using natural (PDAM) and artificial (kaolin-based) water samples with varying initial conditions (pH, temperature, conductivity, zeta potential). Coagulant dosages (Polyaluminum Chloride - PAC) were systematically varied from 12 to 120 mg/L.

Sensors: Real-time turbidity, pH, and electrical conductivity were monitored.
Visual System: A high-resolution camera (Canon 250D, 60 fps) captured the temporal evolution of floc structures during rapid mixing, slow mixing, and settling phases.
Dataset: Image sequences were categorized into four floc evolution stages (dispersion, initial aggregation, growth/densification, and settling) to train deep learning models.

B. Visual Feature Extraction (The "Visual Guide")

Two complementary Convolutional Neural Network (CNN) architectures were employed to extract features from the image sequences:

ResNet-50: A two-stage detector used for high-sensitivity feature extraction to capture subtle variations in floc morphology and density.
YOLOv8: A one-stage detector utilized for real-time detection and tracking of floc evolution.
These models classify floc density and map visual features to a time-varying effective sedimentation velocity, $v_0(t)$ . This velocity serves as a dynamic parameter that bridges raw visual observations with the physical model.

C. Physics-Informed Neural Network (PINN) Architecture

The core of the framework consists of two coupled problems:

Direct Problem (Forward Modeling):
- The model solves the Kynch sedimentation partial differential equation (PDE) to reconstruct the spatiotemporal floc density distribution, $\phi(t, z)$ .
- The time-varying velocity $v_0(t)$ , inferred from the CNN visual features, modulates the PDE.
- The loss function ( $\mathcal{L}_{Total}$ ) combines data fidelity (matching experimental observations), physics constraints (minimizing PDE residuals), initial conditions, and boundary conditions (no-flux at the surface).
Inverse Problem (Dosage Optimization):
- The model estimates the optimal coagulant dosage ( $D$ ) by learning the inverse relationship between operational variables (pH, temperature, initial turbidity, etc.) and process outcomes.
- Physical constraints are embedded via Langmuir adsorption kinetics (modeling zeta potential evolution) and Smoluchowski coagulation kinetics (modeling turbidity evolution via aggregation and breakup rates).
- The framework solves for the dosage that balances aggregation and breakup mechanisms.

3. Key Contributions

Integration of Visual Perception with Physics: The paper introduces a novel mechanism where deep learning-extracted visual features (floc density/structure) dynamically inform the parameters of a physical sedimentation model ( $v_0(t)$ ), effectively using vision as a leading indicator to overcome sensor lag.
Hybrid Learning Architecture: The RTS-VG PINNs framework successfully unifies high-dimensional visual data with first-principles physical laws (Kynch sedimentation, Langmuir-Smoluchowski kinetics), creating a physically consistent learning architecture.
Inverse Prediction under Uncertainty: The study demonstrates the capability of the inverse PINN to estimate optimal coagulant dosage not only deterministically but also with uncertainty quantification using Monte Carlo dropout, enhancing robustness against noisy industrial data.
Reconstruction of Latent States: The framework enables the reconstruction of internal system states (floc density distribution $\phi(t, z)$ ) that are inaccessible to direct measurement, providing a deeper understanding of process dynamics.

4. Experimental Results

Visual Classification: Both ResNet-50 and YOLOv8 demonstrated high accuracy in classifying floc evolution stages. The visual models successfully identified the interface arrival time ( $t_s$ ) and floc density transitions earlier than turbidity sensors could detect clarification.
Direct Solution Performance: The PINN successfully reconstructed the spatiotemporal floc density field with low PDE residuals (on the order of $10^{-3}$ ), confirming that the model adheres to mass conservation and sedimentation dynamics. The predicted internal concentration fields showed physically consistent stratification patterns.
Inverse Solution Performance: In estimating optimal coagulant dosage, the RTS-VG PINNs framework outperformed conventional machine learning models (Random Forest, Gradient Boosting, SVM, and MLP).
- The PINN achieved a coefficient of determination ( $R^2$ ) of 0.498, surpassing Random Forest (0.484), Gradient Boosting (0.434), SVM (0.285), and MLP (0.063).
- The model effectively captured nonlinear trends, such as the initial decrease in turbidity followed by an increase due to overdosing (charge reversal), which data-driven models often failed to represent accurately.
Robustness: The inclusion of Monte Carlo dropout allowed the model to provide uncertainty-aware predictions, maintaining physical consistency even when trained on limited or noisy data.

5. Significance and Claims

The authors claim that the RTS-VG PINNs framework represents a significant advancement in intelligent water treatment control by addressing the critical issue of measurement lag. By leveraging visual information as a proxy for early-stage floc dynamics, the framework enables proactive rather than reactive control strategies.

The study emphasizes that embedding physical laws (governing equations) into the learning process significantly improves model interpretability and generalization, particularly in scenarios where data is sparse or noisy. The framework is presented as a robust tool for real-time coagulant dosage optimization, capable of inferring internal process states and providing physically meaningful predictions that purely data-driven approaches cannot achieve.

The authors maintain a modest stance regarding the current scope, acknowledging that the study is limited to laboratory-scale conditions and a simplified one-dimensional Kynch PDE. They note that future work will be required to extend the framework to pilot-scale industrial thickeners and to integrate more complex physical models (e.g., CFD) to capture multidimensional hydrodynamics.