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Viskositas: Viscosity Prediction of Multicomponent Chemical Systems

The paper introduces "Viskositas," an artificial neural network-based model that outperforms existing linear, nonlinear, and commercial models in predicting the viscosity of multicomponent chemical systems by achieving lower errors, reduced variability, and fewer outliers through optimized hyperparameter tuning.

Original authors: Patrick dos Anjos

Published 2026-08-19

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CC BY 4.0

Original authors: Patrick dos Anjos

Original paper licensed under CC BY 4.0 (http://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

In the high-heat worlds of steelmaking and glass manufacturing, as well as deep within the Earth's crust where rocks melt and flow, a single physical property dictates how materials behave: viscosity. This is simply a measure of a fluid's resistance to flow, or how thick and sluggish it is. Imagine honey pouring slowly from a spoon compared to water rushing from a tap; that difference in resistance is viscosity. For engineers and geologists, knowing this value is critical. In a steel mill, the right thickness of molten slag ensures impurities are removed efficiently; in glass production, it determines whether the material can be shaped or will crack. Yet, measuring this property is a difficult and costly task. It requires specialized, expensive equipment and significant time to heat samples until they are perfectly uniform, and even then, the results can be skewed by tiny errors in the procedure. Because of these hurdles, scientists have long relied on mathematical formulas to predict viscosity based on what a mixture is made of and how hot it is, but these traditional equations often fail when applied to complex, multi-ingredient systems.

A researcher at the Federal Institute of Espírito Santo in Brazil set out to solve this problem by teaching a computer to learn the patterns of flowing liquids directly from data, rather than forcing the data into rigid formulas. Patrick dos Anjos compiled a massive collection of experimental results from scientific literature, gathering thousands of measurements from diverse chemical systems involving oxides of silicon, calcium, aluminum, iron, and many others, all recorded at various temperatures. The goal was to build a new kind of prediction tool that could handle the messy reality of industrial chemistry. Instead of using a standard equation, the researcher trained an artificial neural network, a type of computer program modeled after the human brain, to find the hidden connections between a mixture's chemical recipe, its temperature, and its resulting thickness. The system was fed the chemical composition and temperature as inputs and asked to predict the viscosity, learning from its mistakes over thousands of cycles until it could make accurate guesses on data it had never seen before.

The resulting model, named Viskositas, proved to be a significant improvement over existing methods. When tested against a fresh set of data that the computer had not used during its training, Viskositas made fewer errors and showed less random variation than six other established models found in scientific literature and even a popular commercial software package used by industry professionals. The new model was particularly good at avoiding extreme mistakes, known as outliers, which can be disastrous in an industrial setting where a wrong prediction could lead to a failed batch of glass or a stalled steel process. By analyzing which ingredients the computer paid the most attention to, the study confirmed known scientific principles: certain components like silica tend to make the liquid thicker, while others like calcium oxide or fluorite tend to thin it out, and higher temperatures consistently make the mixture flow more easily. The study demonstrated that by letting a computer learn from a broad database of real-world measurements, it is possible to create a reliable, flexible tool for predicting how complex chemical fluids will behave, offering a more accurate guide for the industries that depend on controlling the flow of molten materials.

Technical Summary: Viskositas – A Neural Network Approach to Viscosity Prediction in Multicomponent Chemical Systems

Problem Statement
Viscosity is a critical parameter in metallurgical processes (e.g., steel desulfurization, inclusion treatment, continuous casting) and the glass industry (e.g., refining, homogenization), as well as in geophysics. However, experimental measurement of viscosity is financially expensive, time-consuming, and prone to procedural errors, with reported accuracy errors ranging from 5–20% and precision errors from 1–5%. While numerical and semi-empirical models exist, they often suffer from restricted applicability due to limitations in the chemical compositions, temperatures, and viscosity ranges they were validated against. There is a need for a robust, nonlinear model capable of predicting viscosity across diverse multicomponent chemical systems without the constraints of traditional empirical equations.

Methodology
The study developed a predictive model named Viskositas using Artificial Neural Networks (ANN). The methodology involved the following steps:

Database Construction: A dataset was compiled from two international scientific articles and one bachelor's thesis, totaling 7,035 initial data points covering a wide range of chemical systems (including oxides like SiO₂, Al₂O₃, CaO, MgO, FeO, etc., and fluorides).
Preprocessing:
- Filtering: Data was filtered to include only fully liquid fluids (temperatures above the calculated liquidus temperature, $T_{liq}$ ) to ensure Newtonian behavior suitable for Arrhenius or VFT modeling.
- Feature Engineering: The degree of depolymerization ($NBO/T$) was calculated to characterize the chemical structure.
- Outlier Removal: Statistical limits based on quartiles were applied to remove outliers in both $NBO/T$ and viscosity distributions.
- Transformation: Viscosity values were converted to logarithmic scale ( $\log_{10} \eta$ ) to reduce dimensionality and adapt to mathematical modeling requirements.
- Standardization: All predictor variables (chemical composition in mass % and temperature in Kelvin) were standardized using the z-score method to obtain a mean of 0 and standard deviation of 1.
- Partitioning: The final dataset of 5,659 unique entries was split into 81% for training, 9% for validation, and 10% for testing.
Model Architecture:
- The ANN utilized 20 input neurons (chemical components and temperature) and 1 output neuron ( $\log_{10} \eta$ ).
- Hyperparameter optimization was conducted to determine the optimal architecture. The selected model, Viskositas, features 3 hidden layers with 22 neurons each (satisfying the universal approximation theorem's minimum width requirement of $w_{min} \leq d_x + d_y + 1$ ).
- The activation function used was ReLU, with He uniform weight initialization and zero bias initialization.
- Training employed the Adam optimizer with Mean Squared Error (MSE) loss and Early Stopping to prevent overfitting.
Statistical Analysis: Model performance was evaluated using Mean Absolute Error (MAE), Standard Deviation of error (Std), and the Coefficient of Determination ( $R^2$ ). Sensitivity analysis was performed using the connection weights algorithm to determine the relative importance of input variables.

Key Contributions

Development of Viskositas: The creation of a specialized ANN model capable of predicting viscosity for complex, multicomponent chemical systems based on composition and temperature.
Comprehensive Database Integration: The synthesis of a large, diverse dataset covering numerous oxide systems, fluorides, and temperature ranges, preprocessed to ensure physical consistency (liquid state only).
Sensitivity Analysis: The application of the connection weights algorithm to quantify the relative importance of specific chemical species (e.g., network modifiers vs. formers) and temperature on the predicted viscosity, aligning with established chemical theories (e.g., the role of $NBO/T$ and specific oxide behaviors).

Results
The Viskositas model was compared against six models from the literature (Shaw, Watt-Fereday, Bomkamp, Riboud, Duchesne, and ANNLiq) and one commercial model (FactSage™ 7.2 Viscosity module).

Performance Metrics: The Viskositas model and the FactSage™ 7.2 Viscosity module presented the best results for MAE, Std, and $R^2$ compared to the other literature models. However, when comparing these two top performers, Viskositas demonstrated superior statistical performance, achieving lower MAE and Standard Deviation, and a higher $R^2$ on the test database.
Error Distribution: Analysis of skewness and kurtosis revealed that Viskositas generated fewer outliers and exhibited lower variability in prediction errors compared to the FactSage™ module. Specifically, Viskositas showed a maximum negative error of -1.3920 and a maximum positive error of 1.0507 (in $\log_{10} \eta$ ), significantly outperforming the FactSage™ module which showed errors of -5.2931 and 2.0832, respectively.
Variable Importance: The sensitivity analysis confirmed that temperature and specific oxides (such as network modifiers like CaO, MgO, and alkali metals) have significant relationships with viscosity. The analysis aligns with theoretical expectations where temperature is inversely proportional to viscosity; a decrease in temperature reduces the degree of agitation between chemical species, thereby decreasing fluidity and increasing viscosity.

Significance
The paper claims that the Viskositas model offers a reliable alternative to expensive and error-prone experimental viscosity measurements. By leveraging a large, preprocessed database and a nonlinear neural network architecture, the model provides predictions with lower errors, less variability, and fewer outliers than existing literature models and the commercial FactSage™ software. This capability is significant for industries relying on precise viscosity data for process optimization in metallurgy and glass manufacturing, where experimental constraints often limit data availability. The study validates the utility of ANNs in overcoming the applicability restrictions of traditional semi-empirical models in multicomponent chemical systems.

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