Discovery of new formula accurately determining organic compounds aqueous diffusion coefficients by symbolic regression
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GRAPHICAL ABSTRACT
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PUBLIC SUMMARY
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A novel formula for determining organic compounds aqueous diffusion coefficients was discovered.
The proposed formula achieved a higher accuracy compared to the currently available empirical equations.
The insights from this study are shedding light on understanding of organic compounds diffusion in water.
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ABSTRACT
Aqueous diffusion coefficients of organic compounds are important parameters for many studies in geosciences and relevant applications, in particular, for modelling solute transport in groundwater. Accurately determining organic compounds aqueous diffusion coefficients still remains challenging due to lack of high-quality experimental data as well as reliable predictive tools. Based on symbolic regression incorporating theoretical constraints derived from the Stokes-Einstein hydrodynamics and Wilke-Chang theory, our study discovered a symbolic formula, which is mathematically linking the diffusion coefficients with water temperature, molecular weight, molecular volume and viscosity of water. The proposed formula achieved a preferential accuracy for predicting different organic compounds diffusion coefficients in water comparing with the currently available empirical equations. The complex interplay of molecular weight, molecular volume and water temperatures on aqueous diffusion coefficients of organic compounds is substantiated by causal inference and controlled test. The insights from this study are shedding light on better understanding of organic compounds diffusion in water.-
Keywords:
- Diffusion coefficient /
- Water /
- Symbolic regression /
- Temperature
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Cite this article:
Han M. and Jin B. (2026). Discovery of new formula accurately determining organic compounds aqueous diffusion coefficients by symbolic regression. The Innovation Geoscience 4:100208. https://doi.org/10.59717/j.xinn-geo.2026.100208
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Han M. and Jin B. (2026). Discovery of new formula accurately determining organic compounds aqueous diffusion coefficients by symbolic regression. The Innovation Geoscience 4:100208. https://doi.org/10.59717/j.xinn-geo.2026.100208
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Figure 1.
Overview for the approach
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Figure 2.
Training and test mean square error (MSE) against the feature complexity for the data-driven models based on mixed dataset (A) and experimental dataset (B).
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Figure 3.
Training and test mean square error (MSE) against the feature complexity for the hybrid models based on mixed dataset (A) and experimental dataset (B).
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Figure 4.
Test accuracy of optimal models
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Figure 5.
Sensitivity analysis of hybrid model performance to progressive synthetic data integration.
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Figure 6.
The validation of symbolic formula
