Composition determination of biodiesel/ethanol blends using dielectric spectroscopy and tabular prior-data fitted networks

Biodiesel/ethanol blends represent a promising alternative to reduce the consumption of fossil diesel. This work employs frequency-domain dielectric spectroscopy to determine the permittivity of biodiesel/ethanol blends across the full range of compositions, at temperatures between 293 K and 333 K, and within a frequency range from 1 MHz to 30 MHz. Within this interval, the real part of the permittivity is frequency-independent, and electrical losses are negligible. Leveraging these experimental results, a transformer-based deep learning model implementing Tabular Prior-data Fitted Networks (TabPFN) was developed to determine the blend composition from temperature and permittivity measurements. Evaluated via Leave-One-Out Cross-Validation, the proposed TabPFN model predicted the composition with high accuracy, yielding a coefficient of determination of 0.997, an average absolute deviation of 1.0 mol%, and a root mean squared error of 1.6 mol%. These results outperform conventional machine learning algorithms as well as standard analytical inversion models, operating in a single forward pass without requiring hyperparameter tuning or data scaling. Overall, using high-frequency dielectric spectroscopy together with tabular foundation models are the basis of a streamlined, highly efficient strategy for non-destructive biofuel quality verification.