Combined ANFIS and numerical methods to reveal the mass transfer mechanism of ultrasound-enhanced extraction of proteins from millet

Millet protein, as a promising plant-based protein substitute source, is an excellent basis for essential amino acids compared to commonly consumed staple grains. Compared with the traditional extraction process, ultrasound has been used to enhance the extraction efficiency of various plant-based proteins. To reveal the mechanism of ultrasound-enhanced extraction of proteins, adaptive neuro-fuzzy inference system (ANFIS) algorithm and numerical simulation based on Fick’s law were applied to illustrate the mass transfer behavior of millet proteins under different ultrasonic conditions including solid–liquid ratios (S/L ratios), pH and acoustic energy density levels (AED). The results showed that AED dominated the changes in effective diffusion coefficient (De), showing a positive correlation relationship (p