Multimodal deep learning models incorporating the adsorption characteristics of the adsorbent for estimating the permeate flux in dynamic membranes

Dynamic membranes (DMs) can improve the overall efficiency and performance of water-treatment processes. However, DM modeling studies are limited by the constraint of interpreting adsorption-layer mechanisms using data acquired solely from DM experiments. This study addressed this issue by training multimodal deep learning (DL) models with independently constructed datasets on temporal variations in adsorption data and DM-experiment data by a fusion approach. The multimodal model with a 2D convolution neural network-based encoder reliably predicted the permeate normalized flux in DMs (the statistical performance metrics for the test dataset, R² and root mean squared error, showed values of 0.9702 and 0.0457, respectively) by extracting crucial features from data on temporal variations in the adsorbed-solute quantity. Model interpretation indicated that vectors extracted from adsorption-experiment data significantly influence the predictive performance; therefore, the adsorption characteristics of the adsorbent were significant for DM-performance predictions. Further analysis indicated that excessive initial adsorption should be prevented in the adsorption layer for membrane-performance improvement. The proposed multimodal DL model is a promising approach for DM-performance predictions and understanding the mechanism of water-treatment processes with heterogeneous membranes. Moreover, the proposed modeling strategy could facilitate the analysis of water-treatment processes involving heterogeneous mechanisms beyond those based on DMs.