Leveraging multi-output modelling for CIELAB using colour difference formula towards sustainable textile dyeing

Textile dyeing requires optimizing combinations of ingredients and process parameters to achieve target colour properties. Modelling the complex relationships between these factors and the resulting colour is challenging. In this case, a physics-informed approach for multi-output regression to model CIELAB colour values from dyeing ingredient and process inputs is proposed. Leveraging attention mechanisms and multi-task learning, the model outperforms baseline methods at predicting multiple colour outputs jointly. Specifically, the Transformer model’s attention mechanism captures the complex interactions between dyeing ingredients and process parameters, while the multi-task learning framework exploits the intrinsic correlations among the L*, a*, and b* dimensions of the CIELAB colour space. In addition, the incorporation of physical knowledge through a physics-informed loss function integrates the CMC colour difference formula. This loss function, along with the attention mechanisms, enables the model to learn the nuanced relationships between the dyeing process variables and the final colour output, thereby improving the overall prediction accuracy. This reduces trial-and-error costs and resource waste, contributing to environmental sustainability by minimizing water and energy consumption and chemical emissions.