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This study develops a comprehensive framework that integrates computational fluid dynamics (CFD) and machine learning (ML) to predict milk flow behavior in lactating breasts. Utilizing CFD and other high-fidelity simulation techniques to tackle fluid flow challenges often entails significant computational resources and time investment. Artificial neural networks (ANNs) offer a promising avenue for grasping complex relationships among high-dimensional variables. This study leverages this potential to introduce an innovative data-driven approach to CFD. The initial step involved using CFD simulations to generate the necessary training and validation datasets. A machine learning pipeline was then crafted to train the ANN. Furthermore, various ANN architectures were explored, and their predictive performance was compared. The design of experiments method was also harnessed to identify the minimum number of simulations needed for precise predictions. This study underscores the synergy between CFD and ML methodologies, designated as ML-CFD. This novel integration enables a neural network to generate CFD-like results, resulting in significant savings in time and computational resources typically required for traditional CFD simulations. The models developed through this ML-CFD approach demonstrate remarkable efficiency and robustness, enabling faster exploration of milk flow behavior in individual lactating breasts compared to conventional CFD solvers.