Multivariate optimization and inverse design of multiphase reactive systems via deep learning and 3D CFD–PBM simulations

This work presents a deep learning-driven framework for multivariate optimization, focusing on the identification of precipitation kinetics parameters in a complex three-dimensional (3D) Computational Fluid Dynamics-Population Balance Model (CFD-PBM) model describing Mg(OH) 2 precipitation in T- and Y-mixer static reactors. A numerical dataset was first generated using the CFD-PBM model to train an inverse design deep leaning neural network (mirror model), which takes characteristic particle dimensions ( d ⃗ ) as input and predicts the corresponding kinetic parameters ( φ ⃗ ) as output. Experimental particle size distributions (PSD) from the T-mixer were then provided to the trained mirror model to predict the kinetic parameter vector. The predicted parameters were subsequently validated by comparing the CFD-PBM outputs with experimental PSD from the Y-mixer configuration. The framework demonstrates excellent generalization, accurately reproducing PSD for conditions not included in the training set. Moreover, the same numerical dataset was also employed to train a surrogate CFD-PBM model which takes kinetic parameters ( φ ⃗ ) as input and returns characteristic particle dimensions ( d ⃗ ) as output. The surrogate CFD-PBM model was subsequently used to perform a sensitivity analysis of the kinetic parameters. Minor deviations are observed in the estimation of the smallest ( d 10 ) and largest ( d 43 ) particle size fractions, consistent with physical aggregation and collision mechanisms. A key outcome of this study is that the proposed framework enables, for the first time, the use of fully 3D CFD–PBM simulations equipped with a rigorously calibrated kinetic model, without requiring empirical simplifications or iterative fitting procedures. This significantly enhances the predictive capability of 3D CFD–PBM models in nonlinear reactive systems, providing a computationally efficient and generalizable tool for kinetic parameter identification in precipitation and crystallization processes. • A predictive 3D CFD-PBM for Mg(OH) 2 precipitation is proposed. • The unknown kinetic parameters are inferred in a T-mixer using deep learning. • The model turns out to have predictive power for the experiments from a Y-mixer.