<p>Electrochemical additive manufacturing (ECAM) can achieve atomic-level deformation manufacturing and has become an important part of modern manufacturing industry. In order to ensure the continuous growth of the manufactured parts and maintain the stability of the electrode gap, the dynamic balance between the growth of the parts and the feed rate of the anode must be maintained during the additive process. Due to the complex nonlinear relationship between the growth of the parts and various process parameters, it is impossible to describe the quantitative relationship between the two through a large number of experiments. To address this challenge, the present study proposes a computational framework that integrates physics-based simulation, data-driven modeling, and experimental optimization. A surrogate model is developed to partially replace conventional physical simulations and experimental trials, thereby establishing a growth model for magnetic field-assisted electrochemical additive manufacturing and enabling dynamic stabilization of the interelectrode gap. Firstly, the process factors that affect the geometric forming are screened through PBD experiments. Then, a coupled multiphysics simulation model is established between the flow field, electric field, magnetic field, electrochemical reaction, and rare material transport. Then, a data-driven approach is used to construct a nonlinear relationship between the growth model and process parameters using BP neural network. Finally, in order to improve the accuracy of the prediction model, genetic algorithm is used for conditional optimization of the fitness function of ANN model, and a GA-BP neural network is constructed to obtain a surrogate model for electrochemical additive manufacturing assisted by magnetic field. The surrogate model is validated through the constructed experimental platform, and it can partially replace the growth model with an average error of 4.49%. The surrogate model can maintain the dynamic stability of the electrode gap during the additive process, and can also provide reference for the prediction of deposition rate and the development of slicing software.</p>