Physics-Informed Dynamical Modeling of Extrusion-Based Three-Dimensional Printing Processes

Abstract The tradeoff between model fidelity and computational cost remains a central challenge in the computational modeling of extrusion-based 3D printing, particularly for real-time optimization and control. Although high-fidelity simulations have advanced considerably for offline analysis, dynamical modeling tailored for online, control-oriented applications is still significantly underdeveloped. In this study, we propose a reduced-order dynamical flow model that captures the transient behavior of extrusion-based 3D printing. The model is grounded in physics-based principles derived from the Navier–Stokes equations and further simplified through spatial averaging and input-dependent parameterization. To assess its performance, the model is identified via a nonlinear least-squares approach using computational fluid dynamics (CFD) simulation data spanning a range of printing conditions and subsequently validated across multiple combinations of training and testing scenarios. The results demonstrate strong agreement with the CFD data within the nozzle, the nozzle–substrate gap, and the deposited-layer regions. Overall, the proposed reduced-order model successfully captures the dominant flow dynamics of the process while maintaining a level of simplicity compatible with real-time control and optimization.