Interpretable surrogate modeling of extrusion flows with deep learning

Predicting the deformed shape of nested co-axial streams after extrusion through a shaped nozzle is a bottleneck for microparticle and microfiber fabrication as well as other extrusion processes, due to the need for fully resolved three-dimensional (3D) computational fluid dynamics simulations requiring significant expertise, computational resources, and time. We recast this problem as an image translation task, mapping a two-dimensional (2D) nozzle shape to a 2D output cross section of a shaped flow. By doing so, we bypass meshing and 3D solvers by using a deep learning (DL) U-Net model to predict fully miscible, low Reynolds number (Re=1) extrusion flow shapes, achieving 450× speedup with second-scale prediction times. The DL model approximately conserves mass and achieves a mean intersection over union of 0.9757 on a held-out test set of nozzle shapes. Saliency-based interpretability analysis of the DL model shows that such extrusion flows are robust to variations in nozzle wall thickness and, for low to moderate inner flow rates, to the shape of the outer flow wall. This robustness, along with the DL model's speed and accuracy, enables efficient and practical data-driven design of co-axial extrusion devices and highlights the broader potential of interpretable surrogates in microfluidic flow engineering.