Physics‐Based Generative Optimization of Fishbone Runner Systems for Multi‐Cavity Injection Molds With <scp>ML</scp> ‐Assisted Initialization

ABSTRACT Unbalanced filling in multi‐cavity molds leads to part‐dimension variations, reduced productivity, and challenges in quality control. Although H‐type runner systems can achieve balanced flow, increasing cavity count intensifies shear heating and material consumption compared with fishbone runner systems. Existing runner‐design approaches are largely based on CAE‐driven trial‐and‐error optimization and often lack a clear physics‐based design framework. This study proposes a physics‐based analytical methodology for optimizing fishbone runner systems with arbitrary cavity counts. The method sequentially determines both runner diameters and lengths using flow‐balancing criteria derived from pressure drop and remaining filling time, rather than adjusting diameters within a fixed layout. The influence of key design variables is explicitly evaluated through their effects on pressure drop and filling‐time distribution, enabling transparent physical interpretation. To enhance robustness and computational efficiency, a lightweight machine‐learning module is introduced as an auxiliary tool. A single‐neuron perceptron model is used to screen feasible initialization ranges and reduce failed optimization restarts caused by unsuitable initial conditions. Machine learning does not generate runner designs or perform multi‐objective optimization; instead, multiple feasible configurations arise naturally from the physics‐based generative framework under different design conditions. The proposed methodology provides a systematic and physically grounded approach for balanced runner design.