System-level multi-stage modeling and multi-criteria optimization of direct ink writing

Direct ink writing (DIW) has emerged as an additive manufacturing technique for fabricating multiple functional structures, but its deployment is often limited by stage-wise optimization that overlooks system-level trade-offs among printability, structural integrity, and energy efficiency. To address this gap, we develop an integrated experimental platform and a unified modeling and optimization framework that spans ink preparation, printing, drying, and product characterization in a DIW system. We conduct an experiment with 81 runs on silica inks by varying material composition and printing speeds, with measurements ranging from rheometry, 3D scanning, drying, to thermal conductivity. Building on these data, we propose the Multi-stage modeling and Multi-criteria Optimization Network (MMO-Net), a deep neural network with GRU-based cross-stage feature transition and multi-task heads that jointly predict rheological properties, printing time, geometric fidelity before and after drying, and cracking probability. Compared with linear regression and a deep multi-stage multi-task learning baseline, MMO-Net achieves the lowest total regression loss and 100% accuracy in cracking classification on the test set. Coupling MMO-Net with Bayesian optimization further enables multi-criteria search over controllable parameters, yielding a process setting that simultaneously reduces cracking probability, printing time, and thermal conductivity while maintaining target thickness, which is confirmed by validation experiments. The proposed framework demonstrates a scalable route toward system-level modeling and optimization of DIW.