Bayesian Optimization of Grayscale Patterns for Layer‐Height Accuracy in Projection Multi‐Photon 3D Printing

Projection multi‐photon lithography (PMPL) is a high‐throughput, layer‐by‐layer nanoscale 3D printing method that can offer orders‐of‐magnitude higher fabrication speed than conventional direct laser writing techniques. Achieving precise geometric accuracy with PMPL requires accurate control of both in‐plane patterning and the height of each printed layer, both of which are strongly affected by nonlinear polymerization kinetics and optical exposure conditions. We present a Bayesian optimization framework that integrates grayscale patterning with in situ quantitative phase imaging to autonomously correct layer‐height deviations during PMPL. A simplified mechanistic model of the projection and polymerization process is incorporated, providing a physics‐informed parameterization of grayscale exposure. Then, both the model's key parameters and specific process variables for grayscale patterning are optimized by the Bayesian framework to minimize layer‐height error. Tests on representative 2D structures demonstrate that the method achieves more uniform, accurate layers in under 300 prints, substantially reducing experimental effort compared with conventional trial‐and‐error approaches. By integrating physics‐informed parameterization, in situ optical metrology, and data‐efficient machine learning, this approach enables precise and repeatable layers in PMPL and provides a broadly applicable strategy for optimization of other micro‐ and nano‐fabrication processes.