Regularized interpolation in 4D neural fields enables optimization of 3D printed geometries

The ability to accurately produce geometries with specified properties is perhaps the most important characteristic of a manufacturing process. 3D printing is marked by exceptional design freedom and complexity but is also prone to geometric and other defects that must be resolved for it to reach its full potential. Ultimately, this will require both astute design decisions and timely parameter adjustments to maintain stability that is challenging even with expert human operators. While machine learning is widely investigated in 3D printing, existing methods typically overlook spatial features that vary across prints and thus find it difficult to produce desired geometries. Here, we encode volumetric representations of printed parts into neural fields and apply a new regularization strategy, based on minimizing the partial derivative of the field's output with respect to a single, non-learnable parameter. By thus encouraging small input changes to yield only small output variations, we encourage smooth interpolation between observed volumes and hence realistic geometry predictions. This framework therefore allows the extraction of 'imagined' 3D shapes, revealing how a part would look if manufactured under previously unseen parameters. The resulting continuous field is used for data-driven optimization to maximize geometric fidelity between expected and produced geometries, reducing post-processing, material waste, and production costs. By optimizing process parameters dynamically, our approach enables advanced planning strategies, potentially allowing manufacturers to better realize complex and feature-rich designs.