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

TL;DR

This work tackles geometric fidelity in material extrusion 3D printing by learning continuous volumetric representations that depend on the process parameter $\phi$, enabling optimization of print parameters to match a target geometry. The core idea is a neural field that maps $(x,y,z,\phi)$ to occupancy (or signed distance) and is regularized with gradient-driven interpolation regularization (GDIR) to enforce Lipschitz-like smoothness across $\phi$, improving interpolation to unseen flow rates. They build a CT-based dataset across four geometries and nine flow-rate settings, demonstrate that GDIR and a volume-to-SDF formulation yield more stable and accurate predictions, and show how the learned field can be used as a simulator to perform per-layer flow-rate optimization (e.g., for the Bunny model) to maximize geometric fidelity. The approach promises lower post-processing, reduced material waste, and dynamic parameter planning for complex designs, with potential extensions to other manufacturing domains and even video frame interpolation. Overall, this work establishes neural-field–driven, physics-informed optimization as a viable pathway to smarter, data-driven additive manufacturing.

Abstract

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.

Figures (6)

• Figure 1: Data collection and processing pipeline.A. Sample axial and voxel frames obtained from the computer tomography procedure. B. Data processing pipeline developed for cleaning and registering different trials from the same geometry manufactured at different flow rate values. C. Rendered parts from the Bolt trials.
• Figure 2: End-to-end domain solver. The domain is solved for a specific flow rate value, $\phi$, through the trained 4D neural field. The calculation of the partial derivative of the output $f_\mathrm{\Theta}$ with respect to $\phi$ and minimization of its magnitude enables smooth interpolation between seen $\phi$s.
• Figure 3: Interpolation results. While SIREN (blue) collapse at unseen regimes, our network (pink) generates smoother interpolation results.
• Figure 5: Geometric fidelity optimization results.A. Renders of the produced geometry of the Stanford bunny as manufactured at 100% and 170% flow rate values. B. The optimization pipeline compares the learned field reconstructions with renderings from the expected geometry. C. The optimization landscape. For every layer of the print, the optimal flow rate value $\phi$* is the selected such that reconstructed and expected geometries match. D. Applying the values on a per-layer basis yields better geometric outcomes.
• Figure A1: An example supplementary figure.