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

arXiv: https://arxiv.org/abs/2502.01517 · HTML: https://mlsanity.com/paper/2502.01517/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 60 references that are in the map.
- First posted on arXiv 3 Feb 2025.

## Builds on (most cited first, 25 of 25)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [Gaussian Splatting SLAM](https://mlsanity.com/paper/2312.06741/) (2023)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [Robustness via curvature regularization, and vice versa](https://mlsanity.com/paper/1811.09716/) (2018)
- [S3CNet: A Sparse Semantic Scene Completion Network for LiDAR Point Clouds](https://mlsanity.com/paper/2012.09242/) (2020)
- [Learning Smooth Neural Functions via Lipschitz Regularization](https://mlsanity.com/paper/2202.08345/) (2022)
- [Physics informed deep learning for computational elastodynamics without labeled data](https://mlsanity.com/paper/2006.08472/) (2020)
- [MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework](https://mlsanity.com/paper/2005.01463/) (2020)
- [NTopo: Mesh-free Topology Optimization using Implicit Neural Representations](https://mlsanity.com/paper/2102.10782/) (2021)
- [Feature-Realistic Neural Fusion for Real-Time, Open Set Scene Understanding](https://mlsanity.com/paper/2210.03043/) (2022)
- [A Multi-Implicit Neural Representation for Fonts](https://mlsanity.com/paper/2106.06866/) (2021)
- [Intuitive Shape Editing in Latent Space](https://mlsanity.com/paper/2111.12488/) (2021)
- [3D Masked Autoencoders with Application to Anomaly Detection in Non-Contrast Enhanced Breast MRI](https://mlsanity.com/paper/2303.05861/) (2023)
- [Capturing dynamical correlations using implicit neural representations](https://mlsanity.com/paper/2304.03949/) (2023)

## Built on by (most cited first, 1 of 1)

- [Hybrid Reasoning for Perception, Explanation, and Autonomous Action in Manufacturing](https://mlsanity.com/paper/2506.08462/) (2025)

## Abstract (arXiv)

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.