Simulation / Modeling / Design

Using Graph Neural Networks for Additive Manufacturing

Image of two simulations.

Lattice structures are naturally and artificially made designs that are important in many scientific fields, such as materials science, aerospace engineering, and biomedical engineering. They are made by repeating patterns that connect smaller truss structures and yield a high strength-to-weight ratio. 

The rise of 3D printing within additive manufacturing has highlighted the significance of lattices, enabling the creation of customized designs with complex geometries and spatially tuned material properties. Lattice designs can be tailored to meet specific needs. For example, they can be made stronger to carry more weight or designed with enhanced thermal conductivity. The ability to customize lattice structures makes them useful in many different fields, particularly in disciplines where theory and practical applications come together.

Researchers at Carbon3D are using AI to create efficient, cost-effective simulations for complex 3D-printed structures, specifically focusing on intricate lattice designs. They are using NVIDIA Modulus to train graph neural networks as AI surrogates that emulate lattice structure dynamics.

This technology addresses a critical challenge in additive manufacturing: — the high cost and time involved in simulating the behavior of complex parts. Traditionally, designing products that absorb energy—like the soles of shoes, helmet padding, and bike seat cushions—requires expensive prototyping and physical testing due to the limitations of simulation tools. 

Carbon3D’s approach uses surrogate models that are simplified digital representations of the actual structure. The researchers use NVIDIA Modulus as their training framework and use optimized network architectures, which provide enhanced memory efficiency and computational performance. This enables high-fidelity analysis while significantly reducing computational demands. 

This breakthrough has the potential to revolutionize the design and adoption of 3D printing for intricate structures. It opens doors to faster development cycles and more innovative product designs.

Image of a composite structure formed from five distinct unit cell types, showing the variety of configurations that can be obtained for additive manufacturing through a limited set of initial repeating blocks.
Figure 1. A sample 3D-printed elastomeric component, used in additive manufacturing

Introducing LatticeGraphNet: A graph network for lattice structures

Understanding the mechanical characteristics of lattice structures often requires costly and time-consuming physical experimentation and high-fidelity numerical simulations. 

These simulations, particularly the Incremental Potential Contact (IPC) method, can precisely describe how elastomeric lattice structures react to compression. However, such simulations are complex and take a long time to run, highlighting the need for faster simulations.

Physics-informed machine learning (physics-ML) techniques, especially physics-informed neural networks (PINNs) and graph neural networks (GNNs), have made significant strides in augmenting numerical method-based simulations. These approaches are particularly effective for learning the dynamics of mesh-based simulations and have been proposed to aid in the characterization of metamaterial components.

LatticeGraphNet (LGN) is a pioneering graph neural operator (GNO) that employs a MeshGraphNet (MGN) architecture. It was developed as a surrogate model for high-fidelity nonlinear neo-Hookean IPC simulations of 3D-latticed metamaterials. 

LGN uses a multi-scale architecture using two MGN-based architectures, LGN-i and LGN-ii, to predict dynamics at different precision levels. This significantly reduces the time of running inference and maintains high accuracy for unseen simulations.

The LGN pipeline begins with an initial 3D lattice represented by a tetrahedral mesh, which is transformed into a reduced (skeletal) representation. LGN-i runs inference on the reduced mesh to get the coarse displacement, and LGN-ii maps these displacements to predict fine volumetric displacements on the tetrahedral mesh.

The theoretical foundation of LGN is rooted in the dynamics of lattices. It considers elastomeric materials described using the hyperelastic neo-Hookean model under large deformations. The training data for the deformation of lattices are generated based on the neo-Hookean elastodynamic formulation using the IPC method.

LGN-i, as part of the LGN pipeline, contains three main parts: 

  • Encoder: Encodes the node and edge features to high-dimensional vectors.
  • Processor: Processes the high-dimensional vectors through a message-passing block.
  • Decoder: Computes the final displacement and stress invariant increments.
Input to the network is a reduced graph representation of the tetrahedral mesh. The node encoder and edge encoder encode the node and edge features to high-dimensional vectors. The message-passing block uses two processor MLPs. LGN-i uses 15 message-passing steps with identical blocks. The two-part decoder contains MLPs to compute the displacement increment and calculate the change in the stress invariants. Upon rollout, the node and edge features for the next timestep are computed.
Figure 2. LGN-i network architecture enables LatticeGraphNet to predict dynamics at different precision levels

LGN-ii iterates over each skeletal node and the positions of its associated tetrahedral nodes to predict the deformation of volumetric tetrahedral nodes. This network also consists of an encoder, a processor, and a decoder, each tailored to handle different aspects of the lattice structure.

LGN-i predicts the displacement of every strut node. Based on this information, LGN-ii predicts the fine local deformation of the jth tetrahedral node. The final tetrahedral node displacement is the sum of the two displacements.
Figure 3. Volumetric deformation prediction set up by the LGN-ii

In addition to predicting deformations, LGN uses a homogenization approach to approximate reaction forces, an essential aspect of understanding lattice mechanics.

The research team used NVIDIA Modulus to explore and experiment with these architectural innovations, using the MeshGraphNet implementation from Modulus as the backbone. 

The team also developed their model training code with the Modulus vortex shedding recipe as a foundation, customizing it to suit their specific use case.

The training dataset included 108 high-fidelity simulations from Carbon’s MetaMaterial library. The training dataset was further augmented during the training phase to ensure robustness and accuracy. The LGN was tested on a set of eight additional simulations spanning a variety of lattice shapes and thicknesses.

A milestone in lattice simulation

The results from LGN demonstrate its ability to accurately predict the deformation of elastomeric lattices, including challenging aspects like buckling. While LGN is only trained until 25% strain, and some inaccuracies were noted in reaction force predictions, the overall performance of LGN marks a significant advancement in the field.

Four 3D renderings of elastomeric lattices, which accurately predicted deformation.
Figure 4. Original latticed puck, predicted deformation at 25% compression by LGN, and the distribution of displacement errors of volumetric nodes.

LatticeGraphNet stands as a significant milestone in simulating lattice structures, providing a powerful tool for rapid and accurate predictions. Its development is a testament to the innovative application of machine learning in manufacturing.

This integration showcases the potential of AI surrogates to emulate the dynamics of engineering structures and opens up new avenues for designing and analyzing complex structures.

Using NVIDIA Modulus for physics simulation and manufacturing 

NVIDIA Modulus is an open-source project under the Apache 2.0 license to support the growing physics-ML community. If you are an AI researcher working in the field of physics-informed machine learning, see the /NVIDIA/Modulus GitHub repo to learn how NVIDIA Modulus can help your project. 

NVIDIA Modulus serves as a versatile toolkit for your research endeavors. It enables you to use a range of GPU-optimized network architectures, much like the Carbon3D researchers who employed the MeshGraphNet model from NVIDIA Modulus for additive manufacturing research. 

NVIDIA Modulus also provides an extensive array of data pipelines, metrics, and utilities, along with a distributed manager that supports both data and model parallelism. You can use the reference applications across various domains and corresponding training recipes that provide a great starting point for your research. Tailor them to fit your needs.

If you would like to contribute your work to the project, follow the contribution guidelines in the project and engage with the NVIDIA Modulus team at /NVIDIA/modulus/discussions.


NVIDIA is celebrating developer contributions across use cases, demonstrating how to build and train physics-ML models using the NVIDIA Modulus framework. Equally important is the effort to systematically organize such innovative work in the Modulus open-source project for the community and the ecosystem to leverage for their engineering and science surrogate modeling problems. 

To learn more about how Modulus is being used across industries, see the NVIDIA Modulus Resources Center. To learn more about Carbon’s lattice designs, see Carbon3D.

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