mlsanityData to 14 Oct 2026

Energy-conserving equivariant GNN for elasticity of lattice architected metamaterials

arXiv 2401.16914 ↗First posted 30 Jan 2024cs.LG cond-mat.mtrl-scicited by 4

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Abstract (arXiv)

Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work, we generate a big dataset of structure-property relationships for strut-based lattices. The dataset is made available to the community which can fuel the development of methods anchored in physical principles for the fitting of fourth-order tensors. In addition, we present a higher-order GNN model trained on this dataset. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate its benefits in terms of predictive performance and reduced training requirements. Finally, we demonstrate an example application of the model to an architected material design task. The methods which we developed are applicable to fourth-order tensors beyond elasticity such as piezo-optical tensor etc.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 12 of its 33 references that are in the map. First posted on arXiv 30 Jan 2024.

Builds on

12 of 33 references.

References · 12

  1. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  2. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  3. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 708
  4. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 474
  5. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 354
  6. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 264
  7. 2019Cormorant: Covariant Molecular Neural Networkscited by 263
  8. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 228
  9. 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 171
  10. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 90
  11. 2022Learning the nonlinear dynamics of soft mechanical metamaterials with graph networkscited by 7
  12. 2022Neural Network Layers for Prediction of Positive Definite Elastic Stiffness Tensorscited by 3

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Cited by year

Citing papers per year: 2024: 2; 2025: 2.

4 papers.

  1. 2024Higher-Rank Irreducible Cartesian Tensors for Equivariant Message Passingcited by 13
  2. 2024Conservation-informed Graph Learning for Spatiotemporal Dynamics Predictioncited by 4
  3. 2025MetamatBench: Integrating Heterogeneous Data, Computational Tools, and Visual Interface for Metamaterial Discoverycited by 2
  4. 2025UniMate: A Unified Model for Mechanical Metamaterial Generation, Property Prediction, and Condition Confirmationcited by 2