mlsanityData to 7 Oct 2026

Micrometer: Micromechanics Transformer for Predicting Mechanical Responses of Heterogeneous Materials

arXiv 2410.05281 ↗First posted 23 Sep 2024cs.CE cond-mat.mtrl-sci cs.LGcited by 5

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Abstract (arXiv)

Heterogeneous materials, crucial in various engineering applications, exhibit complex multiscale behavior, which challenges the effectiveness of traditional computational methods. In this work, we introduce the Micromechanics Transformer (em Micrometer), an artificial intelligence (AI) framework for predicting the mechanical response of heterogeneous materials, bridging the gap between advanced data-driven methods and complex solid mechanics problems. Trained on a large-scale high-resolution dataset of 2D fiber-reinforced composites, Micrometer can achieve state-of-the-art performance in predicting microscale strain fields across a wide range of microstructures, material properties under any loading conditions and We demonstrate the accuracy and computational efficiency of Micrometer through applications in computational homogenization and multiscale modeling, where Micrometer achieves 1% error in predicting macroscale stress fields while reducing computational time by up to two orders of magnitude compared to conventional numerical solvers. We further showcase the adaptability of the proposed model through transfer learning experiments on new materials with limited data, highlighting its potential to tackle diverse scenarios in mechanical analysis of solid materials. Our work represents a significant step towards AI-driven innovation in computational solid mechanics, addressing the limitations of traditional numerical methods and paving the way for more efficient simulations of heterogeneous materials across various industrial applications.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 42 of its 107 references that are in the map. First posted on arXiv 23 Sep 2024.

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42 of 107 references.

References · 42

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 29,915
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  4. 2020Scaling Laws for Neural Language Modelscited by 6,411
  5. 2022Training Compute-Optimal Large Language Modelscited by 2,927
  6. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  7. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  8. 2021Scaling Vision Transformerscited by 993
  9. 2020On Layer Normalization in the Transformer Architecturecited by 906
  10. 2020Convolutional Occupancy Networkscited by 760
  11. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
  12. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
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  1. 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 396
  2. 2020Local Implicit Grid Representations for 3D Scenescited by 372
  3. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 321
  4. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 293
  5. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 292
  6. 2022Transformer for Partial Differential Equations' Operator Learningcited by 270
  7. 2021Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformerscited by 237
  8. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 190
  9. 2024Poseidon: Efficient Foundation Models for PDEscited by 186
  10. 2021Modulated Periodic Activations for Generalizable Local Functional Representationscited by 140
  11. 2024DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Trainingcited by 137
  12. 2023An Expert's Guide to Training Physics-informed Neural Networkscited by 119
  13. 2023Multiple Physics Pretraining for Physical Surrogate Modelscited by 90
  14. 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 87
  15. 2023Getting ViT in Shape: Scaling Laws for Compute-Optimal Model Designcited by 87
  16. 2021Improved architectures and training algorithms for deep operator networkscited by 85
  17. 2024Operator Learning: Algorithms and Analysiscited by 84
  18. 2022NOMAD: Nonlinear Manifold Decoders for Operator Learningcited by 81
  19. 2022Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modelingcited by 65
  20. 2023Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustnesscited by 60
  21. 2023Inverse-design of nonlinear mechanical metamaterials via video denoising diffusion modelscited by 48
  22. 2023MeLM, a generative pretrained language modeling framework that solves forward and inverse mechanics problemscited by 29
  23. 2024Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operatorscited by 25
  24. 2020Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropycited by 22
  25. 2021Stress field prediction in fiber-reinforced composite materials using a deep learning approachcited by 22
  26. 2023Unifying the design space and optimizing linear and nonlinear truss metamaterials by generative modelingcited by 21
  27. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  28. 2020Deep Optimized Priors for 3D Shape Modeling and Reconstructioncited by 20
  29. 2020A numerical method for computing the overall response of nonlinear composites with complex microstructurecited by 18
  30. 2023Deep Operator Learning Lessens the Curse of Dimensionality for PDEscited by 18

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Citing papers per year: 2025: 4; 2026: 1.

5 papers.