mlsanityData to 7 Oct 2026

A Microstructure-based Graph Neural Network for Accelerating Multiscale Simulations

arXiv 2402.13101 ↗First posted 20 Feb 2024cs.LG cs.NA math.NAcited by 7

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Abstract (arXiv)

Simulating the mechanical response of advanced materials can be done more accurately using concurrent multiscale models than with single-scale simulations. However, the computational costs stand in the way of the practical application of this approach. The costs originate from microscale Finite Element (FE) models that must be solved at every macroscopic integration point. A plethora of surrogate modeling strategies attempt to alleviate this cost by learning to predict macroscopic stresses from macroscopic strains, completely replacing the microscale models. In this work, we introduce an alternative surrogate modeling strategy that allows for keeping the multiscale nature of the problem, allowing it to be used interchangeably with an FE solver for any time step. Our surrogate provides all microscopic quantities, which are then homogenized to obtain macroscopic quantities of interest. We achieve this for an elasto-plastic material by predicting full-field microscopic strains using a graph neural network (GNN) while retaining the microscopic constitutive material model to obtain the stresses. This hybrid data-physics graph-based approach avoids the high dimensionality originating from predicting full-field responses while allowing non-locality to arise. By training the GNN on a variety of meshes, it learns to generalize to unseen meshes, allowing a single model to be used for a range of microstructures. The embedded microscopic constitutive model in the GNN implicitly tracks history-dependent variables and leads to improved accuracy. We demonstrate for several challenging scenarios that the surrogate can predict complex macroscopic stress-strain paths. As the computation time of our method scales favorably with the number of elements in the microstructure compared to the FE method, our method can significantly accelerate FE2 simulations.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 20 of its 45 references that are in the map. First posted on arXiv 20 Feb 2024.

Builds on

20 of 45 references.

References · 20

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8 more
  1. 2018A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materialscited by 31
  2. 2022Finite electro-elasticity with physics-augmented neural networkscited by 12
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 4; 2026: 3.

7 papers.

  1. 2026Artificial Intelligence in Materials Science and Engineering: Current Landscape, Key Challenges, and Future Trajectoriecited by 5
  2. 2025Physics-Informed Graph Neural Networks to Reconstruct Local Fields Considering Finite Strain Hyperelasticitycited by 2
  3. 2025Rigid-Deformation Decomposition AI Framework for 3D Spatio-Temporal Prediction of Vehicle Collision Dynamicscited by 1
  4. 2025Towards scientific machine learning for granular material simulations -- challenges and opportunitiescited by 1
  5. 2025A Comparison of Surrogate Constitutive Models for Viscoplastic Creep Simulation of HT-9 Steelcited by 0
  6. 2026Non-linear mechanical field reconstruction coupling recurrent neural networks with physics-informed graph neural networkscited by 0
  7. 2026Microstructure-Conditioned Surrogate Models for Graded Multiscale Optimization of Mycelium Compositescited by 0