# Geometric deep learning for computational mechanics Part II: Graph embedding for interpretable multiscale plasticity

arXiv: https://arxiv.org/abs/2208.00246 · HTML: https://mlsanity.com/paper/2208.00246/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 92 references that are in the map.
- First posted on arXiv 30 Jul 2022.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [LLNet: A Deep Autoencoder Approach to Natural Low-light Image Enhancement](https://mlsanity.com/paper/1511.03995/) (2015)
- [Polyconvex anisotropic hyperelasticity with neural networks](https://mlsanity.com/paper/2106.14623/) (2021)
- [Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticity](https://mlsanity.com/paper/2001.04292/) (2020)
- [Multi-level Convolutional Autoencoder Networks for Parametric Prediction of Spatio-temporal Dynamics](https://mlsanity.com/paper/1912.11114/) (2019)
- [Model-Free Data-Driven Inelasticity](https://mlsanity.com/paper/1808.10859/) (2018)
- [A Physics-Constrained Data-Driven Approach Based on Locally Convex Reconstruction for Noisy Database](https://mlsanity.com/paper/1907.12651/) (2019)
- [Local approximate Gaussian process regression for data-driven constitutive laws: Development and comparison with neural networks](https://mlsanity.com/paper/2105.04554/) (2021)
- [Data-driven fracture mechanics](https://mlsanity.com/paper/2006.03133/) (2020)
- [Comparing the latent space of generative models](https://mlsanity.com/paper/2207.06812/) (2022)
- [Data-driven discovery of interpretable causal relations for deep learning material laws with uncertainty propagation](https://mlsanity.com/paper/2105.09980/) (2021)
- [A cooperative game for automated learning of elasto-plasticity knowledge graphs and models with AI-guided experimentation](https://mlsanity.com/paper/1903.04307/) (2019)
- [Training multi-objective/multi-task collocation physics-informed neural network with student/teachers transfer learnings](https://mlsanity.com/paper/2107.11496/) (2021)
- [A non-cooperative meta-modeling game for automated third-party calibrating, validating, and falsifying constitutive laws with parallelized adversarial attacks](https://mlsanity.com/paper/2004.09392/) (2020)
- [A heteroencoder architecture for prediction of failure locations in porous metals using variational inference](https://mlsanity.com/paper/2202.00078/) (2022)

## Built on by (most cited first, 11 of 11)

- [Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamics](https://mlsanity.com/paper/2304.14369/) (2023)
- [A review on data-driven constitutive laws for solids](https://mlsanity.com/paper/2405.03658/) (2024)
- [Modular machine learning-based elastoplasticity: generalization in the context of limited data](https://mlsanity.com/paper/2210.08343/) (2022)
- [UniPhy: Learning a Unified Constitutive Model for Inverse Physics Simulation](https://mlsanity.com/paper/2505.16971/) (2025)
- [A Microstructure-based Graph Neural Network for Accelerating Multiscale Simulations](https://mlsanity.com/paper/2402.13101/) (2024)
- [Convolution, aggregation and attention based deep neural networks for accelerating simulations in mechanics](https://mlsanity.com/paper/2212.01386/) (2022)
- [Synthesizing realistic sand assemblies with denoising diffusion in latent space](https://mlsanity.com/paper/2306.04411/) (2023)
- [Recurrent neural networks and transfer learning for elasto-plasticity in woven composites](https://mlsanity.com/paper/2311.13434/) (2023)
- [Stress Predictions in Polycrystal Plasticity using Graph Neural Networks with Subgraph Training](https://mlsanity.com/paper/2409.05169/) (2024)
- [Uncertainty Quantification of Graph Convolution Neural Network Models of Evolving Processes](https://mlsanity.com/paper/2402.11179/) (2024)
- [Graph Neural Networks-based Hybrid Framework For Predicting Particle Crushing Strength](https://mlsanity.com/paper/2307.13909/) (2023)

## Abstract (arXiv)

The history-dependent behaviors of classical plasticity models are often driven by internal variables evolved according to phenomenological laws. The difficulty to interpret how these internal variables represent a history of deformation, the lack of direct measurement of these internal variables for calibration and validation, and the weak physical underpinning of those phenomenological laws have long been criticized as barriers to creating realistic models. In this work, geometric machine learning on graph data (e.g. finite element solutions) is used as a means to establish a connection between nonlinear dimensional reduction techniques and plasticity models. Geometric learning-based encoding on graphs allows the embedding of rich time-history data onto a low-dimensional Euclidean space such that the evolution of plastic deformation can be predicted in the embedded feature space. A corresponding decoder can then convert these low-dimensional internal variables back into a weighted graph such that the dominating topological features of plastic deformation can be observed and analyzed.