# Predicting Mechanically Driven Full-Field Quantities of Interest with Deep Learning-Based Metamodels

arXiv: https://arxiv.org/abs/2108.03995 · HTML: https://mlsanity.com/paper/2108.03995/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 83 references that are in the map.
- First posted on arXiv 24 Jul 2021.

## Builds on (most cited first, 27 of 27)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [FlowNet: Learning Optical Flow with Convolutional Networks](https://mlsanity.com/paper/1504.06852/) (2015)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Recent Advances in Convolutional Neural Networks](https://mlsanity.com/paper/1512.07108/) (2015)
- [MultiResUNet : Rethinking the U-Net Architecture for Multimodal Biomedical Image Segmentation](https://mlsanity.com/paper/1902.04049/) (2019)
- [Transfer learning enhanced physics informed neural network for phase-field modeling of fracture](https://mlsanity.com/paper/1907.02531/) (2019)
- [W-Net: A Deep Model for Fully Unsupervised Image Segmentation](https://mlsanity.com/paper/1711.08506/) (2017)
- [Fully Dense UNet for 2D Sparse Photoacoustic Tomography Artifact Removal](https://mlsanity.com/paper/1808.10848/) (2018)
- [Simulation of hyperelastic materials in real-time using Deep Learning](https://mlsanity.com/paper/1904.06197/) (2019)
- [Application of Convolutional Neural Network to Predict Airfoil Lift Coefficient](https://mlsanity.com/paper/1712.10082/) (2017)
- [Using Machine Learning to Augment Coarse-Grid Computational Fluid Dynamics Simulations](https://mlsanity.com/paper/2010.00072/) (2020)
- [Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy](https://mlsanity.com/paper/2012.15744/) (2020)
- [Meta-modeling game for deriving theoretical-consistent, micro-structural-based traction-separation laws via deep reinforcement learning](https://mlsanity.com/paper/1810.10535/) (2018)
- [Machine learning materials physics: Multi-resolution neural networks learn the free energy and nonlinear elastic response of evolving microstructures](https://mlsanity.com/paper/2001.01575/) (2019)
- [Machine Learning-Based Optimal Mesh Generation in Computational Fluid Dynamics](https://mlsanity.com/paper/2102.12923/) (2021)
- [Exploring the potential of transfer learning for metamodels of heterogeneous material deformation](https://mlsanity.com/paper/2010.16260/) (2020)
- [A machine learning approach for efficient uncertainty quantification using multiscale methods](https://mlsanity.com/paper/1711.04315/) (2017)
- [Scale bridging materials physics: Active learning workflows and integrable deep neural networks for free energy function representations in alloys](https://mlsanity.com/paper/2002.02305/) (2020)
- [Difference-Based Deep Learning Framework for Stress Predictions in Heterogeneous Media](https://mlsanity.com/paper/2007.04898/) (2020)
- [A Data-Driven Approach to Full-Field Damage and Failure Pattern Prediction in Microstructure-Dependent Composites using Deep Learning](https://mlsanity.com/paper/2104.04485/) (2021)

## Built on by (most cited first, 10 of 10)

- [Towards out of distribution generalization for problems in mechanics](https://mlsanity.com/paper/2206.14917/) (2022)
- [A finite operator learning technique for mapping the elastic properties of microstructures to their mechanical deformations](https://mlsanity.com/paper/2404.00074/) (2024)
- [Enhancing Mechanical Metamodels with a Generative Model-Based Augmented Training Dataset](https://mlsanity.com/paper/2203.04183/) (2022)
- [Learning Mechanically Driven Emergent Behavior with Message Passing Neural Networks](https://mlsanity.com/paper/2202.01380/) (2022)
- [A spatiotemporal deep learning framework for prediction of crack dynamics in heterogeneous solids: efficient mapping of concrete microstructures to its fracture properties](https://mlsanity.com/paper/2407.15665/) (2024)
- [Investigating Deep Learning Model Calibration for Classification Problems in Mechanics](https://mlsanity.com/paper/2212.00881/) (2022)
- [Segmenting mechanically heterogeneous domains via unsupervised learning](https://mlsanity.com/paper/2308.15697/) (2023)
- [Towards Robust Surrogate Models: Benchmarking Machine Learning Approaches to Expediting Phase Field Simulations of Brittle Fracture](https://mlsanity.com/paper/2507.07237/) (2025)
- [Computational Discovery of Energy-Efficient Heat Treatment for Microstructure Design using Deep Reinforcement Learning](https://mlsanity.com/paper/2209.11259/) (2022)
- [Diffusion-based Generative Machine Learning Model for Predicting Crack Propagation in Aluminum Nitride at the Atomic Scale](https://mlsanity.com/paper/2603.13445/) (2026)

## Abstract (arXiv)

Using simulation to predict the mechanical behavior of heterogeneous materials has applications ranging from topology optimization to multi-scale structural analysis. However, full-fidelity simulation techniques such as Finite Element Analysis can be prohibitively computationally expensive when they are used to explore the massive input parameter space of heterogeneous materials. Therefore, there has been significant recent interest in machine learning-based models that, once trained, can predict mechanical behavior at a fraction of the computational cost. Over the past several years, research in this area has been focused mainly on predicting single Quantities of Interest (QoIs). However, there has recently been an increased interest in a more challenging problem: predicting full-field QoI (e.g., displacement/strain fields, damage fields) for mechanical problems. Due to the added complexity of full-field information, network architectures that perform well on single QoI problems may perform poorly in the full-field QoI problem setting. The work presented in this paper is twofold. First, we made a significant extension to the Mechanical MNIST dataset designed to enable the investigation of full field QoI prediction. Specifically, we added Finite Element simulation results of quasi-static brittle fracture in a heterogeneous material captured with the phase-field method. Second, we established strong baseline performance for predicting full-field QoI with MultiRes-WNet architecture. In addition to presenting the results in this paper, we have released our model implementation and the Mechanical MNIST Crack Path dataset under open-source licenses. We anticipate that future researchers will directly use our model architecture on related datasets and potentially design models that exceed the baseline performance for predicting full-field QoI established in this paper.