# An efficient optimization based microstructure reconstruction approach with multiple loss functions

arXiv: https://arxiv.org/abs/2102.02407 · HTML: https://mlsanity.com/paper/2102.02407/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 59 references that are in the map.
- First posted on arXiv 4 Feb 2021.

## Builds on (most cited first, 6 of 6)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [A Transfer Learning Approach for Microstructure Reconstruction and Structure-property Predictions](https://mlsanity.com/paper/1805.02784/) (2018)
- [Microstructure Representation and Reconstruction of Heterogeneous Materials via Deep Belief Network for Computational Material Design](https://mlsanity.com/paper/1612.07401/) (2016)
- [Inferring low-dimensional microstructure representations using convolutional neural networks](https://mlsanity.com/paper/1611.02764/) (2016)
- [Probabilistic modeling of discrete structural response with application to composite plate penetration models](https://mlsanity.com/paper/2011.11780/) (2020)

## Built on by (most cited first, 6 of 6)

- [Stress field prediction in fiber-reinforced composite materials using a deep learning approach](https://mlsanity.com/paper/2111.05271/) (2021)
- [DA-VEGAN: Differentiably Augmenting VAE-GAN for microstructure reconstruction from extremely small data sets](https://mlsanity.com/paper/2303.03403/) (2023)
- [Machine Learning in Heterogeneous Porous Materials](https://mlsanity.com/paper/2202.04137/) (2022)
- [Reinforcement Learning based Sequential Batch-sampling for Bayesian Optimal Experimental Design](https://mlsanity.com/paper/2112.10944/) (2021)
- [A Hybrid Conditional Diffusion-DeepONet Framework for High-Fidelity Stress Prediction in Hyperelastic Materials](https://mlsanity.com/paper/2603.18225/) (2026)
- [Generative adversarial framework to calibrate excursion set models for the 3D morphology of all-solid-state battery cathodes](https://mlsanity.com/paper/2503.17171/) (2025)

## Abstract (arXiv)

Stochastic microstructure reconstruction involves digital generation of microstructures that match key statistics and characteristics of a (set of) target microstructure(s). This process enables computational analyses on ensembles of microstructures without having to perform exhaustive and costly experimental characterizations. Statistical functions-based and deep learning-based methods are among the stochastic microstructure reconstruction approaches applicable to a wide range of material systems. In this paper, we integrate statistical descriptors as well as feature maps from a pre-trained deep neural network into an overall loss function for an optimization based reconstruction procedure. This helps us to achieve significant computational efficiency in reconstructing microstructures that retain the critically important physical properties of the target microstructure. A numerical example for the microstructure reconstruction of bi-phase random porous ceramic material demonstrates the efficiency of the proposed methodology. We further perform a detailed finite element analysis (FEA) of the reconstructed microstructures to calculate effective elastic modulus, effective thermal conductivity and effective hydraulic conductivity, in order to analyse the algorithm's capacity to capture the variability of these material properties with respect to those of the target microstructure. This method provides an economic, efficient and easy-to-use approach for reconstructing random multiphase materials in 2D which has the potential to be extended to 3D structures.