# Material Microstructure Design Using VAE-Regression with Multimodal Prior

arXiv: https://arxiv.org/abs/2402.17806 · HTML: https://mlsanity.com/paper/2402.17806/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 23 references that are in the map.
- First posted on arXiv 27 Feb 2024.

## Builds on (most cited first, 10 of 10)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Variational AutoEncoder For Regression: Application to Brain Aging Analysis](https://mlsanity.com/paper/1904.05948/) (2019)
- [Capturing Label Characteristics in VAEs](https://mlsanity.com/paper/2006.10102/) (2020)
- [A Transfer Learning Approach for Microstructure Reconstruction and Structure-property Predictions](https://mlsanity.com/paper/1805.02784/) (2018)
- [Learning Multimodal VAEs through Mutual Supervision](https://mlsanity.com/paper/2106.12570/) (2021)

## Built on by (most cited first, 3 of 3)

- [AutoMS: Multi-Agent Evolutionary Search for Cross-Physics Inverse Microstructure Design](https://mlsanity.com/paper/2603.27195/) (2026)
- [Deep Generative Methods and Tire Architecture Design](https://mlsanity.com/paper/2507.11639/) (2025)
- [Generating Heterogeneous 3D Geological Microstructures from 2D Images via a Stable Diffusion-Adversarial Model](https://mlsanity.com/paper/2609.20358/) (2026)

## Abstract (arXiv)

We propose a variational autoencoder (VAE)-based model for building forward and inverse structure-property linkages, a problem of paramount importance in computational materials science. Our model systematically combines VAE with regression, linking the two models through a two-level prior conditioned on the regression variables. The regression loss is optimized jointly with the reconstruction loss of the variational autoencoder, learning microstructure features relevant for property prediction and reconstruction. The resultant model can be used for both forward and inverse prediction i.e., for predicting the properties of a given microstructure as well as for predicting the microstructure required to obtain given properties. Since the inverse problem is ill-posed (one-to-many), we derive the objective function using a multi-modal Gaussian mixture prior enabling the model to infer multiple microstructures for a target set of properties. We show that for forward prediction, our model is as accurate as state-of-the-art forward-only models. Additionally, our method enables direct inverse inference. We show that the microstructures inferred using our model achieve desired properties reasonably accurately, avoiding the need for expensive optimization loops.