# A General Framework Combining Generative Adversarial Networks and Mixture Density Networks for Inverse Modeling in Microstructural Materials Design

arXiv: https://arxiv.org/abs/2101.10553 · HTML: https://mlsanity.com/paper/2101.10553/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 11 references that are in the map.
- First posted on arXiv 26 Jan 2021.

## Builds on (most cited first, 2 of 2)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)

## Built on by (most cited first, 4 of 4)

- [Artificial intelligence approaches for materials-by-design of energetic materials: state-of-the-art, challenges, and future directions](https://mlsanity.com/paper/2211.08179/) (2022)
- [An Uncertainty-aware Deep Learning Framework-based Robust Design Optimization of Metamaterial Units](https://mlsanity.com/paper/2407.20251/) (2024)
- [Physics-Driven ML-Based Modelling for Correcting Inverse Estimation](https://mlsanity.com/paper/2309.13985/) (2023)
- [A Multimodal Conditional Mixture Model with Distribution-Level Physics Priors](https://mlsanity.com/paper/2602.10451/) (2026)

## Abstract (arXiv)

Microstructural materials design is one of the most important applications of inverse modeling in materials science. Generally speaking, there are two broad modeling paradigms in scientific applications: forward and inverse. While the forward modeling estimates the observations based on known parameters, the inverse modeling attempts to infer the parameters given the observations. Inverse problems are usually more critical as well as difficult in scientific applications as they seek to explore the parameters that cannot be directly observed. Inverse problems are used extensively in various scientific fields, such as geophysics, healthcare and materials science. However, it is challenging to solve inverse problems, because they usually need to learn a one-to-many non-linear mapping, and also require significant computing time, especially for high-dimensional parameter space. Further, inverse problems become even more difficult to solve when the dimension of input (i.e. observation) is much lower than that of output (i.e. parameters). In this work, we propose a framework consisting of generative adversarial networks and mixture density networks for inverse modeling, and it is evaluated on a materials science dataset for microstructural materials design. Compared with baseline methods, the results demonstrate that the proposed framework can overcome the above-mentioned challenges and produce multiple promising solutions in an efficient manner.