# A Generalized Framework for Microstructural Optimization using Neural Networks

arXiv: https://arxiv.org/abs/2207.06512 · HTML: https://mlsanity.com/paper/2207.06512/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 55 references that are in the map.
- First posted on arXiv 13 Jul 2022.

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

- [NTopo: Mesh-free Topology Optimization using Implicit Neural Representations](https://mlsanity.com/paper/2102.10782/) (2021)
- [AuTO: A Framework for Automatic differentiation in Topology Optimization](https://mlsanity.com/paper/2104.01965/) (2021)
- [Topology optimization of micro-structured materials featured with the specific mechanical properties](https://mlsanity.com/paper/1808.08647/) (2018)
- [Determination of Metamaterial Parameters by Means of a Homogenization Approach Based on Asymptotic Analysis](https://mlsanity.com/paper/1906.07556/) (2019)
- [Multi-constrained topology optimization via the topological sensitivity](https://mlsanity.com/paper/2203.15111/) (2022)
- [Stress constrained thermo-elastic topology optimization with varying temperature fields via augmented topological sensitivity based level-set](https://mlsanity.com/paper/2203.15117/) (2022)

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

- [Cross-Modal Learning for Chemistry Property Prediction: Large Language Models Meet Graph Machine Learning](https://mlsanity.com/paper/2408.14964/) (2024)
- [Multi-scale Topology Optimization using Neural Networks](https://mlsanity.com/paper/2404.08708/) (2024)
- [Heterogeneous Metamaterials Design via Multiscale Neural Implicit Representation](https://mlsanity.com/paper/2511.03012/) (2025)

## Abstract (arXiv)

Microstructures, i.e., architected materials, are designed today, typically, by maximizing an objective, such as bulk modulus, subject to a volume constraint. However, in many applications, it is often more appropriate to impose constraints on other physical quantities of interest. In this paper, we consider such generalized microstructural optimization problems where any of the microstructural quantities, namely, bulk, shear, Poisson ratio, or volume, can serve as the objective, while the remaining can serve as constraints. In particular, we propose here a neural-network (NN) framework to solve such problems. The framework relies on the classic density formulation of microstructural optimization, but the density field is represented through the NN's weights and biases. The main characteristics of the proposed NN framework are: (1) it supports automatic differentiation, eliminating the need for manual sensitivity derivations, (2) smoothing filters are not required due to implicit filtering, (3) the framework can be easily extended to multiple-materials, and (4) a high-resolution microstructural topology can be recovered through a simple post-processing step. The framework is illustrated through a variety of microstructural optimization problems.