# Consistent machine learning for topology optimization with microstructure-dependent neural network material models

arXiv: https://arxiv.org/abs/2408.13843 · HTML: https://mlsanity.com/paper/2408.13843/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 65 references that are in the map.
- First posted on arXiv 25 Aug 2024.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [Optimal Control Via Neural Networks: A Convex Approach](https://mlsanity.com/paper/1805.11835/) (2018)
- [Polyconvex anisotropic hyperelasticity with neural networks](https://mlsanity.com/paper/2106.14623/) (2021)
- [Neural networks meet hyperelasticity: A guide to enforcing physics](https://mlsanity.com/paper/2302.02403/) (2023)
- [On the use of Artificial Neural Networks in Topology Optimisation](https://mlsanity.com/paper/2208.02563/) (2022)
- [Topology Optimization via Machine Learning and Deep Learning: A Review](https://mlsanity.com/paper/2210.10782/) (2022)
- [Neural network-based multiscale modeling of finite strain magneto-elasticity with relaxed convexity criteria](https://mlsanity.com/paper/2308.16311/) (2023)
- [FEANN - An efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining](https://mlsanity.com/paper/2207.01045/) (2022)
- [De-homogenization of optimal multi-scale 3D topologies](https://mlsanity.com/paper/1910.13002/) (2019)

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

- [Automatically Differentiable Model Updating (ADiMU): conventional, hybrid, and neural network material model discovery including history-dependency](https://mlsanity.com/paper/2505.07801/) (2025)
- [Input convex neural networks: universal approximation theorem and implementation for isotropic polyconvex hyperelastic energies](https://mlsanity.com/paper/2502.08534/) (2025)
- [Single- to multi-fidelity history-dependent learning with uncertainty quantification and disentanglement: application to data-driven constitutive modeling](https://mlsanity.com/paper/2507.13416/) (2025)

## Abstract (arXiv)

Additive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such structures in the presence of nonlinearities remains a challenge due to the expense of computational homogenization methods and the complexity of differentiably parameterizing the microstructural response. A solution to this challenge lies in machine learning techniques that offer efficient, differentiable mappings between the material response and its microstructural descriptors. This work presents a framework for designing multiscale heterogeneous structures with spatially varying microstructures by merging a homogenization-based topology optimization strategy with a consistent machine learning approach grounded in hyperelasticity theory. We leverage neural architectures that adhere to critical physical principles such as polyconvexity, objectivity, material symmetry, and thermodynamic consistency to supply the framework with a reliable constitutive model that is dependent on material microstructural descriptors. Our findings highlight the potential of integrating consistent machine learning models with density-based topology optimization for enhancing design optimization of heterogeneous hyperelastic structures under finite deformations.