# AuTO: A Framework for Automatic differentiation in Topology Optimization

arXiv: https://arxiv.org/abs/2104.01965 · HTML: https://mlsanity.com/paper/2104.01965/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Apr 2021.

## Built on by (most cited first, 7 of 7)

- [NCVX: A General-Purpose Optimization Solver for Constrained Machine and Deep Learning](https://mlsanity.com/paper/2210.00973/) (2022)
- [Nonlinear Inverse Design of Mechanical Multi-Material Metamaterials Enabled by Video Denoising Diffusion and Structure Identifier](https://mlsanity.com/paper/2409.13908/) (2024)
- [GM-TOuNN: Graded Multiscale Topology Optimization using Neural Networks](https://mlsanity.com/paper/2204.06682/) (2022)
- [A Generalized Framework for Microstructural Optimization using Neural Networks](https://mlsanity.com/paper/2207.06512/) (2022)
- [Integrating Material Selection with Design Optimization via Neural Networks](https://mlsanity.com/paper/2112.12566/) (2021)
- [FRC-TOuNN: Topology Optimization of Continuous Fiber Reinforced Composites using Neural Network](https://mlsanity.com/paper/2205.03737/) (2022)
- [FluTO: Graded Multiscale Fluid Topology Optimization using Neural Networks](https://mlsanity.com/paper/2209.08168/) (2022)

## Abstract (arXiv)

A critical step in topology optimization (TO) is finding sensitivities. Manual derivation and implementation of the sensitivities can be quite laborious and error-prone, especially for non-trivial objectives, constraints and material models. An alternate approach is to utilize automatic differentiation (AD). While AD has been around for decades, and has also been applied in TO, wider adoption has largely been absent. In this educational paper, we aim to reintroduce AD for TO, and make it easily accessible through illustrative codes. In particular, we employ JAX, a high-performance Python library for automatically computing sensitivities from a user defined TO problem. The resulting framework, referred to here as AuTO, is illustrated through several examples in compliance minimization, compliant mechanism design and microstructural design.