AuTO: A Framework for Automatic differentiation in Topology Optimization
Aaditya Chandrasekhar*, Saketh Sridhara*, Krishnan Suresh
Engineering Representations and Simulation Lab
University of Wisconsin-Madison
* - contributed equally.
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 conceptualized over 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.
The code can be run in two ways:
- Using Google Colab (recommended)
- Click on the file you want to run (for eg. compliance.ipynb). If file doesn't load, click 'Reload'/refresh
- Click on "Open in Colab"
- Ensure to use GPU by edit-notebook settings-GPU(hardware accelerator)
- Go to "Runtime" and select "Run All"
- Clone and run
- install required dependencies (JAX, numpy, matplotlib, scipy).
- For windows machines: use WSL