# PATO: Producibility-Aware Topology Optimization using Deep Learning for Metal Additive Manufacturing

arXiv: https://arxiv.org/abs/2112.04552 · HTML: https://mlsanity.com/paper/2112.04552/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 81 references that are in the map.
- First posted on arXiv 8 Dec 2021.

## Builds on (most cited first, 11 of 11)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Attention Gated Networks: Learning to Leverage Salient Regions in Medical Images](https://mlsanity.com/paper/1808.08114/) (2018)
- [SA-UNet: Spatial Attention U-Net for Retinal Vessel Segmentation](https://mlsanity.com/paper/2004.03696/) (2020)
- [Superhuman Accuracy on the SNEMI3D Connectomics Challenge](https://mlsanity.com/paper/1706.00120/) (2017)
- [Stress Field Prediction in Cantilevered Structures Using Convolutional Neural Networks](https://mlsanity.com/paper/1808.08914/) (2018)
- [Length Scale Control in Topology Optimization using Fourier Enhanced Neural Networks](https://mlsanity.com/paper/2109.01861/) (2021)
- [Exploring Feasible Design Spaces for Heterogeneous Constraints](https://mlsanity.com/paper/1907.01117/) (2019)
- [Topology Optimization with Accessibility Constraint for Multi-Axis Machining](https://mlsanity.com/paper/2002.07627/) (2020)

## Built on by (most cited first, 2 of 2)

- [Concurrent build direction, part segmentation, and topology optimization for additive manufacturing using neural networks](https://mlsanity.com/paper/2210.01315/) (2022)
- [Advancing Additive Manufacturing through Deep Learning: A Comprehensive Review of Current Progress and Future Challenges](https://mlsanity.com/paper/2403.00669/) (2024)

## Abstract (arXiv)

In this paper, we propose PATO-a producibility-aware topology optimization (TO) framework to help efficiently explore the design space of components fabricated using metal additive manufacturing (AM), while ensuring manufacturability with respect to cracking. Specifically, parts fabricated through Laser Powder Bed Fusion are prone to defects such as warpage or cracking due to high residual stress values generated from the steep thermal gradients produced during the build process. Maturing the design for such parts and planning their fabrication can span months to years, often involving multiple handoffs between design and manufacturing engineers. PATO is based on the a priori discovery of crack-free designs, so that the optimized part can be built defect-free at the outset. To ensure that the design is crack free during optimization, producibility is explicitly encoded within the standard formulation of TO, using a crack index. Multiple crack indices are explored and using experimental validation, maximum shear strain index (MSSI) is shown to be an accurate crack index. Simulating the build process is a coupled, multi-physics computation and incorporating it in the TO loop can be computationally prohibitive. We leverage the current advances in deep convolutional neural networks and present a high-fidelity surrogate model based on an Attention-based U-Net architecture to predict the MSSI values as a spatially varying field over the part's domain. Further, we employ automatic differentiation to directly compute the gradient of maximum MSSI with respect to the input design variables and augment it with the performance-based sensitivity field to optimize the design while considering the trade-off between weight, manufacturability, and functionality. We demonstrate the effectiveness of the proposed method through benchmark studies in 3D as well as experimental validation.