# Speeding up Computational Morphogenesis with Online Neural Synthetic Gradients

arXiv: https://arxiv.org/abs/2104.12282 · HTML: https://mlsanity.com/paper/2104.12282/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 49 references that are in the map.
- First posted on arXiv 25 Apr 2021.

## Builds on (most cited first, 8 of 8)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Deep learning for determining a near-optimal topological design without any iteration](https://mlsanity.com/paper/1801.05463/) (2018)
- [Neural networks for topology optimization](https://mlsanity.com/paper/1709.09578/) (2017)
- [3D Topology Optimization using Convolutional Neural Networks](https://mlsanity.com/paper/1808.07440/) (2018)
- [A deep Convolutional Neural Network for topology optimization with strong generalization ability](https://mlsanity.com/paper/1901.07761/) (2019)
- [Progressive construction of a parametric reduced-order model for PDE-constrained optimization](https://mlsanity.com/paper/1407.7618/) (2014)
- [Optimizing the Kelvin force in a moving target subdomain](https://mlsanity.com/paper/1612.07763/) (2016)

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

- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [FRC-TOuNN: Topology Optimization of Continuous Fiber Reinforced Composites using Neural Network](https://mlsanity.com/paper/2205.03737/) (2022)

## Abstract (arXiv)

A wide range of modern science and engineering applications are formulated as optimization problems with a system of partial differential equations (PDEs) as constraints. These PDE-constrained optimization problems are typically solved in a standard discretize-then-optimize approach. In many industry applications that require high-resolution solutions, the discretized constraints can easily have millions or even billions of variables, making it very slow for the standard iterative optimizer to solve the exact gradients. In this work, we propose a general framework to speed up PDE-constrained optimization using online neural synthetic gradients (ONSG) with a novel two-scale optimization scheme. We successfully apply our ONSG framework to computational morphogenesis, a representative and challenging class of PDE-constrained optimization problems. Extensive experiments have demonstrated that our method can significantly speed up computational morphogenesis (also known as topology optimization), and meanwhile maintain the quality of final solution compared to the standard optimizer. On a large-scale 3D optimal design problem with around 1,400,000 design variables, our method achieves up to 7.5x speedup while producing optimized designs with comparable objectives.