# A machine learning approach for fighting the curse of dimensionality in global optimization

arXiv: https://arxiv.org/abs/2110.14985 · HTML: https://mlsanity.com/paper/2110.14985/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 98 references that are in the map.
- First posted on arXiv 28 Oct 2021.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [An Introduction to Convolutional Neural Networks](https://mlsanity.com/paper/1511.08458/) (2015)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [A Theoretical Analysis of Deep Neural Networks and Parametric PDEs](https://mlsanity.com/paper/1904.00377/) (2019)
- [High-Dimensional Bayesian Optimisation with Variational Autoencoders and Deep Metric Learning](https://mlsanity.com/paper/2106.03609/) (2021)
- [Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systems](https://mlsanity.com/paper/2006.15274/) (2020)
- [Good practices for Bayesian Optimization of high dimensional structured spaces](https://mlsanity.com/paper/2012.15471/) (2020)
- [A practical tutorial on autoencoders for nonlinear feature fusion: Taxonomy, models, software and guidelines](https://mlsanity.com/paper/1801.01586/) (2018)
- [Computing multiple solutions of topology optimization problems](https://mlsanity.com/paper/2004.11797/) (2020)
- [Gradient-free activation maximization for identifying effective stimuli](https://mlsanity.com/paper/1905.00378/) (2019)
- [Recovering Trajectories of Unmarked Joints in 3D Human Actions Using Latent Space Optimization](https://mlsanity.com/paper/2012.02043/) (2020)
- [Shape optimization in laminar flow with a label-guided variational autoencoder](https://mlsanity.com/paper/1712.03599/) (2017)
- [Functional Generative Design: An Evolutionary Approach to 3D-Printing](https://mlsanity.com/paper/1804.07284/) (2018)
- [An In-depth Summary of Recent Artificial Intelligence Applications in Drug Design](https://mlsanity.com/paper/2110.05478/) (2021)

## Built on by (most cited first, 1 of 1)

- [Gradient-free neural topology optimization: Towards effective fracture-resistant designs](https://mlsanity.com/paper/2403.04937/) (2024)

## Abstract (arXiv)

Finding global optima in high-dimensional optimization problems is extremely challenging since the number of function evaluations required to sufficiently explore the search space increases exponentially with its dimensionality. Furthermore, multimodal cost functions render local gradient-based search techniques ineffective. To overcome these difficulties, we propose to trim uninteresting regions of the search space where global optima are unlikely to be found by means of autoencoders, exploiting the lower intrinsic dimensionality of certain cost functions; optima are then searched over lower-dimensional latent spaces. The methodology is tested on benchmark functions and on multiple variations of a structural topology optimization problem, where we show that we can estimate this intrinsic lower dimensionality and based thereon obtain the global optimum at best or superior results compared to established optimization procedures at worst.