# Using Computational Intelligence for solving the Ornstein-Zernike equation

arXiv: https://arxiv.org/abs/2201.05089 · HTML: https://mlsanity.com/paper/2201.05089/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 146 references that are in the map.
- First posted on arXiv 17 Nov 2021.

## Builds on (most cited first, 18 of 18)

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- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Universality of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1805.10769/) (2018)
- [Towards Understanding the Role of Over-Parametrization in Generalization of Neural Networks](https://mlsanity.com/paper/1805.12076/) (2018)
- [Activation Functions: Comparison of trends in Practice and Research for Deep Learning](https://mlsanity.com/paper/1811.03378/) (2018)
- [Minimum Width for Universal Approximation](https://mlsanity.com/paper/2006.08859/) (2020)
- [Learning Activation Functions to Improve Deep Neural Networks](https://mlsanity.com/paper/1412.6830/) (2014)
- [The Modern Mathematics of Deep Learning](https://mlsanity.com/paper/2105.04026/) (2021)
- [AlphaStar: An Evolutionary Computation Perspective](https://mlsanity.com/paper/1902.01724/) (2019)
- [Machine learning & artificial intelligence in the quantum domain](https://mlsanity.com/paper/1709.02779/) (2017)
- [Machine Learning for Condensed Matter Physics](https://mlsanity.com/paper/2005.14228/) (2020)

## Abstract (arXiv)

The main goal of this thesis is to provide an exploration of the use of computational intelligence techniques to study the numerical solution of the Ornstein-Zernike equation for simple liquids. In particular, a continuous model of the hard sphere fluid is studied. There are two main proposals in this contribution. First, the use of neural networks as a way to parametrize closure relation when solving the Ornstein-Zernike equation. It is explicitly shown that in the case of the hard sphere fluid, the neural network approach seems to reduce to the so-called Hypernetted Chain closure. For the second proposal, we explore the fact that if more physical information is incorporated into the theoretical formalism, a better estimate can be obtained with the use of evolutionary optimization techniques. When choosing the modified Verlet closure relation, and leaving a couple of free parameters to be adjusted, the results are as good as those obtained from molecular simulations. The thesis is then closed with a brief summary of the main findings and outlooks on different ways to improve the proposals presented here.