# Gravitational Duals from Equations of State

arXiv: https://arxiv.org/abs/2403.14763 · HTML: https://mlsanity.com/paper/2403.14763/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 51 references that are in the map.
- First posted on arXiv 21 Mar 2024.

## Builds on (most cited first, 5 of 5)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [One-Shot Transfer Learning of Physics-Informed Neural Networks](https://mlsanity.com/paper/2110.11286/) (2021)
- [PyDEns: a Python Framework for Solving Differential Equations with Neural Networks](https://mlsanity.com/paper/1909.11544/) (2019)
- [AdS/Deep-Learning made easy: simple examples](https://mlsanity.com/paper/2011.13726/) (2020)

## Built on by (most cited first, 10 of 10)

- [Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space](https://mlsanity.com/paper/2501.12116/) (2025)
- [Physics-informed neural network solves minimal surfaces in curved spacetime](https://mlsanity.com/paper/2509.10866/) (2025)
- [Machine-learning emergent spacetime from linear response in future tabletop quantum gravity experiments](https://mlsanity.com/paper/2411.16052/) (2024)
- [Learning the Inverse Ryu--Takayanagi Formula with Transformers](https://mlsanity.com/paper/2511.06387/) (2025)
- [AdS/Deep-Learning made easy II: neural network-based approaches to holography and inverse problems](https://mlsanity.com/paper/2511.22522/) (2025)
- [Machine learning modularity](https://mlsanity.com/paper/2601.01779/) (2026)
- [Recovering Sharp Conductivity Features in the Finite-Data Calder'on Problem with Physics-Informed Neural Networks](https://mlsanity.com/paper/2606.28158/) (2026)
- [Gravitational Duals from Equations of State II: Large Hierarchies and False Vacua](https://mlsanity.com/paper/2606.30117/) (2026)
- [Physics-Informed Neural Embeddings of PDE Solution Families](https://mlsanity.com/paper/2607.06348/) (2026)
- [Machine Learning Meets High-Energy Nuclear Physics: From Pattern Recognition to Physics-Integrated Discovery](https://mlsanity.com/paper/2610.12293/) (2026)

## Abstract (arXiv)

Holography relates gravitational theories in five dimensions to four-dimensional quantum field theories in flat space. Under this map, the equation of state of the field theory is encoded in the black hole solutions of the gravitational theory. Solving the five-dimensional Einstein's equations to determine the equation of state is an algorithmic, direct problem. Determining the gravitational theory that gives rise to a prescribed equation of state is a much more challenging, inverse problem. We present a novel approach to solve this problem based on physics-informed neural networks. The resulting algorithm is not only data-driven but also informed by the physics of the Einstein's equations. We successfully apply it to theories with crossovers, first- and second-order phase transitions.