mlsanityData to 7 Oct 2026

Gravitational Duals from Equations of State

arXiv 2403.14763 ↗First posted 21 Mar 2024hep-th astro-ph.CO cs.AIcited by 10

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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.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 5 of its 51 references that are in the map. First posted on arXiv 21 Mar 2024.

Builds on

5 of 51 references.

References · 5

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  3. 2021One-Shot Transfer Learning of Physics-Informed Neural Networkscited by 49
  4. 2019PyDEns: a Python Framework for Solving Differential Equations with Neural Networkscited by 14
  5. 2020AdS/Deep-Learning made easy: simple examplescited by 9

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 4; 2026: 5.

10 papers.

  1. 2025Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Spacecited by 6
  2. 2025Physics-informed neural network solves minimal surfaces in curved spacetimecited by 6
  3. 2024Machine-learning emergent spacetime from linear response in future tabletop quantum gravity experimentscited by 5
  4. 2025Learning the Inverse Ryu--Takayanagi Formula with Transformerscited by 2
  5. 2025AdS/Deep-Learning made easy II: neural network-based approaches to holography and inverse problemscited by 2
  6. 2026Machine learning modularitycited by 0
  7. 2026Recovering Sharp Conductivity Features in the Finite-Data Calder'on Problem with Physics-Informed Neural Networkscited by 0
  8. 2026Gravitational Duals from Equations of State II: Large Hierarchies and False Vacuacited by 0
  9. 2026Physics-Informed Neural Embeddings of PDE Solution Familiescited by 0
  10. 2026Machine Learning Meets High-Energy Nuclear Physics: From Pattern Recognition to Physics-Integrated Discoverycited by 0