# Hamiltonian Neural Networks approach to fuzzball geodesics

arXiv: https://arxiv.org/abs/2502.20881 · HTML: https://mlsanity.com/paper/2502.20881/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 58 references that are in the map.
- First posted on arXiv 28 Feb 2025.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Hamiltonian neural networks for solving equations of motion](https://mlsanity.com/paper/2001.11107/) (2020)
- [Neural Network Approximations for Calabi-Yau Metrics](https://mlsanity.com/paper/2012.15821/) (2020)
- [Learning Size and Shape of Calabi-Yau Spaces](https://mlsanity.com/paper/2111.01436/) (2021)
- [Machine learning Calabi-Yau metrics](https://mlsanity.com/paper/1910.08605/) (2019)
- [QCD-Aware Recursive Neural Networks for Jet Physics](https://mlsanity.com/paper/1702.00748/) (2017)
- [Adaptable Hamiltonian neural networks](https://mlsanity.com/paper/2102.13235/) (2021)
- [Machine Learned Calabi-Yau Metrics and Curvature](https://mlsanity.com/paper/2211.09801/) (2022)
- [Searching the Landscape of Flux Vacua with Genetic Algorithms](https://mlsanity.com/paper/1907.10072/) (2019)
- [Unsupervised Machine Learning Techniques for Exploring Tropical Coamoeba, Brane Tilings and Seiberg Duality](https://mlsanity.com/paper/2309.05702/) (2023)
- [Can Transformers Do Enumerative Geometry?](https://mlsanity.com/paper/2408.14915/) (2024)
- [Machine Learning String Standard Models](https://mlsanity.com/paper/2003.13339/) (2020)
- [Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equations](https://mlsanity.com/paper/2202.12358/) (2022)
- [Adaptive Physics-Informed Neural Networks for Markov-Chain Monte Carlo](https://mlsanity.com/paper/2008.01604/) (2020)
- [A deep surrogate approach to efficient Bayesian inversion in PDE and integral equation models](https://mlsanity.com/paper/1910.01547/) (2019)
- [Machine Learning Regularization for the Minimum Volume Formula of Toric Calabi-Yau 3-folds](https://mlsanity.com/paper/2310.19276/) (2023)
- [Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces](https://mlsanity.com/paper/2412.19778/) (2024)
- [A physics-informed search for metric solutions to Ricci flow, their embeddings, and visualisation](https://mlsanity.com/paper/2212.05892/) (2022)
- [The DNA of Calabi-Yau Hypersurfaces](https://mlsanity.com/paper/2405.08871/) (2024)
- [Generative AI for Brane Configurations and Coamoeba](https://mlsanity.com/paper/2411.16033/) (2024)
- [Neural Network Learning and Quantum Gravity](https://mlsanity.com/paper/2403.03245/) (2024)
- [Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning](https://mlsanity.com/paper/2412.10821/) (2024)

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

- [Machine Learning the 6d Supergravity Landscape](https://mlsanity.com/paper/2505.16131/) (2025)

## Abstract (arXiv)

The recent increase in computational resources and data availability has led to a significant rise in the use of Machine Learning (ML) techniques for data analysis in physics. However, the application of ML methods to solve differential equations capable of describing even complex physical systems is not yet fully widespread in theoretical high-energy physics. Hamiltonian Neural Networks (HNNs) are tools that minimize a loss function defined to solve Hamilton equations of motion. In this work, we implement several HNNs trained to solve, with high accuracy, the Hamilton equations for a massless probe moving inside a smooth and horizonless geometry known as D1-D5 circular fuzzball. We study both planar (equatorial) and non-planar geodesics in different regimes according to the impact parameter, some of which are unstable. Our findings suggest that HNNs could eventually replace standard numerical integrators, as they are equally accurate but more reliable in critical situations.