# Classical integrability in the presence of a cosmological constant: analytic and machine learning results

arXiv: https://arxiv.org/abs/2404.18247 · HTML: https://mlsanity.com/paper/2404.18247/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 35 references that are in the map.
- First posted on arXiv 28 Apr 2024.

## Builds on (most cited first, 4 of 4)

- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [The R-mAtrIx Net](https://mlsanity.com/paper/2304.07247/) (2023)
- [Neural Network Approach to Construction of Classical Integrable Systems](https://mlsanity.com/paper/2103.00372/) (2021)
- [Learning Integrable Dynamics with Action-Angle Networks](https://mlsanity.com/paper/2211.15338/) (2022)

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

- [Deep Learning based discovery of Integrable Systems](https://mlsanity.com/paper/2503.10469/) (2025)

## Abstract (arXiv)

We study the integrability of two-dimensional theories that are obtained by a dimensional reduction of certain four-dimensional gravitational theories describing the coupling of Maxwell fields and neutral scalar fields to gravity in the presence of a potential for the neutral scalar fields. For a certain solution subspace, we demonstrate partial integrability by showing that a subset of the equations of motion in two dimensions are the compatibility conditions for a linear system. Subsequently, we study the integrability of these two-dimensional models from a complementary one-dimensional point of view, framed in terms of Liouville integrability. In this endeavour, we employ various machine learning techniques to systematise our search for numerical Lax pair matrices for these models, as well as conserved currents expressed as functions of phase space variables.