# Deep Learning of the Evolution Operator Enables Forecasting of Out-of-Training Dynamics in Chaotic Systems

arXiv: https://arxiv.org/abs/2502.20603 · HTML: https://mlsanity.com/paper/2502.20603/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 29 references that are in the map.
- First posted on arXiv 28 Feb 2025.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Stand-Alone Self-Attention in Vision Models](https://mlsanity.com/paper/1906.05909/) (2019)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [Stabilized Neural Ordinary Differential Equations for Long-Time Forecasting of Dynamical Systems](https://mlsanity.com/paper/2203.15706/) (2022)
- [Deep learning to discover and predict dynamics on an inertial manifold](https://mlsanity.com/paper/2001.04263/) (2019)
- [Can AI weather models predict out-of-distribution gray swan tropical cyclones?](https://mlsanity.com/paper/2410.14932/) (2024)
- [Deep Learning Models for Global Coordinate Transformations that Linearize PDEs](https://mlsanity.com/paper/1911.02710/) (2019)
- [Predictive Limitations of Physics-Informed Neural Networks in Vortex Shedding](https://mlsanity.com/paper/2306.00230/) (2023)

## Built on by (most cited first, 3 of 3)

- [When is a System Discoverable from Data? Discovery Requires Chaos](https://mlsanity.com/paper/2511.08860/) (2025)
- [Conditioning on PDE Parameters to Generalise Deep Learning Emulation of Stochastic and Chaotic Dynamics](https://mlsanity.com/paper/2509.09599/) (2025)
- [Extrapolating the emergence of Hamiltonian chaos with random-feature Hamiltonian neural networks](https://mlsanity.com/paper/2607.28977/) (2026)

## Abstract (arXiv)

We demonstrate that a deep learning emulator for chaotic systems can forecast phenomena absent from training data. Using the Kuramoto-Sivashinsky and beta-plane turbulence models, we evaluate the emulator through scenarios probing the fundamental phenomena of both systems: forecasting spontaneous relaminarisation, capturing initialisation of arbitrary chaotic states, zero-shot prediction of dynamics with parameter values outside of the training range, and characterisation of dynamical statistics from artificially restricted training datasets. Our results show that deep learning emulators can uncover emergent behaviours and rare events in complex systems by learning underlying mathematical rules, rather than merely mimicking observed patterns.