# Dynamics-Informed Deep Learning for Predicting Extreme Events

arXiv: https://arxiv.org/abs/2603.10777 · HTML: https://mlsanity.com/paper/2603.10777/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 54 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [ResUNet++: An Advanced Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1911.07067/) (2019)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [Sobolev Training for Neural Networks](https://mlsanity.com/paper/1706.04859/) (2017)
- [Learning Dissipative Dynamics in Chaotic Systems](https://mlsanity.com/paper/2106.06898/) (2021)
- [Analog forecasting of extreme-causing weather patterns using deep learning](https://mlsanity.com/paper/1907.11617/) (2019)
- [Learning Composable Energy Surrogates for PDE Order Reduction](https://mlsanity.com/paper/2005.06549/) (2020)
- [Output-weighted and relative entropy loss functions for deep learning precursors of extreme events](https://mlsanity.com/paper/2112.00825/) (2021)
- [Learning Turbulent Flows with Generative Models: Super-resolution, Forecasting, and Sparse Flow Reconstruction](https://mlsanity.com/paper/2509.08752/) (2025)
- [Are extreme dissipation events predictable in turbulent fluid flows?](https://mlsanity.com/paper/1807.10263/) (2018)
- [Model-assisted deep learning of rare extreme events from partial observations](https://mlsanity.com/paper/2111.04857/) (2021)
- [Extreme Event Precursor Prediction in Turbulent Dynamical Systems via CNN-Augmented Recurrence Analysis](https://mlsanity.com/paper/2508.04301/) (2025)

## Built on by (most cited first, 2 of 2)

- [Uncovering Extreme Event Mechanisms for Prediction and Control with Sensitivity-Balanced Projections](https://mlsanity.com/paper/2606.05618/) (2026)
- [Noise-Induced Predictability Redistribution Across Forecast Horizons of Extreme Events in Chaotic Dynamics](https://mlsanity.com/paper/2609.27877/) (2026)

## Abstract (arXiv)

Predicting extreme events in high-dimensional chaotic dynamical systems remains a fundamental challenge, as such events are rare, intermittent, and arise from transient dynamical mechanisms that are difficult to infer from limited observations. Accordingly, real-time forecasting calls for precursors that encode the mechanisms driving extremes, rather than relying solely on statistical associations. We propose a fully data-driven framework for long-lead prediction of extreme events that constructs interpretable, mechanism-aware precursors by explicitly tracking transient instabilities preceding event onset. The approach leverages a reduced-order formulation to compute finite-time Lyapunov exponent (FTLE)-like precursors directly from state snapshots, without requiring knowledge of the governing equations. To avoid the prohibitive computational cost of classical FTLE computation, instability growth is evaluated in an adaptively evolving low-dimensional subspace spanned by Optimal Time-Dependent (OTD) modes, enabling efficient identification of transiently amplifying directions. These precursors are then provided as input to a Transformer-based model, enabling forecast of extreme event observables. We demonstrate the framework on Kolmogorov flow, a canonical model of intermittent turbulence. The results show that explicitly encoding transient instability mechanisms substantially extends practical prediction horizons compared to baseline observable-based approaches.