# Uncovering Extreme Event Mechanisms for Prediction and Control with Sensitivity-Balanced Projections

arXiv: https://arxiv.org/abs/2606.05618 · HTML: https://mlsanity.com/paper/2606.05618/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 87 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Builds on (most cited first, 14 of 14)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [A Mathematical Guide to Operator Learning](https://mlsanity.com/paper/2312.14688/) (2023)
- [Discovering and forecasting extreme events via active learning in neural operators](https://mlsanity.com/paper/2204.02488/) (2022)
- [Grasping Extreme Aerodynamics on a Low-Dimensional Manifold](https://mlsanity.com/paper/2305.08024/) (2023)
- [Output-weighted and relative entropy loss functions for deep learning precursors of extreme events](https://mlsanity.com/paper/2112.00825/) (2021)
- [Operator learning without the adjoint](https://mlsanity.com/paper/2401.17739/) (2024)
- [Optimizing Oblique Projections for Nonlinear Systems using Trajectories](https://mlsanity.com/paper/2106.01211/) (2021)
- [Model Reduction for Nonlinear Systems by Balanced Truncation of State and Gradient Covariance](https://mlsanity.com/paper/2207.14387/) (2022)
- [An adjoint-based approach for finding invariant solutions of Navier-Stokes equations](https://mlsanity.com/paper/1508.06363/) (2015)
- [Closed-loop adaptive control of extreme events in a turbulent flow](https://mlsanity.com/paper/1906.03042/) (2019)
- [Dynamics-Informed Deep Learning for Predicting Extreme Events](https://mlsanity.com/paper/2603.10777/) (2026)
- [Data-Driven Forecasting of High-Dimensional Transient and Stationary Processes via Space-Time Projection](https://mlsanity.com/paper/2503.23686/) (2025)

## Abstract (arXiv)

Extreme events -- such as earthquakes and coronal mass ejections -- are common in many chaotic dynamical systems, yet are difficult to characterize and predict due to the subtle instability mechanisms that drive them. In this work, we develop an interpretable technique that reveals the underlying mechanisms behind extreme events and uses them to build data-driven forecasts and intuitive event suppression controllers. In particular, we utilize the covariance balancing reduction using adjoint snapshots (CoBRAS) method to identify linear oblique projections that best capture the sensitivity of a quantity of interest and reconstruct the original state. Importantly, we bypass the need for cumbersome adjoint calculations, instead using backpropagation via modern automatically differentiable numerical frameworks. To accommodate spatially localized events, we also introduce a new variant of CoBRAS to obtain local sensitivity-balanced projections. We demonstrate the utility of this approach to characterize extreme events across a diverse set of challenging systems, including turbulent bursts of energy dissipation in the 2D Kolmogorov Flow, spontaneous synchronization in networks of coupled FitzHugh-Nagumo oscillators, and the localized formation of ocean rogue waves from a modified nonlinear Schr"odinger equation. For each example, we show that our simple forecast models accurately predict extreme events and that the underlying mechanisms may be used to design control laws to prevent these events. Finally, we demonstrate that by learning a neural network surrogate model of the dynamics directly from data, we may extend this approach to experimental systems and systems that are not natively written in an automatically differentiable programming language.