# Tipping Point Forecasting in Non-Stationary Dynamics on Function Spaces

arXiv: https://arxiv.org/abs/2308.08794 · HTML: https://mlsanity.com/paper/2308.08794/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 90 references that are in the map.
- First posted on arXiv 17 Aug 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [Machine learning prediction of critical transition and system collapse](https://mlsanity.com/paper/2012.01545/) (2020)
- [Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systems](https://mlsanity.com/paper/2207.00521/) (2022)
- [Off-Policy Risk Assessment in Contextual Bandits](https://mlsanity.com/paper/2104.08977/) (2021)
- [Neural Ordinary Differential Equation based Recurrent Neural Network Model](https://mlsanity.com/paper/2005.09807/) (2020)
- [A Generative Adversarial Network for Climate Tipping Point Discovery (TIP-GAN)](https://mlsanity.com/paper/2302.10274/) (2023)
- [Fourier-RNNs for Modelling Noisy Physics Data](https://mlsanity.com/paper/2302.06534/) (2023)

## Built on by (most cited first, 8 of 8)

- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [A Library for Learning Neural Operators](https://mlsanity.com/paper/2412.10354/) (2024)
- [Foundation Models for Weather and Climate Data Understanding: A Comprehensive Survey](https://mlsanity.com/paper/2312.03014/) (2023)
- [Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning](https://mlsanity.com/paper/2506.10973/) (2025)
- [Physics-informed Neural-operator Predictive Control for Drag Reduction in Turbulent Flows](https://mlsanity.com/paper/2510.03360/) (2025)
- [Pretrained Video Models as Differentiable Physics Simulators for Urban Wind Flows](https://mlsanity.com/paper/2603.21210/) (2026)
- [Physics-Informed Neural Operators for Cardiac Electrophysiology](https://mlsanity.com/paper/2511.08418/) (2025)
- [Inertial Manifold Neural Operator for Dissipative Time-Dependent Partial Differential Equations](https://mlsanity.com/paper/2608.23546/) (2026)

## Abstract (arXiv)

Tipping points are abrupt, drastic, and often irreversible changes in the evolution of non-stationary and chaotic dynamical systems. For instance, increased greenhouse gas concentrations are predicted to lead to drastic decreases in low cloud cover, referred to as a climatological tipping point. In this paper, we learn the evolution of such non-stationary dynamical systems using a novel recurrent neural operator (RNO), which learns mappings between function spaces. After training RNO on only the pre-tipping dynamics, we employ it to detect future tipping points using an uncertainty-based approach. In particular, we propose a conformal prediction framework to forecast tipping points by monitoring deviations from physics constraints (such as conserved quantities and partial differential equations), enabling forecasting of these abrupt changes along with a rigorous measure of uncertainty. We illustrate our proposed methodology on non-stationary ordinary and partial differential equations, such as the Lorenz-63 and Kuramoto-Sivashinsky equations. We also apply our methods to forecast a climate tipping point in stratocumulus cloud cover and airfoil wake and stall transitions using only limited knowledge of the governing equations. For the latter, we show that our proposed method zero-shot generalizes to forecasting multiple future tipping points under varying Reynolds numbers. In our experiments, we demonstrate that even partial or approximate physics constraints can be used to accurately forecast future tipping points.