Tipping point forecasting in nonstationary dynamics on function spaces.
- 1Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125.
- 2University of Colorado Boulder, Boulder, CO 80309.
- 3Nvidia Corporation, Santa Clara, CA 95051.
Abstract
Tipping points are abrupt, drastic, and often irreversible changes in the evolution of nonstationary 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 nonstationary dynamical systems using a 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 nonstationary 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.
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BibTeX
@article{liuschiaffini2026tipping,
title = {{Tipping point forecasting in nonstationary dynamics on function spaces.}},
author = {Miguel Liu-Schiaffini and Clare E Singer and Nikola Kovachki and Sze Chai Leung and Hyunji Jane Bae and Kamyar Azizzadenesheli and Anima Anandkumar},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
year = {2026},
month = oct,
doi = {10.1073/pnas.2600331123},
url = {https://europepmc.org/article/MED/42879468},
note = {CC BY},
}
RIS
TY - JOUR
TI - Tipping point forecasting in nonstationary dynamics on function spaces.
AU - Miguel Liu-Schiaffini
AU - Clare E Singer
AU - Nikola Kovachki
AU - Sze Chai Leung
AU - Hyunji Jane Bae
AU - Kamyar Azizzadenesheli
AU - Anima Anandkumar
PY - 2026
DA - 2026/10/15
JO - Proceedings of the National Academy of Sciences of the United States of America
DO - 10.1073/pnas.2600331123
UR - https://europepmc.org/article/MED/42879468
AB - Tipping points are abrupt, drastic, and often irreversible changes in the evolution of nonstationary 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 nonstationary dynamical systems using a 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 nonstationary 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.
SN - 0027-8424
SN - 1091-6490
ER -