Tipping Point Forecasting in Non-Stationary Dynamics on Function Spaces
Miguel Liu-Schiaffini Clare E. Singer Nikola Kovachki Tapio Schneider Kamyar Azizzadenesheli Anima Anandkumar
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. In our experiments, we demonstrate that even partial or approximate
physics constraints can be used to accurately forecast future tipping points.