Master Thesis Defense by Sune Halkjær

Title: Machine Learning Prediction of Climate Multi-Stability

Abstract:
This thesis investigates the possibility for state-of-the-art Machine Learning (ML) techniques to predict multiple coexisting attractors in a complex dynamical system, when only a subset of these attractors have been observed during training. This is a prerequisite for ML models to be able to predict regime shifts to previously unseen states, a problem that arises in the
context of possible future Climate Tipping Points (TPs). The study uses Next-Generation Reservoir Computing (NG-RC), a state-of-the-art ML technique for time series forecasting,
applied to complex models with known multistability. The thesis employs a two-pronged approach: first establishing the methodology using the Li & Sprott system with multiple coexisting attractors, then applying it to the problem of a multistable Atlantic Meriodional Overturning Circulation (AMOC) in a high-dimensional global ocean model.
It has been previously demonstrated that NG-RC achieves exceptional predictive performance when exact nonlinearities are known, reaching predictive horizons of several Lyapunov times and high accuracy in reconstructing basin of attraction. Here we show that when only approximate nonlinearities are known, such as by employing Radial Basis Functions (RBFs), performance degrades significantly for unseen attractors. A strategic sampling technique of RBF centers is presented that partially recovers this capability. For the complex ocean model, single-attractor predictions demonstrate extended predictive horizons due to coherent centennial-scale variability, but struggle to reproduce accurate statistics on the attractor. Multi-attractor predictions show that the ML model can indeed learn multistability with attractors at the correct locations in phase space, but also exhibit a tendency to generate
artificial attractors, as well as long transients.
The thesis identifies significant obstacles in using ML for prediction of regimes shifts in complex systems, such as the climate. Unknown system nonlinearities limit ability to accurately predict unseen regimes, artificial attractor generation risks false tipping point identification, and balancing numerical stability against dynamical fidelity requires case-specific tuning. These findings suggest that while NG-RC offers valuable understanding and forecasting for known climate regimes, predicting genuinely novel states like AMOC collapse requires additional physical constraints or fundamentally new approaches capable of extrapolating beyond training domains.

Supervisor: Johannes Jakob Lohmann 
Censor: Jens Olaf Pepke Pedersen