Zhihao Deng*: Climatological Anomalies Projection using Neural Ordinary Differential Equations
AUTHOR: Zhihao Deng, Chuqi Cao, Hanbo Yang
SUPERVISOR & CO-SUPERVISOR: Andrew Ooi, Vassili Kitsios
Introduction: Many real-world geophysical and engineering systems are defined by ordinary differential equations (ODEs) solved via numerical integration. While white-box models use known physical constraints to derive these equations, they become infeasible for poorly understood systems. In addition, a high-dimensional coupled equations will significantly increase computational costs. This project adopts a black-box deep learning approach to model climatological anomaly components as a first-order autonomous dynamical system for efficient forecasting.
Methodology: We trained a Neural ODE with noise estimation on the primary energetic modes of the reduced-order model dataset. The Neural ODE approximates the underlying dynamics, while the noise estimator captures the residual error left by the Neural ODEs. All network parameters are optimised via stochastic variational inference. This process employs a multi-shot training technique where the training horizon is progressively increased. Within this framework, individual state variables are weighted according to their energetic contributions.
Results: Our approaches generalise well on the dominant energetic modes, while modes with lower contributions are mostly captured by the noise level estimator. Moreover, the statistical properties of the reconstructed forecasts closely match those of the ground truth, indicating that the models preserve the underlying system behaviour.
Audience: For Meteorologists and Computational Scientists, we model atmospheric dynamics more efficiently than traditional simulations. For Reliability Engineer, the model identifies anomalies in complex time series, enabling data-informed decisions regarding extreme events and risk exposure.
Keywords: Climate projection; Machine learning; Anomalies detection.