Analyzing Koopman approaches to physics-informed machine learning for long-term sea-surface temperature forecasting

Abstract

Accurately predicting sea-surface temperature weeks to months into the future is an important step toward long term weather forecasting. Standard atmosphere-ocean coupled numerical models provide accurate sea-surface forecasts on the scale of a few days to a few weeks, but many important weather systems require greater foresight. In this paper we propose machine-learning approaches sea-surface temperature forecasting that are accurate on the scale of dozens of weeks. Our approach is based in Koopman operator theory, a useful tool for dynamical systems modelling. With this approach, we predict sea surface temperature in the Gulf of Mexico up to 180 days into the future based on a present image of thermal conditions and three years of historical training data. We evaluate the combination of a basic Koopman method with a convolutional autoencoder, and a newly proposed "consistent Koopman" method, in various permutations. We show that the Koopman approach consistently outperforms baselines, and we discuss the utility of our additional assumptions and methods in this sea-surface temperature domain.

References in corpus (6)

• Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
• Prediction of Sea Surface Temperature using Long Short-Term Memory
• Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge
• Shallow Neural Networks for Fluid Flow Reconstruction with Limited Sensors
• Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction
• Forecasting Sequential Data using Consistent Koopman Autoencoders

Cited by in corpus (2)

• Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning
• CKNet: A Convolutional Neural Network Based on Koopman Operator for Modeling Latent Dynamics from Pixels