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

arXiv: https://arxiv.org/abs/2010.00399 · HTML: https://mlsanity.com/paper/2010.00399/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2020.

## Built on by (most cited first, 8 of 8)

- [QuACK: Accelerating Gradient-Based Quantum Optimization with Koopman Operator Learning](https://mlsanity.com/paper/2211.01365/) (2022)
- [Koopman Invertible Autoencoder: Leveraging Forward and Backward Dynamics for Temporal Modeling](https://mlsanity.com/paper/2309.10291/) (2023)
- [CKNet: A Convolutional Neural Network Based on Koopman Operator for Modeling Latent Dynamics from Pixels](https://mlsanity.com/paper/2102.10205/) (2021)
- [Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning](https://mlsanity.com/paper/2202.05750/) (2022)
- [Deep Koopman operator framework for causal discovery in nonlinear dynamical systems](https://mlsanity.com/paper/2505.14828/) (2025)
- [Reduced-Order Surrogates for Forced Flexible Mesh Coastal-Ocean Models](https://mlsanity.com/paper/2602.05416/) (2026)
- [Non-intrusive Learning of Physics-Informed Spatio-temporal Surrogate for Accelerating Design](https://mlsanity.com/paper/2604.14424/) (2026)
- [Physics-Informed Tracking (PIT)](https://mlsanity.com/paper/2604.16895/) (2026)

## Abstract (arXiv)

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.