# Data-driven geophysical forecasting: Simple, low-cost, and accurate baselines with kernel methods

arXiv: https://arxiv.org/abs/2103.10935 · HTML: https://mlsanity.com/paper/2103.10935/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 57 references that are in the map.
- First posted on arXiv 13 Feb 2021.

## Builds on (most cited first, 15 of 15)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Tackling Climate Change with Machine Learning](https://mlsanity.com/paper/1906.05433/) (2019)
- [Deep learning to represent sub-grid processes in climate models](https://mlsanity.com/paper/1806.04731/) (2018)
- [Improving data-driven global weather prediction using deep convolutional neural networks on a cubed sphere](https://mlsanity.com/paper/2003.11927/) (2020)
- [Every Model Learned by Gradient Descent Is Approximately a Kernel Machine](https://mlsanity.com/paper/2012.00152/) (2020)
- [Machine Learning for the Geosciences: Challenges and Opportunities](https://mlsanity.com/paper/1711.04708/) (2017)
- [Kernel Flows: from learning kernels from data into the abyss](https://mlsanity.com/paper/1808.04475/) (2018)
- [Analog forecasting of extreme-causing weather patterns using deep learning](https://mlsanity.com/paper/1907.11617/) (2019)
- [Application of Deep Convolutional Neural Networks for Detecting Extreme Weather in Climate Datasets](https://mlsanity.com/paper/1605.01156/) (2016)
- [DeepDownscale: a Deep Learning Strategy for High-Resolution Weather Forecast](https://mlsanity.com/paper/1808.05264/) (2018)
- [Data-driven super-parameterization using deep learning: Experimentation with multi-scale Lorenz 96 systems and transfer-learning](https://mlsanity.com/paper/2002.11167/) (2020)
- [Deep regularization and direct training of the inner layers of Neural Networks with Kernel Flows](https://mlsanity.com/paper/2002.08335/) (2020)
- [Meta-modeling strategy for data-driven forecasting](https://mlsanity.com/paper/2012.00678/) (2020)

## Built on by (most cited first, 15 of 15)

- [Kernel Methods are Competitive for Operator Learning](https://mlsanity.com/paper/2304.13202/) (2023)
- [Computational Graph Completion](https://mlsanity.com/paper/2110.10323/) (2021)
- [One-Shot Learning of Stochastic Differential Equations with Data Adapted Kernels](https://mlsanity.com/paper/2209.12086/) (2022)
- [Learning Dynamical Systems from Data: A Simple Cross-Validation Perspective, Part V: Sparse Kernel Flows for 132 Chaotic Dynamical Systems](https://mlsanity.com/paper/2301.10321/) (2023)
- [Learning dynamical systems from data: A simple cross-validation perspective, part III: Irregularly-Sampled Time Series](https://mlsanity.com/paper/2111.13037/) (2021)
- [Learning "best" kernels from data in Gaussian process regression. With application to aerodynamics](https://mlsanity.com/paper/2206.02563/) (2022)
- [Codiscovering graphical structure and functional relationships within data: A Gaussian Process framework for connecting the dots](https://mlsanity.com/paper/2311.17007/) (2023)
- [Gaussian Process Hydrodynamics](https://mlsanity.com/paper/2209.10707/) (2022)
- [Kernel Sum of Squares for Data Adapted Kernel Learning of Dynamical Systems from Data: A global optimization approach](https://mlsanity.com/paper/2408.06465/) (2024)
- [Deep learning for surrogate modelling of 2D mantle convection](https://mlsanity.com/paper/2108.10105/) (2021)
- [Bridging Algorithmic Information Theory and Machine Learning: A New Approach to Kernel Learning](https://mlsanity.com/paper/2311.12624/) (2023)
- [Analysis of Structured Deep Kernel Networks](https://mlsanity.com/paper/2105.07228/) (2021)
- [Ensemble forecasts in reproducing kernel Hilbert space family](https://mlsanity.com/paper/2207.14653/) (2022)
- [Recurrent Deep Kernel Learning of Dynamical Systems](https://mlsanity.com/paper/2405.19785/) (2024)
- [Discovery of Probabilistic Dirichlet-to-Neumann Maps on Graphs](https://mlsanity.com/paper/2506.02337/) (2025)

## Abstract (arXiv)

Modeling geophysical processes as low-dimensional dynamical systems and regressing their vector field from data is a promising approach for learning emulators of such systems. We show that when the kernel of these emulators is also learned from data (using kernel flows, a variant of cross-validation), then the resulting data-driven models are not only faster than equation-based models but are easier to train than neural networks such as the long short-term memory neural network. In addition, they are also more accurate and predictive than the latter. When trained on geophysical observational data, for example, the weekly averaged global sea-surface temperature, considerable gains are also observed by the proposed technique in comparison to classical partial differential equation-based models in terms of forecast computational cost and accuracy. When trained on publicly available re-analysis data for the daily temperature of the North-American continent, we see significant improvements over classical baselines such as climatology and persistence-based forecast techniques. Although our experiments concern specific examples, the proposed approach is general, and our results support the viability of kernel methods (with learned kernels) for interpretable and computationally efficient geophysical forecasting for a large diversity of processes.