From grids to Graph nodes: The motivation

Observations that are obtained from satellites, radars, and other sources are often in the form of irregularly spaced data points. When the data sources are irregularly spaced, it is often more appropriate to represent the data as a graph, where the nodes represent the data points and the edges represent the relationships between them. The gridded products are obtained from these irregularly spaced data points through interpolation and other techniques. By representing the data as a graph, we can directly work with the observation network based data to capture the underlying relationships and dependencies between the data points.

GNN: they allow us to encode relationships via connectivity, beyond purely spatial proximity. This is particularly useful in scientific applications where the relationships between data points may be complex and not solely based on their spatial locations. GraphCast was a recent work that used Graph Neural Networks for weather forecasting by Google.

Reduced Gaussian Grid:

  • lats are determined by the roots of the Legendre polynomial of degree N, where N is the number of latitudes. The lons are determined by dividing the circumference of the Earth into equal segments based on the number of longitudes. Thus the number of longitudes decreases as we move towards the pole. The reduced Gaussian grid is a type of grid that is used in numerical weather prediction and climate modeling. It is designed to reduce the number of grid points in regions where the data is less important, while maintaining a high resolution in regions where the data is more important. This allows for more efficient computations and better representation of important features in the data.

A priori choice of the node connectivity is a challenge. We want to explore the use of topological descriptors, such as Morse Complex, to determine the connectivity of the graph nodes.

  1. Bipartite Structure - Partition the graph into two sets of nodes, where one set represents the input features and the other set represents the output features.

What was new to me:

Attentional Convolutional Networks (ACNs) are a type of neural network architecture that combines the strengths of convolutional neural networks (CNNs) and attention mechanisms.

In transformer based models,

** Project Ideas: ** Downscaling the rainfall data in Indian region from the coarse resolution of the ERA5 reanalysis to a finer resolution using Graph Neural Networks. The goal is to improve the spatial resolution of the rainfall data while preserving important features and patterns in the data. This can be useful for applications such as hydrological modeling, flood forecasting, and climate impact assessments.

** Project Ideas: extended analysis with morse complex built from the rainfall data ** Related: Predicting the rainfall in the Indian region using Graph Neural Networks. The goal is to develop a model that can accurately predict rainfall patterns based on historical data and other relevant features. This can be useful for applications such as agriculture, water resource management, and disaster preparedness.

** Project Ideas: Can you apply consistency model framework to the rainfall data where you leverage a pre-trained model on the ERA5 reanalysis data and fine-tune it on the rainfall data to improve the accuracy of the predictions.**

2026-07-07_Vertrag_vorbehaltlich_AA-Erlaubnis. 2026-07-06_Erklärung-Beschäftigungsverhältnis_final_incl-Unterlagen_sign.pdf

What You will Learn:

  • How to represent irregularly spaced data as a graph and work with graph-based representations.
  • VIT : Visiion Transformer
  • Graph Neural Networks (GNNs)
  • Sparse Attention( quadratic scaling limits the number of tokens one can process, so we want to explore sparse attention mechanisms that can reduce the computational complexity while maintaining performance. This can be useful for processing large graphs with many nodes and edges, where the number of tokens can be very large.)
  • Shared KV, Quantization, and other techniques to reduce the memory footprint of the model.

Cons of Transformers: They require more data for the same task because of no inductive bias. They also have high memory footprints.

References: