Weather forecasting with graph neural networks using multi-mesh representations

A system comprising:

• one or more computers;
• and
• one or more storage devices communicatively coupled to the one or more computers, wherein the one or more storage devices store instructions that, when executed by the one or more computers, cause the one or more computers to perform operations comprising:
• obtaining current weather data for a current time step, wherein the current weather data is defined on a latitude-longitude grid over a surface of a body and comprises, for each of a plurality of points on the latitude-longitude grid, current weather properties at the point as of the current time step;
• generating, using the current weather data, current graph data representing a current state of a graph of the surface, the graph comprising:
• a plurality of nodes, the plurality of nodes comprising a plurality of grid nodes that each correspond to one of the points on the latitude-longitude grid and a plurality of mesh nodes that each correspond to a node in a first mesh that is placed around the surface at a first scale;
• and
• a plurality of edges, the plurality of edges comprising a plurality of mesh edges that include (i) a respective first scale mesh edge connecting each pair of mesh nodes that are connected in the first mesh that is placed around the surface at the first scale and (ii) for each of one or more second scales that are coarser than the first scale, a respective second scale mesh edge connecting each pair of mesh nodes that would be connected in a corresponding second mesh that is placed around the surface at the second scale, and
• the current graph data comprising respective embeddings for each of the nodes and edges in the graph;
• and
• processing the current graph data using a graph neural network to generate a first prediction output that defines first future weather data that includes, for each of the plurality of points on the latitude-longitude grid, predicted weather properties at the point as of a first future time step that is after the current time step

One or more non-transitory computer storage media storing instructions that when executed by one or more computers cause the one or more computers to perform operations comprising:

• obtaining current weather data for a current time step, wherein the current weather data is defined on a latitude-longitude grid over a surface of a body and comprises, for each of a plurality of points on the latitude-longitude grid, current weather properties at the point as of the current time step;
• generating, using the current weather data, current graph data representing a current state of a graph of the surface, the graph comprising:
• a plurality of nodes, the plurality of nodes comprising a plurality of grid nodes that each correspond to one of the points on the latitude-longitude grid and a plurality of mesh nodes that each correspond to a node in a first mesh that is placed around the surface at a first scale;
• and
• a plurality of edges, the plurality of edges comprising a plurality of mesh edges that include (i) a respective first scale mesh edge connecting each pair of mesh nodes that are connected in the first mesh that is placed around the surface at the first scale and (ii) for each of one or more second scales that are coarser than the first scale, a respective second scale mesh edge connecting each pair of mesh nodes that would be connected in a corresponding second mesh that is placed around the surface at the second scale, and
• the current graph data comprising respective embeddings for each of the nodes and edges in the graph;
• and
• processing the current graph data using a graph neural network to generate a first prediction output that defines first future weather data that includes, for each of the plurality of points on the latitude-longitude grid, predicted weather properties at the point as of a first future time step that is after the current time step