Weather forecasting using graph neural networks.
Weather forecasting using graph neural networks (GNNs) is a novel approach to capture the complex spatial and temporal relationships in weather data.
Traditional weather forecasting methods are dominated by numerical forecasting models (NWPs) and statistical methods, which are often computationally expensive and limited in their ability to improve overall accuracy; GNNs represent the relationships between data as graphs and utilise their structure to improve forecast accuracy, so their application to weather forecasting is This is attracting attention.
The basic structure of a graph neural network (GNN) is as follows.
1. node: each point in the graph. In the case of weather forecasting, these represent weather stations, cities or specific regions.
2. edges: relationships between nodes. Edges can be based on various criteria, such as physical distance, wind flow, correlation of weather patterns, etc.
3. node features: the characteristics of each node. This includes data observed at the weather station, such as temperature, humidity, pressure, wind speed, etc.
4. edge features: the strength and type of relationship between nodes. Distance, direction and historical correlation can be used as features.
The process of weather forecasting using GNNs is as follows.
1. data collection: observation data is collected from weather stations and satellites. The weather data from each station or point is used as the node’s features.
2. graph construction: each point or station is used as a node and the graph is constructed using geographical relationships and weather pattern correlations as edges.
3. model design:
Input layer: feature values for each node are input.
Graph Convolutional Layers: aggregate the node’s feature values together with the information of neighbouring nodes to generate new node feature values.
Recurrent Layer (if required): additional Recurrent Neural Network (RNN) layer to model temporal dependencies.
3. output layer: predicts future weather conditions for each node.
4. training: train the GNN model using historical weather data. The training dataset includes actual observed data as labels.
5. forecasting: future weather conditions are predicted using the trained model.
Advantages of GNNs include: ‘modelling spatial dependencies‘, which effectively models spatial dependencies by representing the relationships between nodes as edges; ‘data integration‘, which allows heterogeneous data (ground data, satellite data, etc.) to be integrated into a single graph and handled in a unified manner; and ‘weather forecasting‘, which can handle large weather Scalability”, which can handle large weather data sets and efficiently process data with complex relationships.
Weather forecasting using GNNs can model spatial and temporal dependencies more effectively than conventional methods, which is expected to improve forecast accuracy, making the use of GNNs a very promising approach in the modern era of large-scale, complex weather data.
Algorithms related to weather forecasting using graph neural networks.
Specific algorithms related to weather forecasting using graph neural networks (GNNs) include the following. These algorithms capture spatial and temporal dependencies between nodes (weather stations or geographic points) and are used to improve the accuracy of weather data forecasts.
1. Graph Convolutional Network (GCN): a GCN is a method that aggregates the features of a node together with the features of its neighbouring nodes to generate new features. In weather forecasting, data from each weather station is used as node features and the relationship between stations is modelled as edges. For more information, see Graph Convolutional Neural Networks (GCN) Overview, Algorithms and Implementation Examples.
Example: Basic GCN
1. input layer: feature values (temperature, humidity, etc.) for each weather station are input.
2. Graph convolution layer: aggregates the features of neighbouring stations and computes new features for the nodes.
3. output layer: predicts future weather data for each station.
2. graph attention network (GAT): the GAT becomes a method for learning node features by assigning different importance levels to edges. It does this by weighting the relationships between stations to emphasise the important relationships and improve forecast accuracy. For more information, see GAT (Graph Attention Network) Overview, Algorithm and Example Implementation.
Example: Basic GAT
1. input layer: features for each weather station;
2. Attention mechanism: weights are assigned to each edge and features of neighbouring nodes are aggregated.
3. graph convolution layer: computes new features for nodes using the weighted features.
4. output layer: predicts future weather data.
3. Temporal Graph Neural Network (TGNN): A TGNN is a model that takes into account temporal variations in graph structure and is used in weather forecasting to capture changing weather patterns over time. For more information, see Overview of Spatio-Temporal Graph Convolutional Networks and Examples of Algorithms and Implementations.
Example: Basic TGNN
1. input layer: features of the weather station as time series data
2. Temporal graph convolution layer: graph convolution along the time axis to compute node features.
3. output layer: prediction of weather data at a specific point in the future.
4. deep graph infomax (DGI): DGI is a model that uses self-supervised learning to learn the node representation of a graph. It is used in meteorological data to capture potential relationships between nodes. For more information, see “Overview of encoder/decoder models in GNNs, algorithms and implementation examples“.
Example: basic DGI
1. input layer: features for each weather station.
2. encoder: learns node embeddings using graph convolution.
3. self-supervised learning: maximising the consistency of the node representation using the original and shuffled graphs.
4. output layer: builds weather prediction models using the learnt node representations.
5. Spatial-Temporal Graph Neural Network (ST-GNN): the ST-GNN becomes a network that simultaneously models spatial and temporal dependencies. In weather forecasting, it is suitable for predicting changing weather patterns over time in a particular region. For more information, see ST-GCN (Spatio-Temporal Graph Convolutional Networks): Overview, Algorithms and Examples of Implementations.
Example: Basic ST-GCN
1. input layer: features of the weather station as time series data
2. Spatial graph convolution layer: modelling spatial dependencies.
3. Temporal graph convolution layer: models temporal dependencies.
4. output layer: predicts future weather data.
GCN and GAT are strong in modelling spatial dependencies and can make predictions considering relationships between regions, TGNN and ST-GNN can capture temporal variability and make more accurate time-dependent predictions DGI can efficiently learn potential relationships between nodes through self-supervised learning approach. These algorithms can be combined and refined according to the characteristics of specific weather data and forecasting objectives, which can significantly improve the accuracy of weather forecasts.
Applications of graph neural networks in weather forecasting.
Specific applications of weather forecasting using graph neural networks (GNNs) are described below.
1. regional forecasting using weather station networks: a network of weather stations is modelled as a graph to provide detailed weather forecasts for each region.
Case study:
Project: a GNN-based weather forecasting system was developed by the Japanese Meteorological Agency using data collected from weather stations across the country.
Methodology: a graph is constructed with each weather station as a node and geographical distance and wind flow as edges; interactions between stations are modelled using GCN and GAT to generate region-specific weather forecasts.
2. short-term forecasts with spatial-temporal graph neural networks (ST-GNN): use models that simultaneously consider spatial and temporal dependencies in short-term weather forecasts.
Case study:
Project: applying ST-GNNs to city-level weather data to provide detailed weather forecasts from one hour ahead to several hours ahead.
Methodology: a graph is constructed by using multiple observation points within a city as nodes and sliding historical weather data over time. Future weather is predicted by combining spatial and temporal graph convolution layers.
3. real-time weather hazard prediction: predicts extreme weather events (e.g. heavy rain, storms) using weather data collected in real time.
Case study:
Project: real-time weather data (e.g. precipitation, wind speed, pressure) in a specific area is modelled as a graph and the occurrence of extreme weather events is predicted using GNN.
Methodology: constructed using real-time data for each observation point as node features and real-time wind speed and precipitation gradients as edges; GNN is applied to estimate the probability of occurrence of extreme weather events.
4. wide-area forecasting using satellite data: weather data from satellites is modelled as a graph to provide a wide-area weather forecast.
Case study:
Project: a wide-area weather forecasting system was developed using global meteorological satellite data. Satellite data are used as nodes and spatial relationships between each node are constructed as edges.
Methodology: Using feature values such as temperature, cloud cover and humidity extracted from satellite data, perform graph convolution with GCN and GAT to predict weather patterns over a wide area.
5. early warning systems for extreme weather: develop early warning systems for extreme weather (e.g. heat waves, cold waves).
Case study:
Project: as an early warning system for extreme weather events, past extreme weather data is learnt by GNN to predict the occurrence of extreme weather events.
Methodology: past extreme weather events are used as a dataset and the characteristics of each event are learnt as node features. Edges are constructed based on correlations between events; GNNs are used to predict future extreme weather events and issue early warnings.
Example implementation of weather forecasting using graph neural networks
This section describes an example implementation of a weather forecast using a graph neural network (GNN). In the following, a basic implementation using Python and the main machine learning libraries (PyTorch and PyTorch Geometric) is presented. The example uses hypothetical weather data to create a simple GNN model that models the relationships between weather stations and predicts future temperatures.
Prerequisites:
Python environment (Python 3.7+)
Installation of required libraries:
pip install torch torch-geometric pandas numpyStep 1: Data preparation
Create a virtual meteorological data set. A data frame is created containing the location of each weather station and historical temperature data.
import pandas as pd
import numpy as np
# Virtual weather station data.
stations = pd.DataFrame({
'station_id': [0, 1, 2, 3],
'latitude': [35.0, 36.0, 34.0, 33.0],
'longitude': [135.0, 136.0, 137.0, 138.0]
})
# Virtual temperature data (last 5 days)
temperature_data = pd.DataFrame({
'station_id': [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3],
'day': [0, 1, 2, 3, 4] * 4,
'temperature': np.random.rand(20) * 30
})Step 2: Define the graph structure
Define the relationships between weather stations as edges. In this example, a complete graph is assumed where all stations are connected to each other.
import torch
from torch_geometric.data import Data
# Node features (latest temperature data)
node_features = torch.tensor([
[temperature_data[temperature_data['station_id'] == i]['temperature'].values[-1]]
for i in range(4)
], dtype=torch.float)
# Edge definition (complete graph)
edge_index = torch.tensor([
[0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3],
[1, 0, 3, 2, 2, 3, 0, 1, 3, 2, 1, 0]
], dtype=torch.long)
# Creating graph data objects
data = Data(x=node_features, edge_index=edge_index)Step 3: Define the model
Define a Graph Convolutional Network (GCN). The model takes the features (temperature data) of each node as input and updated features as output.
import torch.nn.functional as F
from torch_geometric.nn import GCNConv
class WeatherGCN(torch.nn.Module):
def __init__(self):
super(WeatherGCN, self).__init__()
self.conv1 = GCNConv(1, 16)
self.conv2 = GCNConv(16, 1)
def forward(self, data):
x, edge_index = data.x, data.edge_index
x = self.conv1(x, edge_index)
x = F.relu(x)
x = self.conv2(x, edge_index)
return x
# Instantiating the model
model = WeatherGCN()Step 4: Define the training process
Define the training process for the model. Here, the mean squared error (MSE) is used as the loss function and the model is optimised with the Adam optimiser.
optimizer = torch.optim.Adam(model.parameters(), lr=0.01)
criterion = torch.nn.MSELoss()
# Virtual target value (temperature on the following day)
target = torch.tensor([[25.0], [26.0], [24.0], [23.0]], dtype=torch.float)
# training loop
model.train()
for epoch in range(100):
optimizer.zero_grad()
out = model(data)
loss = criterion(out, target)
loss.backward()
optimizer.step()
if epoch % 10 == 0:
print(f'Epoch {epoch}, Loss: {loss.item()}')
print("Training complete!")Step 5: Running the forecast.
The trained model is used to predict future temperatures.
model.eval()
with torch.no_grad():
prediction = model(data)
print("Predicted temperatures:", prediction.numpy())This example shows how a basic graph neural network (GCN) can be used to predict future temperatures based on hypothetical weather data. In real weather forecasting systems, it is important to use more complex models and larger datasets to increase accuracy, e.g. combining recurrent neural networks (RNNs) and Transformer for time-series data to account for temporal dependencies is an effective approach The following are some examples of such approaches.
Challenges and Solution for weather forecasting using graph neural networks.
While there is a lot of potential for weather forecasting using graph neural networks (GNNs), there are also several challenges. The main challenges and measures to address them are described below.
1. data acquisition and pre-processing:
Challenge: The collection and pre-processing of high-quality, comprehensive weather data is a major challenge. Data may be lacking in some areas or there may be missing data.
Solution:
Data augmentation: use data augmentation techniques to supplement missing data. For example, techniques can use data from neighbouring stations to supplement missing values.
Integration of multiple sources: integrating multiple data sources, such as ground observation data, satellite data and weather modelling data, to increase data integrity.
Data cleaning: apply data cleaning methods to remove anomalies and noise. Examples include detecting and correcting temporally and spatially anomalous data points.
2. modelling spatial and temporal dependencies:
Challenge: meteorological data are spatially and temporally dependent. It can be difficult to model these dependencies effectively.
Solution:
Use of ST-GNN: use spatial-temporal graph neural networks (ST-GNN) to model spatial and temporal dependencies simultaneously.
Multi-scale approach: adopt a multi-scale GNN architecture to simultaneously model spatial and temporal data at different scales.
Incorporation of recurrent layers: to capture temporal dependencies, methods that incorporate recurrent neural networks (RNNs) and LSTM layers in GNNs can also be effective.
3. computational costs:
Challenge: Computational costs can be very high when dealing with large graph data.
Solution:
Graph sampling: sample a subset of large graphs to reduce computational complexity. Some methods, e.g. GraphSAGE, are used for efficient sampling.
Efficient algorithms: some employ computationally efficient GNN algorithms (e.g. FastGCN and Cluster-GCN described in “Overview of R-GCN and examples of algorithms and implementations“).
Use of hardware: dedicated hardware such as GPUs and TPUs is used to speed up the computation.
4. lack of interpretability:
Challenge: GNNs are black box models and interpretation of prediction results is difficult.
Solution:
Attention mechanisms: use attention mechanisms such as GAT (Graph Attention Network) to understand which nodes and edges are important for prediction.
Explainable AI (XAI): use methods (e.g. SHAP and LIME) to explain the predictive results of the model.
Feature importance analysis: analysing the impact of node and edge features on prediction results.
5. deployment and real-time forecasting:
Challenge: designing and deploying a system for real-time prediction is complex.
Solution:
Stream processing: use stream processing frameworks such as Apache Kafka and Apache Flink to process and forecast real-time data.
Edge computing: run models on edge devices close to the point where weather data is collected to provide real-time forecasts.
Containerisation and orchestration: use Docker and Kubernetes to streamline the deployment and scaling of models.
Reference Information and Reference Books
For more information on graph data, see “Graph Data Processing Algorithms and Applications to Machine Learning/Artificial Intelligence Tasks. Also see “Knowledge Information Processing Techniques” for details specific to knowledge graphs. For more information on deep learning in general, see “About Deep Learning.
Reference book is
“Graph Neural Networks: Foundations, Frontiers, and Applications“等がある。
“Introduction to Graph Neural Networks“
“Graph Neural Networks in Action“
“Statistical Methods for Forecasting”
“Time Series Analysis: Forecasting and Control”
“ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs“
“HiSTGNN: Hierarchical spatio-temporal graph neural network for weather forecasting“
コメント