A Geometric Algebra-Based Machine Learning Method for Typhoon Intensity Forecasting

Machine learning is well-suited for forecasting typhoon intensity due to its capacity to model complex nonlinear relationships. However, current deep learning methodologies often treat vector field components independently, neglecting the geometric relationships between them. This oversight results in a loss of information and less accurate typhoon intensity forecasts. In contrast, geometric algebra considers multidimensional variables holistically, preserving internal correlations and relevant inductive biases pertinent to wind field data. To address this limitation, this study develops a geometric algebra-based method for typhoon intensity forecasting. Initially, wind field data, encompassing both longitudinal and latitudinal components across various isobaric levels, are represented as multivector inputs. Geometric algebra convolution is subsequently employed to capture the spatial features of typhoon wind speed data. Following this, a geometric algebra-based spatial attention mechanism is introduced to dynamically focus on regions with significant wind speed variations. This is followed by a geometric algebra convolutional fusion, which enhances the representation of typhoon features by integrating data across different stages. Finally, a Wide and Deep framework is utilized to incorporate both two-dimensional and three-dimensional typhoon characteristics, modeling the interrelationships between these variables and typhoon intensity, thereby establishing a forecasting model. A comparative analysis utilizing best track and reanalysis datasets from the North-Western Pacific region (2015–2018) demonstrates that our model not only enhances prediction accuracy but also reduces the number of required parameters. This study offers new insights and advances in the application of geometric algebra for feature extraction and prediction of multidimensional correlated geoscientific data.