Unravelled multilevel transformation networks for predicting sparsely observed spatio-temporal dynamics

Area of Science:

• Dynamical Systems
• Machine Learning
• Scientific Computing

Background:

• Predicting nonlinear spatio-temporal dynamics is challenging with sparse, irregularly spaced data.
• Existing deep learning models often require regular grids or fail to capture spatial relations from sparse data.

Purpose of the Study:

• To develop a deep learning model capable of predicting complex spatio-temporal dynamics from sparsely distributed data sites.
• To address limitations of current models in handling irregular spatial data for dynamic system prediction.

Main Methods:

• A novel deep learning model integrating the radial basis function (RBF) collocation method.
• Utilizing RBF framework to learn spatial interactions among sparse data sites in an RBF-space.
• Employing learned spatial features for multilevel transformations to predict future states.

Main Results:

• Demonstrated the model's advantage in predicting spatio-temporal dynamics using both synthetic and real-world climate data.
• Successfully uncovered spatial relations from sparsely distributed data sites.
• Achieved accurate predictions of complex, nonlinear dynamics.

Conclusions:

• The proposed RBF-based deep learning model effectively predicts spatio-temporal dynamics from sparse, irregular data.
• This approach offers a robust solution for data-driven prediction in dynamical systems with limited spatial sampling.
• The method shows significant potential for applications in climate science and other fields dealing with complex spatio-temporal data.