Sequence-to-sequence prediction of spatiotemporal systems

Area of Science:

• Computational physics
• Artificial intelligence
• Dynamical systems

Background:

• Spatiotemporal systems, such as solitary waves and chaotic dynamics, are complex to predict.
• Traditional methods often require detailed system models, limiting their applicability.

Purpose of the Study:

• To propose and evaluate a novel attention-based sequence-to-sequence neural network architecture for model-free prediction of spatiotemporal systems.
• To demonstrate the architecture's capability in forecasting the evolution of solitary waves and chaotic systems.

Main Methods:

• Developed an encoder-decoder neural network incorporating attention mechanisms.
• Trained the network on data from the Korteweg-de Vries equation (solitary waves).
• Validated the approach on the Lorenz system and three other partial differential equations.

Main Results:

• The attention-based architecture achieved good performance in predicting the evolutionary behavior of the studied spatiotemporal dynamics.
• Successfully predicted the future evolution of solitary waves described by the Korteweg-de Vries equation.
• Demonstrated applicability to chaotic systems like the Lorenz system.

Conclusions:

• The proposed attention-based sequence-to-sequence architecture offers a promising model-free approach for spatiotemporal system prediction.
• This work represents the first application of this architecture to solitary wave prediction.
• The method shows potential for diverse dynamical systems, including chaotic ones.