STENCIL-NET for equation-free forecasting from data.

Area of Science:

• Computational physics
• Machine learning
• Dynamical systems

Background:

• Forecasting spatiotemporal dynamics often requires knowledge of underlying physical laws.
• Existing data-driven methods may struggle with generalization and computational efficiency.

Purpose of the Study:

• Introduce STENCIL-NET, a novel artificial neural network architecture for equation-free forecasting.
• Demonstrate STENCIL-NET's ability to learn discrete propagators for accurate spatiotemporal dynamics prediction.

Main Methods:

• Developed STENCIL-NET, an architecture that learns a discrete propagator directly from data.
• Validated the model's stability and accuracy on regular Cartesian grids, analogous to classic numerical methods.
• Assessed generalization capabilities across different dynamics and grid resolutions.

Main Results:

• STENCIL-NET successfully reproduces spatiotemporal dynamics without learning governing equations.
• The model exhibits superior generalization and computational efficiency compared to CNN and FNO architectures.
• Demonstrated applications include long-term forecasting, chaotic dynamics prediction, coarse-graining, and de-noising.

Conclusions:

• STENCIL-NET provides a powerful and efficient framework for equation-free forecasting of complex dynamics.
• The learned discrete propagator offers a versatile tool for various scientific and engineering applications.
• This approach advances data-driven modeling by bypassing the need for explicit equation discovery.