Data-driven discovery of self-similarity using neural networks

Area of Science:

• Physics
• Complex Systems
• Data Science

Background:

• Identifying self-similarity is crucial for understanding complex physical phenomena.
• Traditional methods often rely on model-specific assumptions, introducing potential bias.
• A model-independent approach is needed to discover self-similarity directly from observed data.

Purpose of the Study:

• To develop and validate a neural network-based method for discovering self-similarity without presupposing physical models.
• To extract power-law exponents characterizing scale-transformation symmetries from data.
• To provide a robust, model-independent tool for analyzing complex systems.

Main Methods:

• A neural network architecture is designed to structurally incorporate power-law monomial forms.
• The neural network is trained using observed data (synthetic and experimental).
• Successful training allows for the extraction of power-law exponents.

Main Results:

• The neural network successfully identifies self-similarity directly from data.
• Power-law exponents characterizing scale-transformation symmetries are extracted.
• The method demonstrates effectiveness on both synthetic and experimental datasets.

Conclusions:

• The proposed neural network approach offers a robust, model-independent tool for discovering self-similarity.
• This method facilitates the exploration of governing laws in complex physical systems.
• The technique has broad applicability in analyzing diverse scientific data.