Data-driven discovery of self-similarity using neural networks
- URL: http://arxiv.org/abs/2406.03896v1
- Date: Thu, 6 Jun 2024 09:36:05 GMT
- Title: Data-driven discovery of self-similarity using neural networks
- Authors: Ryota Watanabe, Takanori Ishii, Yuji Hirono, Hirokazu Maruoka,
- Abstract summary: We present a novel neural network-based approach that discovers self-similarity directly from observed data.
The presence of self-similar solutions in a physical problem signals that the governing law contains a function whose arguments are given by power-law exponents.
We train the neural network model using the observed data, and when the training is successful, we can extract the power exponents that characterize scale-transformation symmetries of the physical problem.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Finding self-similarity is a key step for understanding the governing law behind complex physical phenomena. Traditional methods for identifying self-similarity often rely on specific models, which can introduce significant bias. In this paper, we present a novel neural network-based approach that discovers self-similarity directly from observed data, without presupposing any models. The presence of self-similar solutions in a physical problem signals that the governing law contains a function whose arguments are given by power-law monomials of physical parameters, which are characterized by power-law exponents. The basic idea is to enforce such particular forms structurally in a neural network in a parametrized way. We train the neural network model using the observed data, and when the training is successful, we can extract the power exponents that characterize scale-transformation symmetries of the physical problem. We demonstrate the effectiveness of our method with both synthetic and experimental data, validating its potential as a robust, model-independent tool for exploring self-similarity in complex systems.
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