Data-driven discovery of self-similarity using neural networks
<|reference_start|>Data-driven discovery of self-similarity using neural networks: 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.<|reference_end|>
@article{watanabe2024data-driven,
    title={Data-driven discovery of self-similarity using neural networks},
    author={Ryota Watanabe, Takanori Ishii, Yuji Hirono, Hirokazu Maruoka},
    journal={arXiv preprint arXiv:2406.03896},
    year={2024},
    number={KUNS-3006},
    archivePrefix={arXiv},
    eprint={2406.03896},
    primaryClass={cond-mat.soft cond-mat.stat-mech cs.LG}
}