Data driven modeling for self-similar dynamics

• URL: http://arxiv.org/abs/2310.08282v3
• Date: Mon, 25 Mar 2024 06:21:37 GMT
• Title: Data driven modeling for self-similar dynamics
• Authors: Ruyi Tao, Ningning Tao, Yi-zhuang You, Jiang Zhang,
• Abstract summary: We introduce a multiscale neural network framework that incorporates self-similarity as prior knowledge. For deterministic dynamics, our framework can discern whether the dynamics are self-similar. Our method can identify the power law exponents in self-similar systems.
• Score: 1.0790314700764785
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multiscale modeling of complex systems is crucial for understanding their intricacies. Data-driven multiscale modeling has emerged as a promising approach to tackle challenges associated with complex systems. On the other hand, self-similarity is prevalent in complex systems, hinting that large-scale complex systems can be modeled at a reduced cost. In this paper, we introduce a multiscale neural network framework that incorporates self-similarity as prior knowledge, facilitating the modeling of self-similar dynamical systems. For deterministic dynamics, our framework can discern whether the dynamics are self-similar. For uncertain dynamics, it can compare and determine which parameter set is closer to self-similarity. The framework allows us to extract scale-invariant kernels from the dynamics for modeling at any scale. Moreover, our method can identify the power law exponents in self-similar systems. Preliminary tests on the Ising model yielded critical exponents consistent with theoretical expectations, providing valuable insights for addressing critical phase transitions in non-equilibrium systems.

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