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Data driven modeling for self-similar dynamics

arXiv 2310.08282 ↗First posted 12 Oct 2023cs.LG cond-mat.stat-mechcited by 0

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Abstract (arXiv)

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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References · 17

  1. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 491
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  12. 2021Universality, criticality and complexity of information propagation in social mediacited by 6
5 more
  1. 2019Geometric renormalization unravels self-similarity of the multiscale human connectomecited by 4
  2. 2023Finding emergence in data by maximizing effective informationcited by 4
  3. 2022Neural Information Squeezer for Causal Emergencecited by 3
  4. 2022Learning effective dynamics from data-driven stochastic systemscited by 3
  5. 2020Finite-size scaling of geometric renormalization flows in complex networkscited by 1

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