  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.
