Data driven modeling for self-similar dynamics
This work addresses the problem of efficient multiscale modeling for researchers studying complex systems with self-similarity, representing an incremental advancement by integrating prior knowledge into a neural network framework.
The paper tackles the challenge of modeling self-similar dynamics in complex systems by introducing a multiscale neural network framework that incorporates self-similarity as prior knowledge, achieving results such as extracting scale-invariant kernels and identifying power law exponents, with preliminary tests on the Ising model yielding critical exponents consistent with theoretical expectations.
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.