# Data driven modeling for self-similar dynamics

arXiv: https://arxiv.org/abs/2310.08282 · HTML: https://mlsanity.com/paper/2310.08282/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 76 references that are in the map.
- First posted on arXiv 12 Oct 2023.

## Builds on (most cited first, 17 of 17)

- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Forecasting Sequential Data using Consistent Koopman Autoencoders](https://mlsanity.com/paper/2003.02236/) (2020)
- [Multiscale Simulations of Complex Systems by Learning their Effective Dynamics](https://mlsanity.com/paper/2006.13431/) (2020)
- [Neural Network Renormalization Group](https://mlsanity.com/paper/1802.02840/) (2018)
- [Koopman Operator Dynamical Models: Learning, Analysis and Control](https://mlsanity.com/paper/2102.02522/) (2021)
- [Scale-invariant Feature Extraction of Neural Network and Renormalization Group Flow](https://mlsanity.com/paper/1801.07172/) (2018)
- [Universality, criticality and complexity of information propagation in social media](https://mlsanity.com/paper/2109.00116/) (2021)
- [Geometric renormalization unravels self-similarity of the multiscale human connectome](https://mlsanity.com/paper/1904.11793/) (2019)
- [Finding emergence in data by maximizing effective information](https://mlsanity.com/paper/2308.09952/) (2023)
- [Neural Information Squeezer for Causal Emergence](https://mlsanity.com/paper/2201.10154/) (2022)
- [Learning effective dynamics from data-driven stochastic systems](https://mlsanity.com/paper/2205.04151/) (2022)
- [Finite-size scaling of geometric renormalization flows in complex networks](https://mlsanity.com/paper/2001.09875/) (2020)

## 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.