# Multi-Scale Simulation of Complex Systems: A Perspective of Integrating Knowledge and Data

arXiv: https://arxiv.org/abs/2306.10275 · HTML: https://mlsanity.com/paper/2306.10275/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 216 references that are in the map.
- First posted on arXiv 17 Jun 2023.

## Builds on (most cited first, 30 of 40)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [Multiscale Simulations of Complex Systems by Learning their Effective Dynamics](https://mlsanity.com/paper/2006.13431/) (2020)
- [Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics](https://mlsanity.com/paper/1710.11239/) (2017)
- [The physics of higher-order interactions in complex systems](https://mlsanity.com/paper/2110.06023/) (2021)
- [An exact mapping between the Variational Renormalization Group and Deep Learning](https://mlsanity.com/paper/1410.3831/) (2014)
- [Neural Network Renormalization Group](https://mlsanity.com/paper/1802.02840/) (2018)
- [Simulating Continuum Mechanics with Multi-Scale Graph Neural Networks](https://mlsanity.com/paper/2106.04900/) (2021)
- [Reconstruction of three-dimensional porous media using generative adversarial neural networks](https://mlsanity.com/paper/1704.03225/) (2017)
- [Coarse-scale PDEs from fine-scale observations via machine learning](https://mlsanity.com/paper/1909.05707/) (2019)
- [Mutual Information, Neural Networks and the Renormalization Group](https://mlsanity.com/paper/1704.06279/) (2017)
- [A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials](https://mlsanity.com/paper/1807.09829/) (2018)
- [Coarse-Graining Auto-Encoders for Molecular Dynamics](https://mlsanity.com/paper/1812.02706/) (2018)
- [Variational Encoding of Complex Dynamics](https://mlsanity.com/paper/1711.08576/) (2017)
- [Meta-modeling game for deriving theoretical-consistent, micro-structural-based traction-separation laws via deep reinforcement learning](https://mlsanity.com/paper/1810.10535/) (2018)
- [Revealing hidden dynamics from time-series data by ODENet](https://mlsanity.com/paper/2005.04849/) (2020)
- [Deep learning of contagion dynamics on complex networks](https://mlsanity.com/paper/2006.05410/) (2020)
- [Exploring the 3D architectures of deep material network in data-driven multiscale mechanics](https://mlsanity.com/paper/1901.04832/) (2019)
- [On-the-fly construction of surrogate constitutive models for concurrent multiscale mechanical analysis through probabilistic machine learning](https://mlsanity.com/paper/2007.07749/) (2020)
- [GINNs: Graph-Informed Neural Networks for Multiscale Physics](https://mlsanity.com/paper/2006.14807/) (2020)
- [Noise-injected analog Ising machines enable ultrafast statistical sampling and machine learning](https://mlsanity.com/paper/2112.11534/) (2021)
- [Towards Fast Simulation of Environmental Fluid Mechanics with Multi-Scale Graph Neural Networks](https://mlsanity.com/paper/2205.02637/) (2022)
- [Sparse Identification of Slow Timescale Dynamics](https://mlsanity.com/paper/2006.00940/) (2020)

## Built on by (most cited first, 5 of 5)

- [Artificial Intelligence in Materials Science and Engineering: Current Landscape, Key Challenges, and Future Trajectorie](https://mlsanity.com/paper/2601.12554/) (2026)
- [TDNetGen: Empowering Complex Network Resilience Prediction with Generative Augmentation of Topology and Dynamics](https://mlsanity.com/paper/2408.09825/) (2024)
- [Application of Reduced-Order Models for Temporal Multiscale Representations in the Prediction of Dynamical Systems](https://mlsanity.com/paper/2510.18925/) (2025)
- [Predicting the Energy Landscape of Stochastic Dynamical System via Physics-informed Self-supervised Learning](https://mlsanity.com/paper/2502.16828/) (2025)
- [HPC-AI Coupling Methodology for Scientific Applications](https://mlsanity.com/paper/2507.01025/) (2025)

## Abstract (arXiv)

Complex system simulation has been playing an irreplaceable role in understanding, predicting, and controlling diverse complex systems. In the past few decades, the multi-scale simulation technique has drawn increasing attention for its remarkable ability to overcome the challenges of complex system simulation with unknown mechanisms and expensive computational costs. In this survey, we will systematically review the literature on multi-scale simulation of complex systems from the perspective of knowledge and data. Firstly, we will present background knowledge about simulating complex system simulation and the scales in complex systems. Then, we divide the main objectives of multi-scale modeling and simulation into five categories by considering scenarios with clear scale and scenarios with unclear scale, respectively. After summarizing the general methods for multi-scale simulation based on the clues of knowledge and data, we introduce the adopted methods to achieve different objectives. Finally, we introduce the applications of multi-scale simulation in typical matter systems and social systems.