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

TL;DR

This survey discusses multi-scale simulation of complex systems from the perspective of integrating knowledge and data, addressing both clear and unclear scales across matter and social domains. It introduces a five-objective framework (A–E) that guides how microscale and macroscale dynamics are modeled, coupled, discovered, and learned, with methods spanning pure knowledge-driven, pure data-driven, and data-knowledge jointly driven approaches. The paper surveys domain decomposition, multigrid, homogenization, FE/REV techniques, PINNs, DNN/ML surrogates, GNNs, RG/DMD-based scale discovery, and cross-scale coupling exemplified in molecular, biomolecular, chemical, transportation, and epidemic contexts. The work highlights open challenges—balancing computational cost and fidelity, discovering useful scales, and transferring information across scales—while proposing a generalized, iterative, data-knowledge integrated framework as a promising path forward for robust, scalable simulations with broad practical impact.

Abstract

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.

Figures (5)

• Figure 1: An illustration of simulation of complex systems, where $X(t)$ is the observable system state variables at time $t$, $C(t)$ is the controllable condition variable of the system. $\boldsymbol{X}$ and $\boldsymbol{C}$ are the set of system state variables and controllable condition variables from $t_0$ to $t$, respectively. $S(t)$ is the target variable that we want to obtain through simulation.
• Figure 2: An illustration of scales in complex systems.
• Figure 3: An illustration of objective D and objective E.
• Figure 4: Three different gas–solid two-phase flow with the same amount of solids and the same gas flow rate $U_g$. The different mesoscale structures lead to different properties of the system li1994particle.
• Figure 6: MSDNet tang2023enhancing utilizes multi-scale simulation methods to predict the spatial spread of infectious diseases on the regional scale, where microscopic features derived from microscale user contact graph are incorporated to complete macroscale mechanisms (Objective B).