Analysis of complex systems has migrated from theoretical analysis of model physical systems into the domain of real-world applications with far-reaching implications. This shift has been facilitated by the availability of measurement data, the capability to store and manage large-scale datasets, and significant increase in computational power. These developments have been matched by a concerted effort in the development of new methods of complex systems analysis. Each class of analytical methods are applicable only for certain system types and specific problems, such as estimating causality between coupled complex systems, are still unresolved even for simples cases involving only two connected systems. This study summarizes results for estimating causality using a novel mathematical computational model, System Structure, across several different types of coupled systems. System structure models a system as a dynamic network of connected components and provides a distribution-free and systematic quantification of inter-component dynamics as a basis for making several system-wide inferences including the inference of strength and direction of causal relations. System structure is a non-parametric scalable method that requires few non-restrictive a-priori assumptions, making it generally applicable across a diverse set of problems. The comparative study reported on here demonstrates the ability of system structure to correctly infer different types of causality across diverse system types.

复杂系统的分析已经从模型物理系统的理论分析迁移到了具有深远意义的实际应用程序领域。测量数据的可用性，存储和管理大规模数据集的能力以及计算能力的显着提高促进了这一转变。在开发复杂系统分析的新方法的过程中，这些努力得到了共同的努力。每种分析方法仅适用于某些系统类型，并且即使对于仅涉及两个连接系统的简单情况，仍无法解决特定问题，例如估计耦合的复杂系统之间的因果关系。本研究总结了使用新型数学计算模型“系统结构”估算因果关系的结果，跨几种不同类型的耦合系统。系统结构将系统建模为连接的组件的动态网络，并提供组件间动力学的无分布和系统的量化，作为进行多个系统范围内的推断（包括强度和因果关系的方向推断）的基础。系统结构是一种非参数可伸缩方法，几乎​​不需要非限制性方法先验性假设，使其通常适用于各种问题。此处报告的比较研究证明了系统结构能够正确推断跨不同系统类型的不同因果关系的能力。