Complex systems in CEE

Hao Zhou
4 min readMar 23, 2023

Many systems in civil and environmental engineering (CEE) exhibit chaotic and unpredictable behavior under certain environmental conditions, but nevertheless, produce some sort of order at the macroscopic level. This order-from-chaos behavior is the hallmark of complexity science, which has unveiled the common framework that guides all these apparently disparate systems. Unfortunately, the main insights and lessons from complexity science have not permeated the CEE paradigm, which is falling behind in adopting successful paradigms in other areas of science and technology. This proposal is a step in this direction, where we will tackle our current inability to effectively control urban congestion.

Accordingly, this proposal has an important educational component geared towards revamping the CEE curricula, which currently does not include any relevant course in the subject (at least at Georgia Tech, but this is likely to be universal). The fact that calculus and classical statistics are no longer amenable to analyzing complex systems, where discrete fractals replace continuous functions and distributions with infinite variance replace the normal distribution, is a red flag that surfaced long ago (Wolfram1984 and Newman 2005), but one that we have not taken action on. This may, in part, explain the lower enrollment figures seen across the nation for CEE programs.

Empirical evidence from Beijing (Zeng 2020), shows that the congested network is a complex system undergoing phase transition: a large connected traffic jam breaks into several smaller clusters

Complex systems are loosely defined here as systems composed of a large number of components that interact locally with typically very simple rules. In traffic systems, this rule is simply “advance if you can’’ and yet it produces what appears to us human observers to be disorder and unpredictability.

Traffic jams grow like fractals and the distribution of jam sizes is power-law

Predicting or controlling complex systems still remains a major challenge in many domains including climate, material science, neuroscience, and engineering . One of the primary challenges of controlling complex systems is the nonlinear and often dynamic nature of the systems themselves (Ruelle 1993). Nonlinear relationships between different components can make it difficult to predict how the system will respond to changes or interventions. Additionally, complex systems often exhibit emergent behavior (Johansson 2000, Grieves 2017), which arises from the interactions between components rather than being directly caused by any one component, making them difficult to predict and control. More challenges to complex system control can arise from a variety of sources, such as incomplete information, noise, and external disturbances. This uncertainty can make it difficult to accurately model the system or to make predictions about its behavior (Smith 1999).

The tools taught in our Civil Engineering undergraduate and graduate curricula, such as calculus and classical statistics, are not up to the task of dealing with nowhere-differentiable functions such as fractals, and distributions with infinite variance, respectively. But given the ubiquity of chaotic and fractal behavior across all civil engineering disciplines, a revamp of our curricula is warranted.

“ Fractal structures Do more with Less” from D. Rayneau-Kirkhope et al., Phys. Rev. Lett. (2012)
An ancient Chinese tower was built using fractal-like structure (source: google)
Fractals in water: the world-famous painting “The Great (Water) Wave off Kanagawa”
Water: River pattern or coastline (:

Develop ``Complex Systems in CEE’’ learning modules. A series of at least three learning modules will be developed. Each module will include all the learning/assessment material needed for instructors to present the topics in one or two lectures. The topics will be:
(i) Introduction to Complex Systems in CEE,
(ii) Power law distributions and generalized central limit theorem, and
(iii) Fractal geometry.
(iv) ML for chaos prediction and control. All these learning modules will include interactive content so that students can explore the relevant concepts in a dynamic and engaging way.

Raise awareness of complex systems in CEE by giving presentations at both the undergraduate and graduate committees, with the objective of incorporating the above learning modules in the appropriate existing required courses. Notice that a brand-new course on "Complex Systems in CEE’’ would be ideal, but unfortunately, the trend in our department is to decrease the number of required undergraduate courses. In addition, a new elective course is not ideal as the title of the course might seem intimidating to undergrads, and it would compete with many other electives.