Foundations for Complex Systems Research in the Physical Sciences and Engineering Report from an

Science and engineering have long sought principles for the organization and understanding of complex systems. The impetus to study complex systems is driven both by  curiosity as exemplified in the aphorism " the whole is more than the sum of its parts " and  the need to deal with important problems of national interest such as critical infrastructure, sustainability and epidemics. Many complex systems like the power grid, transportation networks and the web demand immediate attention. They have high levels of uncertainty, lack master plans and are susceptible to breakdowns that could have catastrophic consequences. Stronger foundations for the science of complex systems are needed to mitigate these risks and manage these continually evolving systems. A deeper understanding of complex systems will also facilitate the development of controls and strategies to make systems more efficient. This report is the outcome of a workshop held at the National Science Foundation September 23-24, 2008. The Engineering and Mathematical and Physical Sciences Directorates charged us to identify " barriers " and " gaps " that impede research on complex systems. Our recommendations are our own and do not signify the endorsement of the National Science Foundation. The panel found that there are indeed gaps in our understanding of complex systems and our ability to engineer them. Specifically, general principles for engineering and analyzing complex systems are still inadequate to design and operate the complex systems in transportation, communication and power distribution that have become part of our daily lives. They are also insufficient for the scientific understanding of complex natural systems despite our ability to simulate larger and more detailed models. We highlight four questions which seem timely for increased emphasis: 1. What are the best models for studying complex systems? Simulations of highly detailed models often fail to explain emergent behaviors. Simpler models can lead to more insight. We lack good methodologies for systematically constructing models on different scales and comparing their properties. 2. How does the structure of a complex system constrain its emergent behaviors? When we engineer complex systems, we want to preclude undesirable emergent behaviors and generate or exploit desirable ones. We lack the knowledge to systematically predict these behaviors based upon system structure or design. 3. What are the consequences of evolution and adaptation in complex systems? Many complex systems were not created from a single design. Instead they have been built incrementally and modified incrementally …