Dynamical Methods in Data-based Exploration of Complex Systems

Workshop Report

The main focus of the workshop was on inverse problems in the dynamics of complex systems: what can one say about the composition and operation of a complex dynamical system from its observations? This is a truly interdisciplinary research field with numerous applications in physics, engineering, environmental and life sciences, and in social systems. Big Data is now becoming a widely used and publicly appreciated concept for dealing with complex systems, and we experience rapid development of novel statistical approaches for the analysis of huge data sets from complex systems of different nature. However, in many applications complex systems are intrinsically nonlinear, and their complexity comes quite often not from random, noisy inputs, but from dynamical nonlinear interactions. This makes the approaches based on dynamical reconstruction of complex data sets extremely relevant. The main aspects addressed in invited and contributed presentations have been: general concepts of machine learning and data assimilation from the viewpoint of statistical physics; discovering of complex dynamical networks and partial differential equations from data; concepts of synchronization in data analysis; operator theoretic methods in network identification; applications to particular problems in engineering, neurosciences, physiology, climate research, and social sciences.

Generally, we believe that there has been a good balance between theoretical and experimental talks and that an appreciatedaspectoftheWorkshophasbeentheopportunityforeachparticipanttointeractwithmembersofdifferent communities: experimentalists, theoretical physicists, and data science specialists.

The MPIPKS Colloquium talk by Prof. Ott, one of the world-leading specialists in Nonlinear Dynamics, contributed to placing the recently developed methods of reservoir computing in a broader perspective of complex system theory. When arranging the schedule of the workshop, we allocated many oral presentations of young researchers, and these gave a very lively picture of particular developments and applications. Two poster sessions have been a place of intensive discussions. Finally, the friendly environment at the MPIPKSInstituteessentiallycontributedtofruitfuldiscussionsandhelpedtotriggernewscientificcollaborations.

The Workshop was very timely:  it has allowed a fast spreading of recent novel directions such as machine learning as well as of advances in more traditional methods across the various disciplines. Many participants have indeed expressed afinal positiveopinionthatgoesbeyondaformalcongratulation.Theimpressionofasuccessfuleventisconfirmedbythe very few cancellations.

We are grateful to DFG for the additional financial support which made possible a full support of overseas speakers.  Specialthanks gotoMPIPKS,its secretaryteamandespeciallytoMandy Lochar forher support and a very professional and efficient organization.