Revealing Dynamics and Networks from Data

“Revealing Dynamics and Networks from Data,” the project funded by TÜBİTAK under the coordination of Asst. Prof. Deniz Eroğlu from KHAS Molecular Biology and Genetics Department aims to establish pioneering methods for reconstructing the network from data using tools from the field of dynamical systems and machine learning. Once the connectivity is reconstructed, the project team predicts the sudden behavior changes that the system can undergo, thereby developing strategies to avoid malfunctioning.

“Revealing Dynamics and Networks from Data,” the project funded by TÜBİTAK under the coordination of Asst. Prof. Deniz Eroğlu from KHAS Molecular Biology and Genetics Department aims to establish pioneering methods for reconstructing the network from data using tools from the field of dynamical systems and machine learning. It will allow us to forecast the behavior of complex systems, subsequently predicting emergent behavior in such systems, which is a well-recognized and active research problem in natural sciences and engineering. Along with diverse applications of physical systems with an unknown network structure, this project seeks to develop methods for reconstructing climate and brain neural networks and predicting critical transitions.

Funded within the scope of TÜBİTAK BİDEB 2232 – International Fellowship for Early Stage and Outstanding Researchers, the project’s total budget is TRY 2.730.000. It started in October 2019 and will last for three years. The project team, coordinated by Dr. Deniz Eroğlu, includes one postdoctoral researcher, three doctoral students, a graduate student, and undergraduate students from Kadir Has University. As interdisciplinary research, the project is supported by experts’ consultancy from Imperial College London (UK), Potsdam Institute for Climate Impact Research (Germany), the University of São Paulo (Brazil), and the University of Western Australia.

PALEOCLIMATE NETWORKS. Paleoclimate records have a wealth of information that can uncover the climate dynamics for millions of years; however, their resolution is low. They are naturally irregularly sampled and hampered by highly uneven spatial distributions across the globe. Traditional techniques fail to tackle these challenges, and this proposal fills this gap by developing:

– An innovative approach to preprocessing data. This approach provides a regularly sampled cost time series from data and characterizes the dynamics using the nonlinear recurrence plot method. Tools will be employed from machine learning to define the optimization parameters.
Learning the dynamics of each access point will open the possibility to tackle the significant open problem:

– Reconstruction of paleoclimate network. Discrepancies of dynamic properties will indicate underlying driving forces of climate change. Comparison of the driving forces will allow us to reconstruct the paleoclimate network.

Understanding the dynamics and tele-connectivity of climate systems, like the Asian summer monsoon, will enable us to improve mitigation strategies against societally relevant consequences of climate change.

Reconstructing paleoclimate networks will allow us to understand forcings, triggering effects, and spreading features of climate events. Long-term predictions will be made in different pan-regional climate systems, such as the Asian monsoon. Three approaches will be followed to achieve these goals:

(i) Developing a high-pass filter by a machine learning-based metric distance to measure the difference between segments of irregularly sampled data for regularization.

(ii) After regularization, the team will embed the time series into its phase space and apply nonlinear methods to reveal the involved dynamics. The nonlinear recurrence plot method (based on Poincaré recurrences) will be used to examine the dynamical behavior of embedded time series.

(iii) Learning the dynamics of each accessible climate point will open the possibility of tackling the major problem: Differences between dynamics of each data will be an indicator of driving climate forces. By comparing pairwise similarities of the driving forces, they will be able to reconstruct the paleoclimate network.
Inferring the rules and interaction structure(s) of the targeted paleoclimate system will help inform society and policymakers to mitigate the dire and potentially irreversible consequences of climate change.

NEURAL NETWORKS. It is possible to probe high-quality data for the entire neural system, although they are more complex than paleoclimate networks. The traditional techniques are ineffectual to reconstruct the network and predict emergent behavior. This part of the project fills this gap by developing:

– A probabilistic theory for the complex network. This theory will provide a low-dimensional description over finite time scales for complex neuron dynamics. Thereby, it allows for a description of collective phenomena in terms of the network structure. A theory for emergent phenomena, such as epilepsy crisis or schizophrenia, explains how interactions affect the system and opens the possibility to address the significant problem:

– Behavior prediction in neural networks. Since the emergent properties of the network from a single time series are understood, the inverse problem can be considered, and a model from data can be obtained. Thereby, the team can predict critical transitions from data that would be impossible otherwise. Predicting the transitions may allow for precautionary measures to avert potential disasters in neurological disorders such as epilepsy.

An open major scientific challenge is developing spatiotemporal data techniques to learn the network structure, network communities and predict brain systems’ behavior. 

The proposed research aims at blending ideas and techniques from dynamical systems and machine learning to tackle the challenging and typical case of erratic network dynamics with multiple scales. This is executed in three steps:

(i) Using dynamical systems techniques to obtain essential information about local node dynamics such as its effective dimension during the node low-dimensional excursion.

(ii) Learning the evolution rule at each node by employing machine learning techniques. Changes in the rules at each node are due to the interaction. So by applying a dynamical Bayesian inference, the model for the isolated Dynamics can be obtained, the network’s statistical properties, and clustering information.

(iii) Using the obtained model to predict critical transitions using a mixture of numerical simulation and theoretical tools.

Indeed, to make predictions, the team needs to obtain the rules that govern the underlying evolution in time. Without insight into these rules, it is impossible to predict future behavior as parameters vary and critical transitions appear.