Deep Dynamics Group

Welcome - Willkommen - Bienvenue - 歡迎 - Benvenuto - 반갑습니다 - Bienvenido - What's up?

I am professor in the Centre for Human and Machine Intelligence at Frankfurt School of Finance & Management and Head of the Deep Dynamics Group

Prof. Dr. Jan Nagler

Email: jan.nagler[at]gmail[dot]com

Publications Projects (see below) On Air: Podcasts


Congestion pricing

Resolving conflicts

Explosive phenomena

Universal response in games

Unfair evolutionary dynamics

Socio-economic systems design

Universality in network dynamics

Ethically aligned artificial intelligence

Decision-making in autonomous systems

Machine Learning based on fundamental principles

Selected Publications & Highlights

Nature Phys. 16: 455 (2020)

Nature Phys. 15: 308 (2019)

Nature Commun. 7:10441 (2016)

Nature Phys. 11: 531 (2015)

Nature Commun. 3: 2222 (2013)

Science 334: 1183 (2011)

Nature Phys. 7: 930 (2011)

Nature 479: 153 (2011)

Nature Phys. 7: 265 (2011)

Nature 455: 434 (2008)

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Want to join us?

You shot not only the sheriff but also the deputy?

You can't spell mainstream?

You are in love with any of the listed projects below?

You care about (pressing socio-economic networked) problems?

You want to combine machine learning with fundamental principles?

You have your own way?

Then get in contact here: jan.nagler[at]gmail[dot]com

Project: Future mobility
[network + economic sciences + machine learning]

We are living in a networked world. Almost all pressing techno-socio-economic problems of our time (mass migration, traffic jams, growing megacities, climate change, biodiversity loss, public health) are related to networks. Thus, we cannot solve the problems without attacking those from a network perspective. Building on fundamental principles from network science and machine learning (with well-chosen optimization objectives) may help to develop solutions that have appeared unfeasible for decades (Timme & Nagler, Propagation patterns unravelled, Nature Phys. 15: 308, 2019). In a number of projects, we will study the limits of optimization of ride-hailing due to hysteresis and other fundamental (network) effects. The pressing problem of congestion pricing may be even solved by a combination of fundamental principles, network science and computational methods. To demonstrate proof-of-concept and robustness, we will perform large-scale traffic ride-hailing simulations where also long-term business strategies of car fleets based on traffic forecast (similar to Waze or Uber) and congestion game theory are formulated and simulated.

Project: Universal gap scaling [network + data science]

Please find part of a press release of the most recent publication [Fan, Meng, Liu, Saberi, Kurths, Nagler, Universal gap scaling in percolation, Nature Phys. 16: 455, 2020]:

>>Jan Nagler (…) led a team of researchers to explain the emergence and collapse of large networks. Their study was published on 20 February in Nature Physics. The international research team, which also includes scientists from the Potsdam Institute for Climate Impact Research, evaluated large amounts of data and simulated the emergence and decay of various networks. In doing so, they discovered a generally applicable law that explains the largest network disruptions. For example, a perfectly functioning network of proteins in our cells generally correlates with the absence of diseases such as Alzheimer's. In a protein-protein-interaction network with thousands of proteins and known interactions, the scientists were able to show how accumulated disturbances in a few interactions affects the entire network.

"We have developed a mathematical model that describes the probability of global collapse, regardless of the details of the particular network," said Dr Jingfang Fan from the Potsdam Institute for Climate Impact Research and first author of the study. Professor Nagler adds: “Our research was helped by a concept from the financial world that quantifies extreme changes in fluctuating financial markets. We have shown that this concept also describes rapid growth or collapse of large-scale networks.”

In their interdisciplinary work, the scientists combined methods from finance, physics, biochemistry, engineering and social sciences, and were able to establish for the first time a conceptual link between small and large-scale network disruptions. In the future, the theory may help to rein in percolation with timely countermeasures - such as closing airports when an epidemic spreads.<<

The established universal framework for percolation will be used to estimate the risk of large-scale breakdowns, given only a few network snapshots. Specifically, the universality of extreme value theory applied to networks will help my group devise an early-warning method for future crises in networked socio-economic systems and ecosystems. The combination with other early-warning signals, in particular, appears promising.

Project: Homeokinesis in social networks [network + data science + machine learning + digitization]

In essence, a (social or living) system that follows a homeokinetic principle would explore the environment in order to maximize the number of choices, or options, at a given time and for the future. For example, toddlers try to learn to stand up and master upright gait due to their homeokinetic desire to be able to better explore the environment. This evolutionary program of maximization of options can ensure survival (in fluctuating environments) and the development of intelligent (social or robotic) behaviors.

Can we build social networks that could give us a different perspective on our work life balance, or provide incentives in favor for, e.g., changing our (unhealthy) life style? The implementation of homeokinetic principles could guide us to escape through bottlenecks, away from recurrent personal behavioral patterns, to places where we want to be, to behaviors which are better for us. My group will combine machine learning and network science to translate homeokinetic principles to algorithms with the objective to evolve (online) social networks in ways that reflect our long-term goals and development. Building on research in homeokinetics in robotics [Der & Martius, PNAS: 112, E6224, 2015], we will develop algorithms that suggest new online social contacts. Can we better reorganize social networks in such a way that our community follows a collective homeokinesis? Can homeokinetic principles coexist with existing myopic attention-driven maximization objectives of “Facebook & Co”? How to use Big Data? And how not to use it? An ethically aligned design of data-driven human-centered homeokinetic networked systems lies at the heart of my most ambitious long-term scientific goals

Project: Ecosystems and Climate Change [network + data science]

We showed when and how exactly environmental fluctuations can transform winning evolutionary strategies to losing ones, or vice versa (Stollmeier & Nagler, Unfair and anomalous evolutionary dynamics from fluctuating payoffs, Phys. Rev. Lett. 120: 058101, 2018). The fundamental mechanism behind this is called ergodicity breaking and can lead, e.g., to a reversal of natural selection. In complex ecosystems (Stollmeier, Geisel, Nagler, Possible Origin of Stagnation and Variability of Earth's Biodiversity, Phys. Rev. Lett. 112: 228101, 2014), both in theory and in ecological data, we will analyze the impact of ergodicity breaking on biodiversity on large and global scales. Since temperature fluctuations cause this effect, we will be able to predict the impact of temperature fluctuations from climate change on ecosystems.

In a number of collaborations, first experiments in vivo (in nematodes from La Reunion, M. Leaver) have shown that our theoretical prediction is exact. We could show that we can predict population growth from first principles, without fitting. We will develop a framework to predict biodiversity loss in networked ecological systems.

Project: Reinforcement learning based on survival [machine learning]

Current reinforcement learning schemes typically generalize insufficiently. Changes of functionally irrelevant features such as the color of objects in Atari games may render a well-trained (DQN)network originally exhibiting super-human performance a losing algorithm. In a recent paper (Thomas et al., Preventing undesirable behavior of intelligent machines, Science 366: 999, 2019), the authors study a maximization objective subject to an additional constraint. Specifically, the performance must not fall below a certain accuracy at no time. A robosurgeon, e.g., must not make a single big mistake during a surgery, otherwise it would be useless, even if the average performance would be high.

Some birds may lose more than 20% of their body weight in a single winter night, if they cannot find food. Thus, in an evolutionary setting, to survive, the reward rate must be higher than a certain threshold. On the other hand, rewards cannot always accumulate forever. Squirrels may collect a large number of nuts to survive periods of scarcity but collecting nuts may be too energy-consuming and dangerous for other reasons, e.g., foraging may expose squirrels to predators.

Human evolution may be the main driving force of the emergence and long-term maintenance of human general intelligence. Taken together, we will develop reinforcement schemes based on a non-extremal reward objective that represents survival, formalized by using a critical threshold of the reward rate – but not reward maximization. In terms of economics, we impose a utility function with a constant tail (“minus reverse ReLU”, in CS jargon). With the choice of the proper loss function (objective), we will redesign reinforcement learning such that a deep neural network representation that ensures survival in an unpredictable fluctuating environment, as typical for life on not-too-small time scales, necessarily emerges. Depending on the time-scale of the environmental changes (training data), and their predictability and magnitude (covariance), rapid activity switching between learned modular structures may emerge: a generalist who avoids overfitting through long-term survival.

Book chapters

Nagler, J., Hoven, J., Helbing, D. An Extension of Asimov´s Robotics Laws, in: Dirk Helbing (ed): Towards Digital Enlightenment, Cham: Springer, pp. 41-46 (2018).

X. Chen, J. Nagler, X. Fu, Information dissemination in social-featured opportunistic networks. In: Social Network Analysis: Interdisciplinary Approaches and Case Studies 10(15):309-342, CRC Press (2017).

K. Zhu, X. Fu, W. Li, S. Lu, J. Nagler, Population growth in online social networks. In: Social Network Analysis: Interdisciplinary Approaches and Case Studies 10(15):285-306, CRC Press (2017).

M. Timme, J. Nagler, Network Dynamics: Growth, Risk, Design and Control - Mathematical Concepts for “intelligent” self-organizing processes in Nature and Technology. In: Yearbook 2014 of the Max Planck Society.

J. Nagler, P.H. Richter, How does God play dice? In Reviews of Nonlinear Dynamics and Complexity: Volume 3 (2010),
Ed. H. G. Schuster, VCH Wiley.

Selected media coverage

Frankfurt School of Finance & Management + Potsdam Institute for Climate Impact (2020):

Editor’s suggestion for Phys. Rev. Lett. 112: 228101 (2014), available at

Various features and interviews in newspapers including Süddeutsche Zeitung, Göttinger Tageblatt, Der Standard (Austrian national daily newspaper), Laborpraxis and Harvard Gazette, available at

Permanent feature article on How random is dice tossing? In Welt der Physik (German, 2012), available at

Radio podcast by T. Pinch & M. Lane on Zipf’s law (2012), available at

Features in scientific journals:

Physics Today (cover July 3rd, 2012)

Spektrum der Wissenschaften (2012)

Nature Physics 7: 930 (2011); Science 334: 1183 (2011); Nature 479: 153 (2011)

Nature 455: 434 (2008)

German radio features including NDR Info, NDR Kultur, Radio Eins, Göttinger Stadtradio & PI Radio (2011-2012).

6 Max Planck Society / MPI DS Press Releases (2011-2015)

Wired, New Laws Explain Why Fast-Growing Networks Break (2015), available at

Online media coverage includes dradio, innovations-report, idw-online, ahano,
strategie news, extremnews, science one, scinexx,, physorg and other online services (2011-2015)

My group in the Centre for Human and Machine Intelligence
(photo outdated)

Group Members & Projects

Graduate students

Sergey Sosnovskiy [Game theory: ZD strategies, Growth Optimal Portfolio Insurance, Hierarchical (Bayesian Net) model of asset returns]

Haowei Shi [Mirror Reponse in Games, Universal Strategies]

Master students

Felix Schmid [Recommender System for Internal Project Staffing using Unsupervised and Supervised Document Embeddings]

Mattis Deisen [Optimizing Classification of Small Cloud Particles Using Neural Networks]

Ashish Kashav [Crop failure detection in sugarcane using UAV imagery]

External Bsc/MSc students (w/ M Timme, TU DD, DE)

Christoph Steinacker [Data-driven optimization of bike networks]

Jonathan Diez [Nonlinear Dynamics of Systemic CO2 Amortization of Electromobility]

Completed MSc students projects (2020)

Hao-Chien Hsueha, Wen-Hui Tinga [Timing Prediction for Future Bond Issuance with Ensemble Learning Approach]

David Duemig [Dissecting Characteristics via Machine Learning for Stock Selection]

Getting too personal: Little Literary Lumps in German