
Centre for Human and Machine Intelligence
About Us
The Centre for Human and Machine Intelligence develops fundamental methods in artificial intelligence, machine learning, and decision science to understand how humans, algorithms, and networked systems learn, decide, adapt, and fail. We combine theoretical foundations with empirical data and responsible applications across finance, management, biology, and society.
Prof. Dr. Jan Nagler, Director of HMI
Recent publications
Predicting Physical Links in Networks
Jan Nagler and collaborators introduce InVaXMap, a physics-informed causal-inference method for reconstructing direct physical links from time-series data. The work helps distinguish causal influence from correlation or indirect association in networked systems.
Community structure-regulation coupling reveals optimal information diffusion
This work develops a theoretical and data-validated framework for understanding when information remains local, when it crosses community boundaries, and where targeted interventions can prevent large cascades at low cost.
Temporal self-similarity reveals percolation universality classes in complex networks
Published in Nature Communications, this study introduces a dynamic way to measure how complex networks lose resilience and collapse by tracking the sequence of connectivity jumps during breakdown.
Modelling the role of the microbiome in antimicrobial resistance across scales
Lucas Böttcher contributes to a Nature Microbiology Perspective on how microbiome dynamics influence antimicrobial resistance across molecular, ecological, clinical, and population scales. The paper highlights how mathematical modelling can connect biological mechanisms with intervention strategies, strengthening HMI's work at the interface of AI, machine learning, complex systems, and human health.
Recent publications
Predicting Physical Links in Networks
Jan Nagler and collaborators introduce InVaXMap, a physics-informed causal-inference method for reconstructing direct physical links from time-series data. The work helps distinguish causal influence from correlation or indirect association in networked systems.
Community structure-regulation coupling reveals optimal information diffusion
This work develops a theoretical and data-validated framework for understanding when information remains local, when it crosses community boundaries, and where targeted interventions can prevent large cascades at low cost.
Temporal self-similarity reveals percolation universality classes in complex networks
Published in Nature Communications, this study introduces a dynamic way to measure how complex networks lose resilience and collapse by tracking the sequence of connectivity jumps during breakdown.
Modelling the role of the microbiome in antimicrobial resistance across scales
Lucas Böttcher contributes to a Nature Microbiology Perspective on how microbiome dynamics influence antimicrobial resistance across molecular, ecological, clinical, and population scales. The paper highlights how mathematical modelling can connect biological mechanisms with intervention strategies, strengthening HMI's work at the interface of AI, machine learning, complex systems, and human health.
Our Members
Francesco Sangiorgi
Vahe Andonians Salmas
Sebastian Köhler
Gregory Wheeler
Christine Tiefensee
Ronald Klingebiel
Rainer Hegselmann
Lucas Böttcher
Jan Nagler
Grigory Vilkov
Scientific profile
HMI advances fundamental AI and machine learning research with a focus on causal inference, complex networks, information diffusion, robust decision-making, and the stability of data-driven systems. The centre connects mathematical and computational foundations with questions of trust, risk, and responsible deployment.
This profile is further strengthened by HMI's role in the EUR 1.7 million FAIR Data Publisher project, part of Germany's national AI and data-infrastructure agenda with academic and industry partners including DFKI, DIN, Fraunhofer, KIT, RWTH Aachen, and FIZ Karlsruhe. HMI contributes expertise in causal inference and trustworthy data use so that data infrastructures are not only reusable and interoperable, but also useful for understanding what actually causes change.
OUR CAMPUS
Selection of topics
Focus topics of:
Jan Nagler, Lucas Böttcher & Gregory Wheeler
- D'Angelo, F., Böttcher, L., 2020. Learning the Ising Model with Generative Neutral Networks, Physical Review Research Vol. 2(2), pp. 1-15.
- 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)
- Gregory Wheeler (2021). Discounting Desirable Gambles, Proceedings of Machine Learning Research 147: 331-341, 2021.
- Arthur Paul Pedersen and Gregory Wheeler (2018). Dilation and Asymmetric Relevance, Proceedings of Machine Learning Research 103: 324--326, 2019.
- Gregory Wheeler (2017). Machine Epistemology and Big Data, in Lee MacIntyre and Alex Rosenberg (Eds.), The Routledge Companion to Philosophy of Social Science, New York: Routledge, pp. 321-329, 2017.
Focus topics of:
Jan Nagler, Lucas Böttcher & Pia Domschke
- Wald, S., Böttcher, L., 2021. From classical to quantum walks with stochastic resetting on networks, Physical Review E Vol. 103(1).
- Richter, P., Henkel, M., Böttcher, L., 2020. Aging and relaxation in bistable contagion dynamics, Physical Review E Vol. 102(4).
- Böttcher, L., 2020. A Random-Line-Graph Approach to Overlapping Line Segments, Journal of Complex Networks Vol. 8, pp. 1-8.
- Böttcher, L., Antulov-Fantulin, N., 2020. Unifying continuous, discrete, and hybrid susceptible-infected-recovered processes on networks, Physical Review Research Vol. 2(3).
- Nauer, S., Böttcher, L., Porter, M., 2019. Random-Graph Models and Characterization of Granular Networks, Journal of Complex Networks Vol. 7, pp. 1-27.
- Böttcher, L., Herrmann, H., Henkel, M., 2018. Dynamical universality of the contact process, Journal of Physics A Vol. 51(12).
- Böttcher, L., Nagler, J., Herrmann, H., 2017. Critical behaviors in contagion dynamics, Physical Review Letters Vol. 118(8).
- Böttcher, L., Lukovic, M., Nagler, J., Havlin, S., Herrmann, H., 2017. Failure and recovery in dynamical networks, Scientific Reports Vol. 7.
- Fan, Meng, Liu, Saberi, Kurths, Nagler, Universal gap scaling in percolation, Nature Phys. 16: 455 (2020).
- D'Souza, R., Gómez-Gardeñes, J., Nagler, J., Arenas, A. Explosive phenomena in complex networks, Adv. in Phys. 68(3):123-223 (2019).
- Timme, M., Nagler, J. Propagation patterns unravelled, Nature Phys., Vol. 15, pp. 308-309 (2019).
- Böttcher, M. Lukovic, J. Nagler, S. Havlin, H.J. Herrmann, Failure and recovery in dynamical networks, Sci. Rep. 7: 41729 (2017).
- 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).
- Schröder, S. Chakraborty, D. Witthaut, J. Nagler, M. Timme, Interaction Control to Synchronize Non-synchronizable Networks, Sci. Rep. 6: 37142 (2016).
- Schröder, W. Chen, J. Nagler, Discrete scale invariance in supercritical percolation, New J. Phys. 18: 013042 (2016).
- D’Souza and J. Nagler, Anomalous critical and supercritical phenomena in explosive percolation, Nature Physics, 11: 531 (2015);
- Chen, M. Schröder, R. M. D'Souza, D. Sornette, J. Nagler, Micro-transition Cascades to Percolation, Phys. Rev. Lett. 112: 155701 (2014)
- Chen, X. Cheng, Z. Zheng, N.N. Chung, R.M. D'Souza, J. Nagler, Unstable supercritical discontinuous percolation transitions, Phys. Rev. E 88: 042152 (2013).
- Chen, J. Nagler, X. Cheng, X. Jin, H. Shen, Z. Zheng, and R. M. D'Souza, Phase transitions in supercritical explosive percolation, Phys. Rev. E 87: 052130 (2013).
- Schröder, H.E. Rabari, and J. Nagler, Crackling noise in fractional percolation, Nature Commun. 3: 2222 (2013)
- Nagler, T. Tiessen, H.W. Gutch, Continuous percolation with discontinuities, Phys. Rev. X 2: 031009 (2012)
- Nagler, A. Levina, M. Timme, Impact of single links in competitive percolation, Nature Physics 7: 265-270 (2011); accompanied by media coverage.
- Y.S. Cho, M.G. Mazza, B. Kahng, J. Nagler, Genuine non-self-averaging and ultra-slow convergence in gelation, Phys. Rev. E 94:022602 (2016)
- A. Saberi, S. H. Ebrahimnazhad Rahbari, H. Dashti-Naserabadi, A. Abbasi, Y. S. Cho, J. Nagler, Universality in boundary domain growth by sudden bridging, Sci. Rep. 6: 21110 (2016).
- Domschke, P., Lang, J., Strauch, E., 2021. Adaptive Single- and Multilevel Stochastic Collocation Methods for Uncertain Gas Transport in Large-Scale Networks, arXiv:2012.03565
- Domschke, P., Kolb, O., Lang, J., 2021. Fast and Reliable Transient Simulation and Continuous Optimization of Large-Scale Gas Networks. arXiv:2012.02737
- Mindt, P., Lang, J., Domschke, P., 2019. Entropy-Preserving Coupling of Hierarchical Gas Models, SIAM Journal of Mathematical Analysis Vol. 51(6), pp. 4754-4775.
- Domschke, P., Dua, A., Stolwijk, J., Lang, J., Mehrmann, V., 2018. Adaptive refinement strategies for the simulation of gas flow in networks using a model hierarchy, Electronic Transactions on Numerical Analysis Vol. 48, pp. 97-113.
- Domschke, P., Kolb, O., Lang, J., 2016. Adaptive Modelling, Simulation and Optimization of Gas and Water Supply Networks, Proceedings in Applied Mathematics and Mechanics Vol. 16(1), pp. 839-840.
- Domschke, P., Kolb, O., Lang, J., 2015. Adjoint-based error control for the simulation and optimization of gas and water supply networks, Applied Mathematics and Computation Vol. 259, pp. 1003-1018.
- Domschke, P., Kolb, O., Lang, J., 2011. Adjoint-based control of model and discretisation errors for gas flow in networks, International Journal of Mathematical Modelling and Numerical Optimisation Vol. 2(2), p. 175.
- Domschke, P., Geissler, B., Kolb, O., Lang, J., Martin, A., Morsi, A., 2011. Combination of Nonlinear and Linear Optimization of Transient Gas Networks, INFORMS Journal on Computing Vol. 23(4), pp. 493-655.
- Domschke, P., Kolb, O., Lang, J., 2010. An adaptive model switching and discretization algorithm for gas flow on networks, Procedia Computer Science Vol. 1(1), pp. 1331-1340.
- Kolb, O., Domschke, P., Lang, J., 2010. Modified QR decomposition to avoid non-uniqueness in water supply networks with extension to adjoint calculus, Procedia Computer Science Vol. 1(1), pp. 1427-1434.
- Kolb, O., Lang, J., Bales, P., Domschke, P., 2010. An implicit box scheme for subsonic compressible flow with dissipative source term, Numerical Algorithms Vol. 53(2-3), pp. 293-307.
Focus topics of:
Jan Nagler
- Schröder, M., Nagler, J., Timme, M., Witthaut, D. Hysteretic percolation from locally optimal individual decisions, Phys. Rev. Lett.120(24) (2018)
- Schröder, N.A.M. Araújo, D. Sornette, J. Nagler, Controlling percolation with limited resources, Phys. Rev. E 96: 062302 (2017).
- 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.
- Verma, N.A.M. Araujo, J. Nagler, J.S. Andrade Jr. and H.J. Herrmann, Model for the growth of the World Airline Network, Int. J. Mod. Phys. C 27(12): 1650141 (2016).
- T. Verma, F. Russmann, N.A.M Araujo, J. Nagler, H. J. Herrmann, Emergence of core-peripheries in networks, Nature Comm. 7: 10441 (2016)
Focus topics of:
Jan Nagler, Lucas Böttcher & Rainer Hegselmann
- Böttcher, L., Gersbach, H., 2020. The Great Divide: Drivers of Polarization in the US Public, EPJ Data Science Vol. 9(32), pp. 1-13.
- Böttcher, L., Montealegre, P., Goles, E., Gersbach, H., 2020. Competing activists - Political polarization, Physica A Vol. 545.
- Hoferer, M., Böttcher, L., Herrmann, H., Gersbach, H., 2020. The impact of technologies in political campaigns, Physica A Vol. 538.
- Böttcher, L., Herrmann, H., Gersbach, H., 2018. Clout, activists and budget: The road to presidency, PLoS ONE.
- Böttcher, L., Woolley-Meza, O., Brockmann, D., 2017. Temporal dynamics of online petitions, PLoS ONE Vol. 12(5).
- Böttcher, L., Araujo, N., Nagler, J., Mendes, J., Helbing, D., Herrmann, H., 2016. Gender Gap in the ERASMUS Mobility Program, PLoS ONE Vol. 11(2).
- Mani, R., Böttcher, L., Herrmann, H., Helbing, D., 2014. Extreme power law in a driven many-particle system without threshold dynamics, Physical Review E Vol. 90(4).
- 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).
- Zhu, W. Li, X. Fu, J. Nagler, How do online social networks grow? PLoS One, 9(6):e100023 (2014).
- Böttcher, N. A. M. Araújo, J. Nagler, J. F. F. Mendes, D. Helbing, H. J. Herrmann, Gender Gap in the ERASMUS Mobility Program, PLoS One 11(2):e0149514 (2016).
Focus topics of:
Ronald Klingebiel & Jan Nagler
- Klingebiel, R., Rammer, C., 2021. Optionality and selectiveness in innovation, Academy of Management Discoveries. (forthcoming) Klingebiel, R., 2018. Risk-type preference shifts in response to performance feedback, Strategic Organization Vol. 16(2), pp. 141-166.
- Klingebiel, R., Joseph, J., 2016. Entry timing and innovation strategy in feature phones, Strategic Management Journal Vol. 37(6), pp. 1002-1020.
- Klingebiel, R., Adner, R., 2015. Real options logic revisited: the performance effects of alternative resource allocation regimes, Academy of Management Journal Vol. 58(1), pp. 221-242.
- Klingebiel, R., Rammer, C., 2014. Resource allocation strategy for innovation portfolio management, Strategic Management Journal Vol. 35(2), pp. 246-268.
- Klingebiel, R., de Meyer, A., 2013. Becoming aware of the unknown: decision making during the implementation of a strategic initiative, Organization Science Vol. 24(1), pp. 133-153.
- Peter Collins, Karolina Krzyzanowska, Stephan Hartmann, Gregory Wheeler and Ulrike Hahn (2020). Conditionals and Testimony (with), Cognitive Psychology 122, November 2020, 101329.
- Gregory Wheeler (2020). Less is More for Bayesians, Too. Routledge Handbook on Bounded Rationality, Riccardo Viale (Ed.). New York: Routledge.
- Lee Elkin and Gregory Wheeler (2018). Resolving Peer Disagreements Through Imprecise Probabilities, Noûs 52(2): 260–94, 2018.
- Arthur Paul Pedersen and Gregory Wheeler (2015). Dilation, Distintegrations, and Delayed Decisions, Proceedings of the 9th International Symposium on Imprecise Probability: Theories and Applications, Pescara, Italy: 227-236, 2015.
- Arthur Paul Pedersen and Gregory Wheeler (2014). Demystifying Dilation, Erkenntnis 79(6): 1305-1342, 2014.
Focus topics of:
Jan Nagler & Lucas Böttcher
- Böttcher, L., Xia, M., Chou, T., 2020. Why case fatality ratios can be misleading: individual- and population-based mortality estimates and factors influencing them, Physical Biology Vol. 17(6), pp. 1-14.
- Xu, S., Böttcher, L., Chou, T., 2019. Diversity in Biology: definitions, quantification, and models, Physical Biology Vol. 16.
- Böttcher, L., Andrade Jr., J., Herrmann, H., 2017. Targeted Recovery as an Effective Strategy against Epidemic Spreading, Scientific Reports Vol. 7.
- Böttcher, L., Woolley-Meza, O., Goles, E., Helbing, D., Herrmann, H., 2016. Connectivity disruption sparks explosive epidemic spreading, Physical Review E Vol. 93.
- Böttcher, L., Woolley-Meza, O., Araujo, N., Herrmann, H., Helbing, D., 2015. Disease-induced resource constraints can trigger explosive epidemics, Scientific Reports Vol. 5(16571).
- Böttcher, J. Nagler, H.J. Herrmann, Critical behaviors in contagion dynamics, Phys. Rev. Lett. 118: 088301 (2017).
- D. Lamouroux, J. Nagler, T. Geisel, S. Eule, Paradoxical effects of coupling infectious livestock populations and imposing transport restrictions, Proc. R. Soc. B (London): 2015282, 20142805 (2014), accompanied with an MPI DS press release.
Focus topics of:
Pia Domschke
- Hodgkinson, A., Chaplain, M., Domschke, P., Trucu, D., 2018. Computational Approaches and Analysis for a Spatio-Structural-Temporal Invasive Carcinoma Model, Bulletin of Mathematical Biology Vol. 80(4), pp. 701-737.
- Domschke, P., Trucu, D., Gerisch, A., Chaplain, M., 2017. Structured models of cell migration incorporating molecular binding processes, Journal of Mathematical Biology Vol. 75(6-7), pp. 1517-1561.
- Domschke, P., Trucu, D., Gerisch, A., Chaplain, M., 2014. Mathematical modelling of cancer invasion: implications of cell adhesion variability for tumour infiltrative growth patterns, Journal of Theoretical Biology Vol. 361, pp. 41-60.
Focus topics of:
Jan Nagler & Gregory Wheeler
- Nagler, J., Stollmeier, F. Long-Term Behavior in Evolutionary Dynamics from Ergodicity Breaking, in: Complex Networks X: Proceedings of the 10th Conference on Complex Networks CompleNet 2019, Cham: Springer, pp. 85-95 (2019).
- Stollmeier, J. Nagler, Unfair and anomalous evolutionary dynamics from fluctuating payoffs, Phys. Rev. Lett. 120: 058101 (2018).
- Zimmer, P., Kruse, K., Nagler, J. Anomalous percolation features in molecular evolution, Phys. Rev. E Vol. 98(2) (2018)
- M.A. Böttcher, J. Nagler, Promotion of cooperation by selective group extinction, New J. Phys. 18: 063008 (2016).
- Stollmeier, T. Geisel, J. Nagler, Possible Origin of Stagnation and Variability of Earth's Biodiversity, Phys. Rev. Lett. 112: 228101 (2014)
- Lamouroux, S. Eule, T. Geisel, J. Nagler, Discriminating the effects of spatial extent and population size in cyclic competition among species, Phys. Rev. E 86: 021911 (2012).
- S. Uppaluri, J. Nagler, E. Stellamanns, N. Heddergott, S. Herminghaus, and T. Pfohl, Impact of Microscopic Motility on the Swimming Behavior of Parasites: Straighter Trypanosomes are More Directional, PLoS Comput. Biol. 7(6): e1002058 (2011)
Gregory Wheeler and Fabio Cozman (2022). On the Imprecision of Full Conditional Probabilities, Synthese, in press.Gregory Wheeler (2021). Moving Beyond Sets of Probabilities, Statistical Science 36(2): 201--204, 2021.
Conor Mayo-Wilson and Gregory Wheeler (2016). Scoring Imprecise Credences: A Mildly Immodest Proposal, Philosophy and Phenomenological Research 93(1):55-78, 2016.
Rolf Haenni, Jan-Wilem Romejn, Gregory Wheeler, and Jon Williamson (2011). Probabilistic Logics and Probabilistic Networks The Synthese Library, Springer, 2011.


