Einstein Visiting Fellows

The Einstein Foundation Berlin funds several Fellowships to enhance the international profile of universities and research institutions in Berlin by involving leading scientists and scholars from abroad in long-term academic research collaborations. The CRC 1114 is glad to welcome the following Einstein Visiting Fellows at Freie Universität Berlin:

Prof. Dr. Edriss Titi
Texas A&M University, U.S.A.
The Weizmann Institute of Science, Israel
January 1st, 2018, to December 31st, 2020

Edriss Titi is an internationally renowned expert for applied mathematics with broad interests in nonlinear science and scientific computation who specializes in the mathematical study of problems from fluid dynamics, nonlinear partial differential equations, and in a dynamical systems approach to turbulence. His contributions to these areas are of the highest calibre and practical impact. During his stay in Germany, Professor Titi will focus on theoretical and practical advances in the understanding and simulation of atmosphere and ocean dynamics. As an Einstein Visiting Fellow Edriss Titi will be part of the collaborative research centre “Scaling Cascades in Complex Systems“ (CRC 1114) at Freie Universität Berlin.
For more Information see: Webpage of Einstein Foundation

Prof. Ioannis Kevrekidis
John Hopkins University, U.S.A.
Princeton University, U.S.A.
April 1st, 2016, to March 31st, 2018

Ioannis Kevrekidis is an Einstein Visiting Fellow with CRC 1114. With the help of computational methods and machine learning he is striving to achieve a new modeling approach of complex systems. Therefore, he combines methods of mathematics and scientific computing with modern data mining-technics. He closely cooperates with Project B03 and young investigator Stefan Klus. During his stay as Einstein Visiting Fellow Prof. Kevrekidis was a special guest lecturer in the CRC’s 2016 PhD Workshop.
For more Information see: Webpage of Einstein Foundation

 

Mercator Fellow - 1st funding phase (2014 - 2018)

IlliaHorenko avatar 

Prof. Dr. Illia Horenko

 

Home University:

Institute of Computational Science
Faculty of Informatics

Via Giuseppe Buffi 13
6900 Lugano
Switzerland

+41 58 666 4123

illia.horenko-at-usi.ch

 

 

 

 

A central scientific issue in our work programme, which recurs in several of the individual projects, is the unbiased characterization of observation, measurement, and simulation data. Over the past several years, Prof. Horenko has developed non-parametric, non-stationary, non-homogeneous data analysis techniques which, in our view, belong to the most advanced methodologies in this field. Moreover, besides having introduced some fundamentally new techniques, he has also tested them against and applied them to real-life data from a range of application areas that are part of the CRC 1114, such as Meteorology and Bio-Informatics, with related publications in high-ranking journals. He has already accounted for the challenges that arise from the shear amount of data that have to be processed in real-life applications to obtain robust and credible results, and his group has generated high-performance ready implementations of these data analysis algorithms.

Prof. Horenko's FEM-BV family of time series analysis techniques allows for systematic time dependent model identification when assumptions of stationarity or homogeneity of some underlying statistics are not justifiable. Finite Element Methods are employed in the numerical representation of indicator functions for the space-time domains of applicability of different models from a common model class. These indicators are regularized using a Bounded Variation constraint, hence the acronym FEM-BV. The choice of the model class from which to select the individual models in each of the regimes depends on the type of data considered. Implemented versions include Vector Auto-Regressiv models with eXternal influences (VARX) with finite memory depth, K-means for geometric clustering of continuous data, Empirical Orthogonal Function (EOF) decompositions for model reduction of continuous data in high-dimensional vector spaces, Markov/Bernoulli models for discrete (categorical) data, and Generalized Extreme-Value distributions (GEV) for regression analysis with emphasis on extreme event characteristics.

The number of different spatio-temporal regimes, the model parameters to be chosen within these regimes, such as memory depth and number of EOFs, and the indicator functions signalling activation of the respective models are all determined simultaneously in a global optimization procedure. This yields a judicious compromise between low residuals in reproducing the data of a training set on the one hand, and the demand for the smallest-possible overall number of free parameters of the complete model on the other. The optimization is based on a new non-parametric modified Akaike Information Criterion (mAIC) and may be interpreted as a constructive implementation of ``Occam's Razor''. By addressing directly a scalar model error functional to characterize the model-data-distance, the optimization problem remains solvable in high dimensions. Versions of this methodology have been applied successfully to a variety of data from different application areas.

 Project cooperations with the Mercator Fellow:

  • Within Project A01, an appropriate version of these techniques will serve as an independent, data-based method for optimizing hierarchical multi-scale stochastic precipitation models, and for the quantitative data-based evaluation of the project's hypotheses and theoretical derivations.
  • In most recent work, the model identification procedures have been generalized for successive incorporation of new data as they become available in the course of time. This extension is based on Bayesian learning ideas and complements the framework of the Data Assimilation project A02. Here, Prof. Horenko's techniques could be used to represent and assimilate the influences of possible non-observed external influences, which materialize in the FEM-BV family of models as regime changes in the identified FEM-BV indicator functions.
  • Project B01 will generate a wealth of three-dimensional displacement fields from laboratory ``earthquakes''. The FEM-BV-VARX techniques, in combination with model reduction in terms of spatial patterns, e.g., through EOF-decompositions, will allow for a detailed characterization of these data that goes considerably beyond what is currently available in this laboratory setting. At the same time, this methodology will be provide insights into connections between the measured three-dimensional fields and displacements measured at the surface. This is important as only surface displacements can directly be measured out in the field. The three-dimensional displacements under an observed surface are ``non-observed degrees of freedom'' in the sense of the FEM-BV technology, and their influence is reflected in potential model regime changes. In conjunction with the three-dimensional laboratory measurements, there is a unique opportunity to establish a direct, quantifiable connection between such three- dimensional processes and the surface displacements.
  • Project B04 investigates the compact representation of complex data using tensor-product decompositions, considering direct numerical simulations of turbulent flows and experimental as well as simulation data from project B01 (see above). There are two routes of fruitful developments in conjunction with Prof. Horenko's data analysis techniques in this project. The first route simply consists in a mutual benchmarking of the data compression capability of the tensor product decompositions with what is achievable using Prof. Horenko's EOF-based multiple-regime representations. The second route of development involves extending the data analysis technology by incorporating tensor product representations in the data representation ansatz. Tensor product decompositions could replace the EOF-based decompositions in cases where the data reveal scale self-similarities.
  • Prof. Horenko will also guide the data-based development of triggering mechanisms for unstable updraftes in Project C06.

 

Project publications (Mercator Fellow)

Gerber, S. and Olsson, S. and Noé, F. and Horenko, I. (2018) A scalable approach to the computation of invariant measures for high-dimensional Markovian systems. Sci. Rep., 8 (1796). ISSN 2045-2322

Pospisil, L. and Gagliardini, P. and Sawyer, W. and Horenko, I. (2017) On a scalable nonparametric denoising of time series signals. Communications in Applied Mathematics and Computational Science . pp. 1-28. (In Press)

Gerber, S. and Horenko, I. (2017) Toward a direct and scalable identification of reduced models for categorical processes. Proceedings of the National Academy of Sciences, 114 (19). pp. 4863-4868.

O'Kane, T.J. and Monselesan, D.P. and Risbey, J.S. and Horenko, I. and Franzke, Ch.L.E. (2017) On memory, dimension, and atmospheric teleconnection patterns. Math. Clim. Weather Forecast, 3 (1). pp. 1-27.

Horenko, I. and Gerber, S. and O'Kane, T.J. and Risbey, J.S. and Monselesan, D.P. (2017) On inference and validation of causality relations in climate teleconnections. In: Nonlinear and Stochastic Climate Dynamics. Cambridge University Press, pp. 184-208. ISBN 9781107118140

Horenko, I. and Gerber, S. (2015) Improving clustering by imposing network information. Science Advances, 1 (7). ISSN 2375-2548

O’Kane, T.J. and Risbey, J.S. and Monselesan, D.P. and Horenko, I. and Franzke, Ch.L.E. (2015) On the dynamics of persistent states and their secular trends in the waveguides of the Southern Hemisphere troposphere. Climate Dynamics . ISSN Print: 0930-7575, Online: 1432-0894

Mercator Fellow

Link to Mercator Fellow - 1st funding phase (2014 - 2018)

IlliaHorenko avatar  
Prof. Dr. Illia Horenko

 

Home University:
L’Università della Svizzera italiana (USI)
Institute of Computational Science
Faculty of Informatics

Via Giuseppe Buffi 13
6900 Lugano
Switzerland

+41 58 666 4123
illia.horenko-at-usi.ch

 

A central scientific issue in the work programme of CRC1114 recurring in several of the individual projects is the unbiased characterization of observation, measurement, and simulation data in multiscale systems. The size of the data emerging in the CRC’s application domains, e.g., in molecular dynamics and the geosciences, together with the multiscale character of the underlying systems necessitate not only the deployment of High-Performance-ready data analysis tools, but also call for overcoming the usual parametric assumptions of common statistical tools, such as stationarity, Gaussianity or linearity.

The Mercator Fellow will offer his expertise and experience with multiscale data analysis problems in the natural sciences accumulated by him and his group at USI Lugano; he will contribute with a direct possibility to use Europe’s most powerful supercomputer “Piz Daint” (place 3 in the TOP 500) at CSCS Lugano for data analysis problems in CRC1114; and he will provide access to and user advice for the high-performance multiscale data analysis methods developed in recent years under his guidance. The latter include a Finite Element Framework for nonparametric denoising and nonstationary model inference, that are scalable to be used even on emerging supercomputing architectures involving Graphical Processing Units. The role of the Mercator Fellow in the CRC is thus twofold: He will (i) support the individual projects in addressing questions related to the analysis of multiscale data, and (ii) develop new multiscale data analysis tools and software applications, motivated by the problems and questions emerging in CRC.

 

Project publications (Mercator Fellow)

Gerber, S. and Olsson, S. and Noé, F. and Horenko, I. (2018) A scalable approach to the computation of invariant measures for high-dimensional Markovian systems. Sci. Rep., 8 (1796). ISSN 2045-2322

Pospisil, L. and Gagliardini, P. and Sawyer, W. and Horenko, I. (2017) On a scalable nonparametric denoising of time series signals. Communications in Applied Mathematics and Computational Science . pp. 1-28. (In Press)

Gerber, S. and Horenko, I. (2017) Toward a direct and scalable identification of reduced models for categorical processes. Proceedings of the National Academy of Sciences, 114 (19). pp. 4863-4868.

O'Kane, T.J. and Monselesan, D.P. and Risbey, J.S. and Horenko, I. and Franzke, Ch.L.E. (2017) On memory, dimension, and atmospheric teleconnection patterns. Math. Clim. Weather Forecast, 3 (1). pp. 1-27.

Horenko, I. and Gerber, S. and O'Kane, T.J. and Risbey, J.S. and Monselesan, D.P. (2017) On inference and validation of causality relations in climate teleconnections. In: Nonlinear and Stochastic Climate Dynamics. Cambridge University Press, pp. 184-208. ISBN 9781107118140

Horenko, I. and Gerber, S. (2015) Improving clustering by imposing network information. Science Advances, 1 (7). ISSN 2375-2548

O’Kane, T.J. and Risbey, J.S. and Monselesan, D.P. and Horenko, I. and Franzke, Ch.L.E. (2015) On the dynamics of persistent states and their secular trends in the waveguides of the Southern Hemisphere troposphere. Climate Dynamics . ISSN Print: 0930-7575, Online: 1432-0894

Research Areas - 1st funding phase (2014 - 2018)

The design of this CRC’s Research Areas is guided by structural similarities in the application problems we intend to investigate. The individual research areas address three structurally different problem classes.

 

Research Area A: Efficient modelling of macro scales

We aim to predict large-scale/longtime features of the considered processes accurately, while accounting for smaller space and shorter time scales only to the extent necessary to achieve this goal. This entails, e.g., a progressive shift to probabilistic, averaged, or – more generally – set-based reduced representations at the smaller scales.

Projects
A01 - Coupling a multiscale stochastic precipitation model to large scale atmospheric flow dynamics (Ulbrich, Névir, Rust)
A02 - Multiscale data and asymptotic model assimilation for atmospheric flows (Reich, Klein)
A04 - Efficient calculation of slow and stationary scales in molecular dynamics (Noé, Weikl)
A05 - Probing scales in equilibrated systems by optimal nonequilibrium forcing (Schütte, Hartmann, Weber)
A06 - Enabling Bayesian uncertainty quantification for multiscale systems and network models via mutual likelihood-informed dimension reduction (Sullivan)

Research Area B: Uniform meso scale behavior in scaling cascades

We consider processes involving a discrete or continuous range of scales all of which contribute collectively to the processes’ target features. Scale interactions are structurally similar across at least part of the scale range so that asymmetric representations of the larger and smaller scales, as in Research Area A, are not an option.

Projects
B01 - Fault networks and scaling properties of deformation accumulation (Kornhuber, Oncken, Rosenau, Mielke)
B02 - Polymer dynamic theories, Markov state models and protein folding free energy landscapes (Netz, Noe)
B03 - Multilevel coarse graining of multiscale problems (Schütte, Kornhuber, Koksch)
B04 - Multiscale tensor decomposition methods for partial differential equations (Klein, Schneider, Yserentant)
B05 - Origin of the scaling cascades in protein dynamics (Keller, Hartmann, Imhof, Heyne)

Research Area C: Bridging the micro-macro scale range

We are interested in processes in which a determining part of the physics arises at the smallest scales only, and we study how the smallest and largest scales communicate across the scale range.

Projects
C01 - Adaptive coupling of scales in molecular dynamics and beyond to fluid dynamics (Delle Site, Klein)
C02 - Water diffusion at biological molecules and interfaces: Bridging stochastic and hydrodynamic descriptions (Netz)
C03 - Multiscale modelling and simulation for spatiotemporal master equations (Schütte, Noé, Höfling)
C05 - Effective models for interfaces with many scales (Mielke)
C06 - Multi-scale structure of atmospheric vortices (Klein)
C08 - Stochastic spatial coagulation particle processes (König, Patterson)

Research Area AP: Associated Projects

Projects
AP01 - Particles in lipid bilayers (Kornhuber, Hartmann, Gräser)

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