**Hosts:** Prof. Dr. R. Klein (FU), Prof. Dr. R. Kornhuber (FU), Prof. Dr. C. Schütte (FU/ZIB)

**Location:** Freie Universität Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin-Dahlem, Room: 032 ground floor

**Time:** The seminar takes place on Thursday at 4:00 pm

## Thursday, 26.04.2018: Colloquium

### Hao Wu, Freie Universität Berlin

"What is .. variational approach for Markov processes (VAMP)?"

Inference, prediction and control of complex dynamical systems from time series is important in many areas, including financial markets, power grid management, climate and weather modeling, or molecular dynamics. The analysis of such highly nonlinear dynamical systems is facilitated by the fact that we can often find a (generally nonlinear) transformation of the system coordinates to features in which the dynamics can be excellently approximated by a linear Markovian model. Moreover, the large number of system variables often change collectively on large time- and length-scales, facilitating a low-dimensional analysis in feature space. In this talk, we introduce a variational approach for Markov processes (VAMP) that allows us to find optimal feature mappings and optimal Markovian models of the dynamics from given time series data. The key insight is that the best linear model can be obtained from the top singular components of the Koopman operator. This leads to the definition of a family of score functions called VAMP-r which can be calculated from data, and can be employed to optimize a Markovian model. In addition, based on the relationship between the variational scores and approximation errors of Koopman operators, we propose a new VAMP-E score, which can be applied to cross-validation for hyper-parameter optimization and model selection in VAMP. VAMP is valid for both reversible and nonreversible processes and for stationary and non-stationary processes or realizations.

## Thursday, 24.05.2018: Lecture

### Samir Kanaan, Universitat Politécnica de Catalunya

Multiview data: what, why, and how

Most pattern recognition methods are designed to process data inputs from a single source. Therefore, they are not well equipped to deal with data inputs from several, possibly heterogeneous sources. However, in real life applications it is often the case that there are several sources available. In the classical data processing pipeline there are two options: to stack all the data together, with potential data coherence problems, or to discard some of the data sources. None of these options extracts the full potential of the data available. Multiview pattern recognition methods are designed to tackle with such multiple source datasets, processing each data source as a independent input while merging all the relevant information into a single result. This talk is an introduction to multiview data, possible multiview aspects and applications, and the associated multiview pattern recognition methods in the state of the art, as well as the differences between the classical, single-view data processing pipeline and a multiview data processing pipeline.

## Thursday, 07.06.2018: Lecture

### Christian Kühn, TU München

A Tour through Multiple Time Scale Systems

In this talk, I am going to start with an introduction to the theory and applications of multiple time scale dynamical systems. These systems appear in a wide variety of contexts in the natural sciences and engineering whenever coupled processes on different scales occur. The mathematical analysis for deterministic fast-slow ordinary differential equations is, by now, quite well-developed and I shall introduce the main concepts of slow manifold, asymptotics, geometric desingularization, and exchange lemma. In the second part of the talk, I am going to explain several recent extensions to stochastic fast-slow systems such as stochastic bifurcations for SODEs and patterns for SPDEs. I am going to conclude with a brief outlook on current frontiers in the area.

## Thursday, 21.06.2018: Colloquium

### Wei Zhang, Freie Universität Berlin

"What is .. Jarzynski equality for non-equilibrium stochastic processes?"

Jarzynski equality is an identity in non-equilibrium statistical physics. It relates the free energy of two states and the work that is done in order to drive the system from one state to the other. Since its discovery in 1997, generalization and application of Jarzynski equality has been an increasingly interesting research topic in literature. In this talk, I will briefly explain this equality and discuss issues when it is used in free energy calculation.

## Thursday, 28.06.2018: Lecture - abgesagt -

### Oliver Junge, TU München

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories

Transport and mixing properties of aperiodic flows are crucial to a dynamical analysis of the flow, and often have to be carried out with limited information. Finite-time coherent sets are regions of the flow that minimally mix with the remainder of the flow domain over the finite period of time considered. In the purely advective setting this is equivalent to identifying sets whose boundary interfaces remain small throughout their finite-time evolution. Finite-time coherent sets thus provide a skeleton of distinct regions around which more turbulent flow occurs. They manifest in geophysical systems in the forms of e.g. ocean eddies, ocean gyres, and atmospheric vortices. In real-world settings, often observational data is scattered and sparse, which makes the difficult problem of coherent set identification and tracking even more challenging. We develop three FEM-based numerical methods to rapidly and reliably extract finite-time coherent sets from models or scattered, possibly sparse, and possibly incomplete observed data.

## Thursday, 28.06.2018: Lecture

### Davide Faranda, LSCE (Laboratoire des Sciences du Climat et de l’Environnement),

CNRS, Paris-Saclay

Computation and characterisation of local subfilter-scale energy transfer in atmospheric flows

Atmospheric motions are governed by turbulent motions associated to nontrivial energy transfers at small scales (direct cascade) and/or at large scales (inverse cascade). Although it is known that the two cascades coexist, energy fluxes have been previously investigated from the spectral point of view but not on their instantaneous spatial and local structure. Here, we compute local and instantaneous subfilter-scale energy transfers in two sets of reanalyses (NCEP–NCAR and ERA-Interim) in the troposphere and the lower stratosphere for the year 2005. The fluxes are mostly positive (toward subgrid scales) in the troposphere and negative in the stratosphere, reflecting the baroclinic and barotropic nature of the motions, respectively. The most intense positive energy fluxes are found in the troposphere and are associated with baroclinic eddies or tropical cyclones. The computation of such fluxes can be used to characterize the amount of energy lost or missing at the smallest scales in climate and weather models.

## Tuesday, 03.07.2018: Lecture

### Dimitris Giannakis, Courant Institute

Data-driven approaches for spectral decomposition of ergodic dynamical systems

We discuss techniques for approximating the spectra of Koopman operators governing the evolution of observables in ergodic dynamical systems. These methods are based on representations of Koopman operators in bases for appropriate Hilbert spaces of observables learned from time-ordered measurements of the system using kernel algorithms for machine learning. We establish spectral convergence results for the point spectrum, and present regularization approaches applicable to systems with continuous spectra. We illustrate this framework with applications to toy dynamical systems and climate data.

## Thursday, 05.07.2018: Colloquium

### Tim Sullivan, Zuse Institut Berlin

"What is .. a well-posed Bayesian inverse problem?"

Inverse problems, meaning the recovery of states or parameters in a mathematical model that match some observed data, are ubiquitous in applied sciences. They are also prime examples of ill-posed problems in the sense of Hadamard: either there is no solution in the strict sense, or there are multiple solutions, or the solution(s) depend sensitively upon the observed data and other parts of the problem specification. Regularisation of the inverse problem, whether deterministic or Bayesian, is intended to overcome these difficulties. This "What is...?" talk will outline the mathematical theory of well-posed Bayesian inverse problems for continuum quantities, exemplified by PDE-constrained inverse problems, as advanced by Andrew Stuart and collaborators over the last decade.

## Thursday, 19.07.2018: Lecture

### Jutta Rogal, Ruhr-Universität Bochum

Extended timescale simulations of atomistic processes during phase transformations in materials

Obtaining atomistic insight into the fundamental processes during phase transformations and their dynamical evolution up to experimental timescales remains one of the great challenges in materials modelling. In particular, if the mechanisms of the phase transformations are governed by so-called rare events the timescales of interest will reach far beyond the applicability of regular molecular dynamics simulations. In addition to the timescale problem the simulations provide a vast amount of data in the high-dimensional phase space. A physical interpretation of these data requires the projection into a low-dimensional space and the identification of suitable reaction coordinates.

In this presentation, I will give an overview of our recent progress in the application of advanced atomistic simulation techniques to capture the dynamical behaviour during phase transformations over a large range of timescales. One of the key results is the analysis of nucleation and growth mechanisms that can be extracted from the simulation data. By applying a likelihood maximisation scheme the quality of different reaction coordinates is evaluated which enables us to identify the most important order parameters that characterise the atomistic transformation processes.