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## Frontiers of coarse graining in molecular dynamics

#### CECAM-DE-MMS

#### Organisers

## How to register

In order to register for this workshop, please send an email to **cg2018@math.fu-berlin.de**, including the following information:

- Full name
- Affiliation
- Dates of attendance
- Interest to give a
**talk**(please include a preliminary title and a short abstract) or present a**poster**

Alternatively, if you already have a CECAM account, you can send this information by clicking the "Apply" button at the top of this page.

#### Deadlines

~~If you wish to ~~**give a talk**, please register until ~~April 15 2018 ~~~~(notifications of acceptance will be sent shortly after).~~

The registration of contributed talks is now closed and the program is published online.

~~If you wish to ~~**present a poster** or to just **attend the workshop**, please register until ~~June 30 2018~~~~.~~

The registration is now closed.

## Venue information

The workshop takes place at Zuse Institute Berlin (ZIB) on the southern campus of Freie Universität Berlin.

A map of the area, information on nearby hotels and available public transport can be found here.

## Workshop topic

Coarse-graining techniques represent a systematic way to bridge the well-known time- and length-scale gap present in many macro-molecular systems. The aim is 1) to replace the full state space of the original system by a reduced state space and 2) to define a dynamical process on this reduced space, whose numerical analysis requires less computational resources. Of course, the challenge is to choose both the reduced space and process in such a way that the properties of interest—typically the dominant time scales—are retained. Over the last years, a plethora of coarse graining approaches has been developed based, for instance, on eigenfunctions of associated transfer operators, committor functions, or the characteristic properties of the molecule itself.

For many simple, yet commonly used and sufficiently realistic molecular models (stationary and in equilibrium), the so-called kinetic coarse graining has been hugely successful [12, 1]. Kinetic coarse graining effectively “collapses” continuums of atomistic states into discrete macro-states and then studies transitions between those states. However, while statistical information is preserved during this reduction, much dynamical information about the transition process is lost (e.g., the location of and dynamics on the transition pathways). Thus, there has recently been a push to construct dynamical surrogate models that retain some of this information by reducing the dynamics to a suitably chosen continuous reaction coordinate space. While this approach is not new in dynamical systems theory in general (cf. for example the Mori-Zwanzig formalism, or averaging & homogenization theory [11]), computational methods have only recently been developed.

At the same time, there have been successful attempts to extend kinetic coarse graining to systems with more general structure than the original methods were designed for. E.g., non-stationary and non-equilibrium molecular systems are now considered in coarse graining [8, 9], partially relying on analysis techniques for coherent sets in non-autonomous flows [7].

In summary, this workshop will attempt to push different current frontiers of molecular coarse graining. This can mean enriching the dynamical information content of reduced models (e.g., reaction coordinates), or considering a richer base model from the beginning by alleviating standard assumptions (like stationarity and equilibrium).

## Open problems and objectives

While there is ample theory for the construction of reduced dynamics for given reaction coordinates [10], the identification and computation of good reaction coordinates remains a hot topic. A multitude of computational methods, such as the zero and finite temperature string method [4], diffusion maps [2], ATLAS [3], transfer operator eigenfunctions [6], and committor functions [5] have been suggested, each with their own characterization of reaction coordinates and their own theoretical justification. As such, each of these methods is valid in its own domain, but there is no broad consensus about what characterizes a “good” reaction coordinate. A related issue is the question about how to validate a coarse grained model. Current methods rely solely on the comparison of the dominant time scales of the full and reduced system, but the full system’s time scales may be a) impossible to compute, and b) may not correspond to the specific property of interest. Moreover, many of these methods, especially those relying on eigenfunctions of a transfer operator, can and have only been applied to smaller systems, but do not scale to very high dimensional systems.

Due to these and other shortcomings, the aforementioned computational methods for the identification of good reaction coordinates are not used in practice by the computational molecular chemistry community. Instead, hand-picked reaction coordinates (like certain inter-atomic distances or the number of native side-chain contacts in peptides) are still state of the art. Of course, this procedure requires a lot of expert knowledge, is non-automatable, and difficult to verify rigorously.

A further shortcoming of many established methods for coarse graining is a reliance on spectral properties of self-adjoint operators. These properties fail to hold in the non-stationary and non-equilibrium regimes, which makes a new type of analysis with new conceptual tools necessary. Unlike for systems in equilibrium, a straightforward definition of a metastable set in the non-stationary, non-equilibrium case may only be given case-by-case, and therefore is not directly useful any more, in particular in cases where the slowest relaxation time scales are comparable to the time scales at which the external field driving the system varies. This is still largely an open problem with only a few recent developments.

We believe that it is about time to bring experts of the community together to discuss some of the recent conceptual developments and the remaining difficulties. The main objectives of the workshop will be to

- try to stir a discussion about the characterization of reaction coordinates and a possible unification in both terminology and objectives among methodologists
- discuss possible notions of metastability for non-equilibrium, and even non-stationary problems, and try to work out sensible generalizations of coars graining concepts, and
- promote the use of computational coarse graining methods by providing a platform for exchange between theorists and practitioners.

## References

**Germany**

Ralf Banisch (Freie Universität Berlin) - Organiser

Andreas Bittracher (Freie Universität Berlin) - Organiser

Stefan Klus (Freie Universität Berlin) - Organiser

Peter Koltai (Freie Universität Berlin) - Organiser