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B03 - Multilevel coarse graining of multiscale problems

Head(s): Prof. Dr. Beate Koksch (FU Berlin), Prof. Dr. Roland Netz (FU Berlin), Prof. Dr. Christof Schütte (FU Berlin)
Project member(s): Cihan Ayaz, Dr. Andreas Bittracher, Laura Lavacchi
Participating institution(s): FU Berlin

Project Summary

Molecular dynamics (MD) describes the dynamical behaviour of molecular systems in atomistic resolution. In many cases of biological interest one is interested in the dynamical behaviour on long timescales related to the biological function of the molecular system under consideration. Due to the cascades of time and length scales involved, extension of MD simulations to the biologically relevant timescales is infeasible in many cases, and thus coarse graining (CG) methods are required to construct lower-dimensional and easier evaluated surrogate models. The central requirement on such reduced models is that they can reproduce the interesting long timescales of the full dynamics. We are interested in CG methods using reaction coordinates (RC) or order parameters that are observables of the system but span a low-dimensional manifold allowing the characterisation of effects on long timescales by free energies or related concepts.
In this project, we are aiming at creating an integrated, mathematically verifiable multilevel CG scheme that is applicable to high-dimensional molecular systems and accurately reproduces the effective dynamics. We will do so by building on the progress made by the projects B02 and B03 in the first funding period, expanding the individually developed methods and combining them into a joint algorithmic framework. The basis of our efforts will be the theory of transition manifolds, recently developed in project B03, that places RC-based CG approaches onto a solid mathematical footing. Its core object is the transition manifold, the “dynamical backbone” of the effective dynamics, that characterises good RCs as parametrisations of this backbone. Using this theory, we developed a CG algorithm requiring only local information about the full system, that was demonstrated to be very accurate in first applications to molecular systems with some dominant long timescales. One primary task for the coming funding period is the extension of the theory of transition manifolds to systems with cascades of scales. We expect this will lead to an adaptive multilevel method for the computation of RCs and accurate simulation of the effective dynamics. One of the achievements of project B02, on the other hand, was the formulation of generalised Langevin dynamics for arbitrary one-dimensional RCs, and the data-based estimation of the corresponding drift-, diffusion- and memory terms. Further steps towards our goal are thus the extension of this model to multi-dimensional RCs, and integration into the aforementioned multilevel approach. The performance of the resulting joint multilevel algorithm will be demonstrated in application to different realistic molecular systems.

Publications B03