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Project C8: Numerical approximation of high-dimensional Fokker-Planck equations Stochastic processes driven by Brownian motion, which play a fundamental role in soft matter physics, can also be described by associated deterministic Fokker-Planck equations for probability distributions, where the dimensionality of the space on which this equation is posed increases linearly with respect to the number of particles. The aim of this project is to develop numerical solution methods for such high-dimensional problems that allow for the efficient extraction of quantities of interest, which typically take the form of certain integrals with respect to the computed distributions. In the high-dimensional case, beyond the basic numerical feasibility, a central issue is to ensure the accuracy of the computed solutions by suitable a posteriori error control. The initial focus of the project, which started during the second funding period, was on the development of numerical methods. On the one hand, we considered adaptive low-rank […]

Project B3: Coarse-graining of solvent effects in force-probe molecular dynamics simulations The study of the conformational kinetics of biomolecules and supramolecular complexes using molecular simulations often is complicated by the fact that these processes are very slow. Various simulation techniques have been developed in order to resolve this issue. One very efficient way to investigate the atomistic details of conformational changes is provided by force-probe molecular dynamics (FPMD) simulations. In the most common realization of this technique, one end of the (supra)molecular system under consideration is fixed in space and the other end is pulled apart with a constant velocity via the application of a harmonic potential. From the distributions of the forces needed to unfold the system important information regarding the kinetics and the thermodynamics of the relevant conformational rearrangements can be obtained via a statistical analysis. The direct comparison to the results of experimental realizations of force spectroscopy […]

Project B5: Multi-resolution methods including quantum chemistry, force fields, and hybrid particle-field schemes Multiscaling techniques that involve a quantum-chemical treatment of the electronic structure for the part with the highest resolution are promising computational tools. They are particularly useful for dealing with problems involving large systems like enzymes, membranes, polymers, etc., where, for example, chemical reactions take place. Having completed in the previous funding period of the TRR (i.e., the first funding period of this project) a corresponding QM/MM implementation that allows to include high-accuracy quantum-chemical methods from either coupled-cluster (CC) theory (i.e., CCSD, CCSD(T), etc.) or of multiconfigurational nature (i.e., CASSCF), we intend to complete the envisioned QM/MM/CG/hPF implementation that extends the QM/MM approach to coarse-grained (CG) treatments. In particular, we plan on using hybrid particle-field (hPF) theory based on its Hamiltonian reformulation, where the latter has been accomplished in the first funding period of this project. This reformulation […]

Project B7: Automated model building and representation learning for multiscale simulations Project B7 addresses applications of machine learning techniques to multi-scale simulation of soft-matter systems. Multi-scale methods address the problem that the complexity of high-resolution base-line models grows too quickly for problems at relevant scales. Thus, they assumed that there is a coarser-resolution structure emerging from the details that can be efficiently computed with many fewer operations but that can still inform us about relevant behavioural aspects of the system. Machine learning can help in discovering such simplified surrogate computations by fitting a restricted computational model (such as a parametrized model, a kernel regressor, or a deep feed-forward network) to example results obtained from a full-resolution simulation. Conceptually, this involves two aspects: The first is to build a coarser-grained (CG) model. Learning of a CG model can take the form of just parametrizing a force-field or a mapping procedure motivated […]

Project A3: Coarse-graining frequency-dependent phenomena and memory in colloidal systems The purpose of this project is to develop numerical strategies for dynamic coarse-graining in situations where the separation of time scales is incomplete and memory effects are important. This entails the reconstruction of coarse-grained dynamical equations that include memory (generalized Langevin equations, GLE), the efficient simulation of coarse-grained models with memory and the application to colloidal dispersions at equilibrium and non-equilibrium. This project is complementary to project A2, where related problems are addressed in the context of dynamic coarse-graining of molecular liquids. In the second funding period, we have extended our previous work on iterative memory reconstruction for single colloids (first funding period) to systems containing multiple colloids, where pair memory effects must be taken into account. A benchmark simulation of 125 colloids in solution showed that a speedup of at least three orders of magnitude can be obtained by […]

Project A4 (Completed): Understanding Water Relaxation Dynamics at Interfaces The aim of the project is to develop multiscale approaches to understand the mechanisms of vibrational energy relaxation in water at interfaces and in confined environment. In the first funding period, we have developed an efficient method to describe molecular vibrational relaxation based on single molecule excitations and the use of new descriptors. In the second funding period, we plan to include nuclear quantum effects (NQEs), which may be important in water. We aim to develop a multi resolution scheme where the electronic structure is included with an effective force field, which accurately reproduces high-level ab initio calculations, while the NQEs are explicitly addressed with the path integral formalism. This project has ended in June 2022.

Project B1: Inverse problems in coarse-grained particle simulations Coarse-graining (CG) methods are an indispensable tool in computational materials science, but the associated upscaling and downscaling processes have to be designed with great care to allow for a proper interpretation of the computed results. Each of these interscale transfers comes along with important inverse problems to be resolved, most of which are ill-posed, or ill-conditioned at the very least. The purpose of this project is to apply rigorous techniques from the mathematical field of inverse and ill-posed problems to attack these fundamental problems in the multiscale simulation of soft matter, and to provide a mathematically rigorous foundation of existing and/or new upscaling processes. n the first two funding phases we have developed the mathematical foundation for a rigorous analysis of iterative methods that are currently being used for the computation of effective pair potentials of sophisticated CG models. We have used […]

Integrated research training group (IRTG) The integrated research training group (IRTG) of the TRR 146 provides a joint structured graduate education in the area of Computational Materials Science for the graduate students and young postdocs in the TRR 146 as well as other interested candidates working in related areas. The goals of the IRTG are threefold: 1) to provide students with the interdisciplinary background required for the research activities in the TRR 146, and to prepare them for a possible career in the area of theoretical Materials Sciences 2) to ensure common standards in the education of all graduate students in the TRR 146 by means of a well structured supervision and management program, 3) to establish and strengthen links within the TRR 146 already at the level of graduate students and young postdoctoral researchers. Special emphasis is placed on promoting exchange between groups within and outside of the TRR […]

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