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 this insight to come up with new algorithms for this purpose, which are well suited to match certain structural as well as thermodynamical quantities of interest. These methods have been implemented and explored on real physical test cases.

In the third funding phase we want to extend these algorithms to systems with different types of CG beads in bonded and nonbonded chemical environments. We further plan to reformulate the mathematical foundation and study the inverse problem as a variational problem from a relative entropy point of view. This should allow for alternative mathematical techniques to treat convergence and stability issues of established iterative schemes. With the newly available algorithms we want to derive a transferable CG model for aqueous solutions of a thermo-responsive polymer. We plan to study structural transitions at the level of single and multiple chains in relation to the macroscopic solution phase behavior in the presence of cosolvents. To bridge the gap between local structure and macroscopic phase behavior, we plan to couple the CG particle model to a fieldtheoretical description (collaboration with project C1). The workplan involves critical testing of transferability properties of the CG particle model required to predictively model macroscopic phase behavior and polymer coil-globule transitions occurring upon crossing of phase boundaries. As a second demonstration of the ad-
vances made with the methods developed in this project we plan to improve nonpolarizable force fields for strongly hydrated ions based on ab-initio MD reference ensembles obtained with multi-resolution algorithms (collaboration with project B5).

A variational framework for the inverse Henderson problem of statistical mechanics
Fabio Frommer and Martin Hanke
Letters in Mathematical Physics 112, 71, (2022)
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Where Lennard-Jones Potentials Fail: Iterative Optimization of Ion–Water Pair Potentials Based on Ab Initio Molecular Dynamics Data
Marvin P.Bernhardt, Yuki Nagata, Nico F.A. van der Vegt
The Journal of Physical Chemistry Letters. 2022, 13, 16, 3712–3717
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Coarse-grained model of a nanoscale-segregated ionic liquid for simulations of low-temperature structure and dynamics
Sebastian Kloth, Marvin P Bernhardt, Nico F A van der Vegt, Michael Vogel
Journal of Physics: Condensed Matter 33 (20), 204002 (2021)
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An interplay of excluded-volume and polymer–(co)solvent attractive interactions regulates polymer collapse in mixed solvents
Swaminath Bharadwaj, Divya Nayar, Cahit Dalgicdir, Nico F. A. van der Vegt
The Journal of Chemical Physics154 (13), 134903 (2021)
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Iterative integral equation methods for structural coarse-graining
Marvin P. Bernhardt, Martin Hanke, Nico F. A. van der Vegt
The Journal of Chemical Physics 154 (8), 084118 (2021)
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Application of the 2PT model to understanding entropy change in molecular coarse-graining
Marvin P. Bernhardt, Marco Dallavalle, Nico F. A. Van der Vegt
Soft Materials 18 (2-3), 274-289 (2020)
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A generalized Newton iteration for computing the solution of the inverse Henderson problem
Fabrice Delbary, Martin Hanke, Dmitry Ivanizki
Inverse Problems in Science and Engineering, 1-25 (2020)
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Does Preferential Adsorption Drive Cononsolvency?
Swaminath Bharadwaj, Nico F. A. van der Vegt
Macromolecules 52 (11), 4131-4138 (2019)
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A note on the uniqueness result for the inverse Henderson problem
F. Frommer, M. Hanke, S. Jansen
Journal of Mathematical Physics 60 (9), 093303 (2019)
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Relative entropy indicates an ideal concentration for structure-based coarse graining of binary mixtures
David Rosenberger and Nico F. A. van der Vegt
Physical Review E99, 053308 (2019)
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Transferability of Local Density-Assisted Implicit Solvation Models for Homogeneous Fluid Mixtures
David Rosenberger, Tanmoy Sanyal, M. Scott Shell, and Nico F. A. van der Vegt
Journal of Chemical Theory and Computation 15, 2881-2895 (2019)
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Cosolute effects on polymer hydration drive hydrophobic collapse
Divya Nayar and Nico F. A. van der Vegt
The Journal of Physical Chemistry B122, 3587-3595 (2018)
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Addressing the temperature transferability of structure based coarse graining models
David Rosenberger and Nico F. A. van der Vegt
The Journal of Physical Chemistry 20, 6617-6628 (2018)
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The Hydrophobic Effect and the Role of Cosolvents
Nico F. A. van der Vegt, Divya Nayar
The Journal of Physical Chemistry B121 (43), 9986-9998 (2017)
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Molecular origin of urea driven hydrophobic polymer collapse and unfolding depending on side chain chemistry
Divya Nayar, Angelina Folberth, Nico F. A. van der Vegt
Physical Chemistry Chemical Physics 19 (28), 18156-18161 (2017)
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Fréchet differentiability of molecular distribution functions I. L^∞ analysis
Martin Hanke
Letters in Mathematical Physics 108 (2), 285-306 (2017)
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Well-Posedness of the Iterative Boltzmann Inversion
Martin Hanke
Journal of Statistical Physics 170 (3), 536-553 (2017)
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An inverse problem in statistical mechanics
Martin Hanke
in Oberwolfach Reports, Editor: Gerhard Huisken, ChapterReport No. 08/2017, EMS, Zürich, Series:Oberwolfach Reports, Vol.14 (2017)
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Comparison of Different TMAO Force Fields and Their Impact on the Folding Equilibrium of a Hydrophobic Polymer
Francisco Rodríguez-Ropero, Philipp Rötzscher, Nico F. A. van der Vegt
The Journal of Physical Chemistry B120 (34), 8757-8767 (2016)
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Study of Hydrophobic Clustering in Partially Sulfonated Polystyrene Solutions with a Systematic Coarse-Grained Model
Ran Zhang, Nico F. A. van der Vegt
Macromolecules 49 (19), 7571-7580 (2016)
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Comparison of iterative inverse coarse-graining methods
David Rosenberger, Martin Hanke, Nico F.A. van der Vegt
The European Physical Journal Special Topics 225 (8-9), 1323-1345 (2016)
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Mechanism of Polymer Collapse in Miscible Good Solvents
Francisco Rodríguez-Ropero, Timir Hajari, Nico F. A. van der Vegt
The Journal of Physical Chemistry B119 (51), 15780-15788 (2015)
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