# B1: Inverse problems in coarse-grained particle simulations

Coarse-graining (CG) is an indispensable tool in computational materials science, but the associated upscaling and downscaling processes have to be designed with great care. Each of these interscale transfers comes with important inverse problems to be solved, most of which are ill-posed or ill-conditioned. In this project, we apply rigorous techniques from the mathematical field of inverse and ill-posed problems to provide a mathematically rigorous foundation of existing and/or new upscaling processes. Furthermore, we develop novel CG algorithms in which one can incorporate thermodynamic constraints in a more natural way.

A generalized Newton iteration for computing the solution of the inverse Henderson problem

Inverse Problems in Science and Engineering, 1-25 (2020);
doi:10.1080/17415977.2019.1710504

A note on the uniqueness result for the inverse Henderson problem

Journal of Mathematical Physics 60 (9), 093303 (2019);
doi:10.1063/1.5112137

The inverse Henderson problem of statistical mechanics is the theoretical foundation for many bottom-up coarse-graining techniques for the numerical simulation of complex soft matter physics. This inverse problem concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles. Roughly stated, it asks for the interaction potential given the equilibrium pair correlation function of the system. In 1974 Henderson proved that this potential is uniquely determined in a canonical ensemble and he claimed the same result for the thermodynamical limit of the physical system. Here we provide a rigorous proof of a slightly more general version of the latter statement using Georgii's variant of the Gibbs variational principle.

Relative entropy indicates an ideal concentration for structure-based coarse graining of binary mixtures

Phys. Rev. E 99, 053308 (2019);
doi:10.1103/PhysRevE.99.053308

Transferability of Local Density-Assisted Implicit Solvation Models for Homogeneous Fluid Mixtures

J. Chem. Theory Comp 15, 2881-2895 (2019);
doi:10.1021/acs.jctc.8b01170

Cosolute effects on polymer hydration drive hydrophobic collapse

J. Phys. Chem. B 122, 3587-3595 (2018);
doi:10.1021/acs.jpcb.7b10780

Addressing the temperature transferability of structure based coarse graining models

Phys.Chem.Chem.Phys 20, 6617-6628 (2018);
doi:10.1039/c7cp08246k

The Hydrophobic Effect and the Role of Cosolvents

The Journal of Physical Chemistry B 121 (43), 9986-9998 (2017);
doi:10.1021/acs.jpcb.7b06453

Molecular origin of urea driven hydrophobic polymer collapse and unfolding depending on side chain chemistry

Physical Chemistry Chemical Physics 19 (28), 18156-18161 (2017);
doi:10.1039/c7cp01743j

Fréchet differentiability of molecular distribution functions I. $$L^\infty$$ L ∞ analysis

Letters in Mathematical Physics 108 (2), 285-306 (2017);
doi:10.1007/s11005-017-1009-0

Well-Posedness of the Iterative Boltzmann Inversion

Journal of Statistical Physics 170 (3), 536-553 (2017);
doi:10.1007/s10955-017-1944-2

An inverse problem in statistical mechanics

in Oberwolfach Reports, Editor: Gerhard Huisken, Chapter Report No. 08/2017, EMS, Zürich, Series: Oberwolfach Reports , Vol. 14 (2017);
doi:10.4171/OWR/2017/8

Comparison of Different TMAO Force Fields and Their Impact on the Folding Equilibrium of a Hydrophobic Polymer

The Journal of Physical Chemistry B 120 (34), 8757-8767 (2016);
doi:10.1021/acs.jpcb.6b04100

Study of Hydrophobic Clustering in Partially Sulfonated Polystyrene Solutions with a Systematic Coarse-Grained Model

Macromolecules 49 (19), 7571-7580 (2016);
doi:10.1021/acs.macromol.6b01132

Comparison of iterative inverse coarse-graining methods

The European Physical Journal Special Topics 225 (8-9), 1323-1345 (2016);
doi:10.1140/epjst/e2016-60120-1

Mechanism of Polymer Collapse in Miscible Good Solvents

The Journal of Physical Chemistry B 119 (51), 15780-15788 (2015);
doi:10.1021/acs.jpcb.5b10684

## Contact

• Prof. Dr. Martin Hanke-Bourgeois
• Institut für Mathematik
• Universität Mainz
• Staudingerweg 9
• D-55128 Mainz
• Tel: +49 6131 39 22528
• Fax: +49 6131 39 23331
• hanketTGZl@aTuIVmathematik.uni-mainz.de
• http://www.mathematik.uni-mainz.de/Members/hanke
• Prof. Dr. Nico van der Vegt
• Institut für Physikalische Chemie