Editorial: Multiscale simulation methods for soft matter systems

Schmid, Friederike

doi:10.1088/1361-648x/ac5071

Cited by 6 publications

(6 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The density profile is resolved over a system size of 1 mm with nanometric precision on a numerical grid with 10 nm spacing. Such 'simulation beyond the box' is both powerful in terms of multiscale description of soft matter [74][75][76], but is also serves as template for the more general situation of using artificial intelligence methods far outside their original training realm.…”

Section: Neural Functional Conceptsmentioning

confidence: 99%

“…Thereby the training is only required for a single neural network, from which then all further neural functionals are created in straightforward ways. The method allows for multi-scale application [41] as is pertinent for many areas of soft matter [74][75][76]. It is furthermore applicable to general interactions, as exemplified by successfully addressing a supercritical Lennard-Jones fluid [41], thus complementing analytical efforts to construct density functional approximations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Why neural functionals suit statistical mechanics

Sammüller,

Hermann,

Schmidt

2024

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

We describe recent progress in the statistical mechanical description of many-body systems via machine learning combined with concepts from density functional theory and many-body simulations. We argue that the neural functional theory by Sammüller et al. [Proc. Natl. Acad. Sci. 120, e2312484120 (2023)] gives a functional representation of direct correlations and of thermodynamics that allows for thorough quality control and consistency checking of the involved methods of artiﬁcial intelligence. Addressing a prototypical system we here present a pedagogical application to hard core particle in one spatial dimension, where Percus’ exact solution for the free energy functional provides an unambiguous reference. A corresponding standalone numerical tutorial that demonstrates the neural functional concepts together with the underlying fundamentals of Monte Carlo simulations, classical density functional theory, machine learning, and diﬀerential programming is available online at https://github.com/sfalmo/NeuralDFT-Tutorial.

show abstract

Section: Neural Functional Conceptsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Why neural functionals suit statistical mechanics

Sammüller,

Hermann,

Schmidt

2024

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

“…In the terminology of multiscale simulation methods for soft matter systems [155], in our method we learn the characteristics of a fine-grained model (chosen as the LJ fluid in the present model study) and, while not strictly obtaining a coarse-grained model, are able to reduce the fine-grained information systematically to the one-body level in a microscopically resolved way. It would be interesting to see whether our approach is useful in the context of adaptive simulation techniques [156][157][158] as applied e.g.…”

Section: Implications and Related Workmentioning

confidence: 99%

Perspective: How to overcome dynamical density functional theory

Heras

Zimmermann

Sammüller

et al. 2023

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

We argue in favour of developing a comprehensive dynamical theory for rationalizing, predicting, designing, and machine learning nonequilibrium phenomena that occur in soft matter. To give guidance for navigating the theoretical and practical challenges that lie ahead, we discuss and exemplify the limitations of dynamical density functional theory. Instead of the implied adiabatic sequence of equilibrium states that this approach provides as a makeshift for the true time evolution, we posit that the pending theoretical tasks lie in developing a systematic understanding of the dynamical functional relationships that govern the genuine nonequilibrium physics. While static density functional theory gives a comprehensive account of the equilibrium properties of many-body systems, we argue that power functional theory is the only present contender to shed similar insights into nonequilibrium dynamics, including the recognition and implementation of exact sum rules that result from the Noether theorem. As~a~demonstration of the power functional point of view, we consider an idealized steady sedimentation flow of the three-dimensional Lennard-Jones fluid and machine-learn the kinematic map from the mean motion to the internal force field. The trained model is capable of both predicting and designing the steady state dynamics universally for various target density modulations. This demonstrates the significant potential of using such techniques in nonequilibrium many-body physics and overcomes both the conceptual constraints of dynamical density functional theory as well as the limited availability of its analytical functional approximations.

show abstract

“…This is particularly true for soft matter, where spatial scales may bridge from the electron scale up to the millimeter scale of biomaterials or polymers. Concerning examples we refer to the excellent survey by Noid [31], the collected volume edited by Monticelli and Salonen [28], or the recent special issue [40] of Journal of Physics: Condensed Matter.…”

Section: Introductionmentioning

confidence: 99%

A variational framework for the inverse Henderson problem of statistical mechanics

Frommer

Hanke

2022

Lett Math Phys

View full text Add to dashboard Cite

The inverse Henderson problem refers to the determination of the pair potential which specifies the interactions in an ensemble of classical particles in continuous space, given the density and the equilibrium pair correlation function of these particles as data. For a canonical ensemble in a bounded domain, it has been observed that this pair potential minimizes a corresponding convex relative entropy functional, and that the Newton iteration for minimizing this functional coincides with the so-called inverse Monte Carlo (IMC) iterative scheme. In this paper, we show that in the thermodynamic limit analogous connections exist between the specific relative entropy introduced by Georgii and Zessin and a proper formulation of the IMC iteration in the full space. This provides a rigorous variational framework for the inverse Henderson problem, valid within a large class of pair potentials, including, for example, Lennard-Jones-type potentials. It is further shown that the pressure is strictly convex as a function of the pair potential and the chemical potential, and that the specific relative entropy at fixed density is a strictly convex function of the pair potential. At a given reference potential and a corresponding density in the gas phase, we determine the gradient and the Hessian of the specific relative entropy, and we prove that the Hessian extends to a symmetric positive semidefinite quadratic functional in the space of square integrable perturbations of this potential.

show abstract

Editorial: Multiscale simulation methods for soft matter systems

Cited by 6 publications

References 28 publications

Why neural functionals suit statistical mechanics

Why neural functionals suit statistical mechanics

Perspective: How to overcome dynamical density functional theory

A variational framework for the inverse Henderson problem of statistical mechanics

Contact Info

Product

Resources

About