arXiv subjects

Jens Weimar

Publications and source records attributed to Jens Weimar.

4 recordsLinked to original sources

arXiv2026

Cubic-Equivariant Neural Density Functional Theory for Three-Dimensional Lattice Fluids

We construct a neural classical density functional that acts directly on unrestricted three-dimensional density profiles. As a computationally tractable test bed, we consider parallel hard cubes of side length three on a simple cubic lattice. A fully convolutional network learns the one-body direct-correlation functional $c^{(1)}[\rho]$ from data obtained with grand-canonical Monte Carlo simulations in randomized external potentials. Complete profiles are used during both training and inference; a stochastic Bernoulli mask on the output sites makes full-profile training effective without explicitly extracting and storing overlapping local density windows. Averaging the first-layer kernels over all 48 rotations and reflections of the cubic point group additionally imposes exact cubic equivariance without data augmentation. We compare the learned functional with independent simulation data and with the lattice fundamental-measure functional of Lafuente and Cuesta. The neural functional markedly improves the homogeneous equation of state and the density profile at a planar hard wall. For the anisotropic pair distribution around a fixed particle, both functionals reproduce the principal packing shells, with their relative accuracy depending on crystallographic direction. These results demonstrate neural density-functional calculations on complete three-dimensional profiles while also identifying accurate full-dimensional training data, thermodynamic consistency, and structural correlations as the central challenges for extensions to continuum fluids.

cond-mat.stat-mech↗

arXiv2025

Neural Density Functional Theory in Higher Dimensions with Convolutional Layers

Based on recent advancements in using machine learning for classical density functional theory for systems with one-dimensional, planar inhomogeneities, we propose a machine learning model for application in two dimensions (2D) akin to density functionals in weighted density forms, as e. g. in fundamental measure theory (FMT). We implement the model with fast convolutional layers only and apply it to a system of hard disks in fully 2D inhomogeneous situations. The model is trained on a combination of smooth and steplike external potentials in the fluid phase. Pair correlation functions from test particle geometry show very satisfactory agreement with simulations although these types of external potentials have not been included in the training. The method should be fully applicable to 3D problems, where the bottleneck at the moment appears to be in obtaining smooth enough 3D histograms as training data from simulations.

cond-mat.stat-mech↗

arXiv2024

Effective patchiness from critical points of a coarse-grained protein model with explicit shape and charge anisotropy

Colloidal model systems are successful in rationalizing emergent phenomena like aggregation, rheology and phase behaviour of protein solutions. Colloidal theory in conjunction with isotropic interaction models is often employed to estimate the stability of such solutions. In particular, a universal criterion for the reduced second virial coefficient at the critical point $B_2^*$ is frequently invoked which is based on the behavior of short-range attractive fluids (Noro-Frenkel rule, $B_2^*\approx-1.5$). However, if anisotropic models for the protein-protein interaction are considered, e.g. the Kern-Frenkel (KF) patchy particle model, the value of the $B_2^*$ criterion is shifted to lower values and explicitly depends on the number of patches. If an explicit shape anisotropy is considered, as e.g. in a coarse-grained protein model, the normalization of $B_2^*$ becomes ambiguous to some extent, as no unique exclusion volume can be defined anymore. Here, we investigate a low-resolution, coarse-grained model for the globular protein bovine serum albumin (BSA) and study effects of charge-anisotropy on the phase diagram (determined by simulations) at the isoelectric point. We present methods of assigning an ``effective patchiness'' to our protein model by comparing its critical properties to the KF model. We find that doubling the native charges increases the critical temperature $T_c$ by $\approx$ 14 % and that our BSA model can be compared to a 3 to 5 patch KF model. Finally, we argue that applying existing $B_2^*$ criteria from colloidal theory should be done with care, due to multiple, physically plausible ways of how to assign effective diameters to shape-anisotropic models.

cond-mat.soft↗

arXiv2023

Machine learning of a density functional for anisotropic patchy particles

Anisotropic patchy particles have become an archetypical statistical model system for associating fluids. Here we formulate an approach to the Kern-Frenkel model via classical density functional theory to describe the positionally and orientationally resolved equilibrium density distributions in flat wall geometries. The density functional is split into a reference part for the orientationally averaged density and an orientational part in mean-field approximation. To bring the orientational part into a kernel form suitable for machine learning techniques, an expansion into orientational invariants and the proper incorporation of single-particle symmetries is formulated. The mean-field kernel is constructed via machine learning on the basis of hard wall simulation data. Results are compared to the well-known random-phase approximation which strongly underestimates the orientational correlations close to the wall. Successes and shortcomings of the mean-field treatment of the orientational part are highlighted and perspectives are given for attaining a full density functional via machine learning.

cond-mat.stat-mech↗