Machine learning many-body potentials for colloidal systems

Abstract

Simulations of colloidal suspensions consisting of mesoscopic particles and smaller species such as ions or depletants are computationally challenging as different length and time scales are involved. Here, we introduce a machine learning (ML) approach in which the degrees of freedom of the microscopic species are integrated out and the mesoscopic particles interact with effective many-body potentials, which we fit as a function of all colloid coordinates with a set of symmetry functions. We apply this approach to a colloid–polymer mixture. Remarkably, the ML potentials can be assumed to be effectively state-independent and can be used in direct-coexistence simulations. We show that our ML method reduces the computational cost by several orders of magnitude compared to a numerical evaluation and accurately describes the phase behavior and structure, even for state points where the effective potential is largely determined by many-body contributions.

Machine-learning effective many-body potentials for anisotropic particles using orientation-dependent symmetry functions

“…From each simulation of 1 × 10 7 MC cycles, consisting of N c attempts of rotating or translating particles, we collect 300 equilibrated, well-spaced configurations and measure V f using a numerical integration. 20,26 The resulting data set contains a total of 27, 900 representative particle configurations at different colloid densities, from which 80% are used for training and 20% for testing. Among the different thermodynamic states used for training, isotropic (I), nematic (N), smectic (Sm) and crystal (X) phases 35 , which are characterized by different degrees of orientational and positional order, are considered.…”

“…Among the different thermodynamic states used for training, isotropic (I), nematic (N), smectic (Sm) and crystal (X) phases 35 , which are characterized by different degrees of orientational and positional order, are considered. To quantify the importance of the many-body contributions to the effective potential in each of the stable phases, we calculate P(n), the probability that we find n = n(r) overlapping depletion layers at spatial coordinate r. 20,26 In Fig. 6 we show P(n) for varying packing fraction η c , including examples of I, N, Sm and X phases.…”

“…24 In the field of soft matter and colloidal systems, a ML approach based on simple linear regression has been recently employed to efficiently represent many-body interactions in spherical microgel particles in 2D 25 and to build an effective one-component interaction Hamiltonian for a mixture of colloidal hard spheres and non-adsorbing polymer. 26 In these approaches, the use of ML techniques was shown to serve as a powerful tool for speeding up by several orders of magnitude simulations that incorporate effective many-body interactions.…”

“…Here, we propose two-and three-body orientationdependent particle-centered descriptors suitable for describing local structure and constructing many-body potentials for systems composed of rod-like particles, including spherocylinders, rigid linear chains, and ellipsoids. Using a recently proposed feature selection scheme and linear regression, 25,26 we construct effective many-body potentials for model systems of colloidal hard rods and non-adsorbing polymer and for core-shell microgel rods. Furthermore, the same approach is used to represent the effective orientation-dependent two-body potential of mean force (PMF) of ligand-stabilized nanorods.…”

Diagrammatics for the Inverse Problem in Spin Systems and Simple Liquids

“…One question we wish to adress is how to choose the corresponding couplings so that the distribution generates the correct two-point correlations. Such inverse problems are of course ubiquitous in the study of complex systems from simple fluids to neurons or proteins (see for instance [1,2,3,4,5,6]). In general, making analytical progress for inverse problems requires to resort to approximation schemes.…”