Machine-learned interaction potentials for colloidal systems
Anton I. Shvetsov1, Raniya R. Nafikova1, Nikita P. Kryuchkov1, Stanislav O. Yurchenko1, Ivan V. Simkin1; 1Bauman Moscow State Technical University, Moscow, Russia
Abstract
In dense colloidal systems the interaction of a particle with its neighbors is genuinely many-body: the induced multipole moments of a particle are set by the fields of all its neighbors rather than by any single one, so the interaction within a pair is modified by everything around it. These many-body contributions grow with concentration and at short separations, and they govern the structures the system assembles into, from chains and compact clusters to ordered phases, which a pairwise description reproduces only approximately. Computing the many-body interaction directly, with boundary-element or multipole solvers, is far too slow for trajectory-scale analysis or simulation. In this work we present a machine-learning approach to predicting the interaction potential of a particle directly from the point cloud of its neighbors.
Two datasets were generated for the same configurations: a large set of pairwise-additive Lennard-Jones energies and a smaller set of many-body energies from a multipole solver, both with neighbor coordinates given relative to the central particle.
The models are permutation-invariant neural networks operating on point clouds of variable size. They combine pointwise feature extraction with global self-attention, which serves as the many-body channel, take rotation-invariant radial descriptors at the input, and aggregate neighbor features by masked pooling.
Training follows a transfer-learning scheme: pretraining on the large inexpensive dataset, then fine-tuning on the scarce many-body data. Beyond validation error, models are assessed by physical probes – recovery of the pair potential curve, forces obtained by automatic differentiation of the predicted energy, and vanishing net force in symmetric configurations.
The approach provides a fast, differentiable approximation of the many-body interaction potential, intended for molecular-dynamics studies and for the analysis of colloidal self-assembly.
The research was funded by the Russian Science Foundation (project No. 25-22-00870).
Speaker
Anton Shvetsov
Bauman Moscow State Technical University
Russia
Discussion
Ask question
