Neural force functional for non-equilibrium many-body colloidal systems
arxiv(2024)
摘要
We combine power functional theory and machine learning to study
non-equilibrium overdamped many-body systems of colloidal particles at the
level of one-body fields. We first sample in steady state the one-body fields
relevant for the dynamics from computer simulations of Brownian particles under
the influence of randomly generated external fields. A neural network is then
trained with this data to represent locally in space the formally exact
functional mapping from the one-body density and velocity profiles to the
one-body internal force field. The trained network is used to analyse the
non-equilibrium superadiabatic force field and the transport coefficients such
as shear and bulk viscosities. Due to the local learning approach, the network
can be applied to systems much larger than the original simulation box in which
the one-body fields are sampled. Complemented with the exact non-equilibrium
one-body force balance equation and a continuity equation, the network yields
viable predictions of the dynamics in time-dependent situations. Even though
training is based on steady states only, the predicted dynamics is in good
agreement with simulation results. A neural dynamical density functional theory
can be straightforwardly implemented as a limiting case in which the internal
force field is that of an equilibrium system. The framework is general and
directly applicable to other many-body systems of interacting particles
following Brownian dynamics.
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