Neural force functional for non-equilibrium many-body colloidal systems
- URL: http://arxiv.org/abs/2406.03606v1
- Date: Wed, 5 Jun 2024 19:57:23 GMT
- Title: Neural force functional for non-equilibrium many-body colloidal systems
- Authors: Toni Zimmerman, Florian Sammüller, Sophie Hermann, Matthias Schmidt, Daniel de las Heras,
- Abstract summary: We combine power functional theory and machine learning to study non-equilibrium overdamped many-body systems of colloidal particles.
We first sample in steady state the one-body fields relevant for the dynamics from computer simulations of Brownian particles.
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.
- Score: 0.20971479389679337
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
Related papers
- Addressing the Non-perturbative Regime of the Quantum Anharmonic Oscillator by Physics-Informed Neural Networks [0.9374652839580183]
In quantum realm, such approach paves the way to a novel approach to solve the Schroedinger equation for non-integrable systems.
We investigate systems with real and imaginary frequency, laying the foundation for novel numerical methods to tackle problems emerging in quantum field theory.
arXiv Detail & Related papers (2024-05-22T08:34:52Z) - Performance of wave function and Green's functions based methods for non equilibrium many-body dynamics [2.028938217928823]
Non equilibrium dynamics of quantum many-body systems are studied in terms of strong driving and weak driving fields.
We show that the compressed formulation based on similarity transformed Hamiltonians is practically exact in weak fields and, hence, weakly or moderately correlated systems.
The dynamics predicted by Green's functions in the (widely popular) GW approximation are less accurate by improve significantly upon the mean-field results in the strongly driven regime.
arXiv Detail & Related papers (2024-05-14T17:59:29Z) - Real-time Dynamics of the Schwinger Model as an Open Quantum System with Neural Density Operators [1.0713888959520208]
This work develops machine learning algorithms to overcome the difficulty of approximating exact quantum states with neural network parametrisations.
As a proof of principle demonstration in a QCD-like theory, the approach is applied to solve the Lindblad master equation in the 1+1d lattice Schwinger Model as an open quantum system.
arXiv Detail & Related papers (2024-02-09T18:36:17Z) - Learning locally dominant force balances in active particle systems [1.933681537640272]
We learn locally dominant force that explain macroscopic pattern formation in self-organized active particle systems.
We investigate a classic hydrodynamic model of self-propelled particles that produces a wide variety of patterns, like asters and moving density bands.
Our method also reveals analogous physical principles of pattern formation in a system where the speed of the particle is influenced by local density.
arXiv Detail & Related papers (2023-07-27T16:06:03Z) - Machine learning in and out of equilibrium [58.88325379746631]
Our study uses a Fokker-Planck approach, adapted from statistical physics, to explore these parallels.
We focus in particular on the stationary state of the system in the long-time limit, which in conventional SGD is out of equilibrium.
We propose a new variation of Langevin dynamics (SGLD) that harnesses without replacement minibatching.
arXiv Detail & Related papers (2023-06-06T09:12:49Z) - Capturing dynamical correlations using implicit neural representations [85.66456606776552]
We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data.
In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
arXiv Detail & Related papers (2023-04-08T07:55:36Z) - Dilute neutron star matter from neural-network quantum states [58.720142291102135]
Low-density neutron matter is characterized by the formation of Cooper pairs and the onset of superfluidity.
We model this density regime by capitalizing on the expressivity of the hidden-nucleon neural-network quantum states combined with variational Monte Carlo and reconfiguration techniques.
arXiv Detail & Related papers (2022-12-08T17:55:25Z) - Learning Physical Dynamics with Subequivariant Graph Neural Networks [99.41677381754678]
Graph Neural Networks (GNNs) have become a prevailing tool for learning physical dynamics.
Physical laws abide by symmetry, which is a vital inductive bias accounting for model generalization.
Our model achieves on average over 3% enhancement in contact prediction accuracy across 8 scenarios on Physion and 2X lower rollout MSE on RigidFall.
arXiv Detail & Related papers (2022-10-13T10:00:30Z) - Spreading of a local excitation in a Quantum Hierarchical Model [62.997667081978825]
We study the dynamics of the quantum Dyson hierarchical model in its paramagnetic phase.
An initial state made by a local excitation of the paramagnetic ground state is considered.
A localization mechanism is found and the excitation remains close to its initial position at arbitrary times.
arXiv Detail & Related papers (2022-07-14T10:05:20Z) - Convex Analysis of the Mean Field Langevin Dynamics [49.66486092259375]
convergence rate analysis of the mean field Langevin dynamics is presented.
$p_q$ associated with the dynamics allows us to develop a convergence theory parallel to classical results in convex optimization.
arXiv Detail & Related papers (2022-01-25T17:13:56Z) - Approximation Bounds for Random Neural Networks and Reservoir Systems [8.143750358586072]
This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights.
In particular, this proves that echo state networks with randomly generated weights are capable of approximating a wide class of dynamical systems arbitrarily well.
arXiv Detail & Related papers (2020-02-14T09:43:28Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.