Evolutionary optimization of the Verlet closure relation for the hard-sphere and square-well fluids

• URL: http://arxiv.org/abs/2205.07104v1
• Date: Sat, 14 May 2022 18:03:31 GMT
• Title: Evolutionary optimization of the Verlet closure relation for the hard-sphere and square-well fluids
• Abstract summary: The Ornstein-Zernike equation is solved for the hard-sphere and square-well fluids. For the hard-sphere fluid, the results show good agreement when compared with mean-field equations of state. For the square-well fluid, a good agreement is observed at low and high densities.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: The Ornstein-Zernike equation is solved for the hard-sphere and square-well fluids using a diverse selection of closure relations; the attraction range of the square-well is chosen to be $\lambda=1.5.$ In particular, for both fluids we mainly focus on the solution based on a three-parameter version of the Verlet closure relation [Mol. Phys. 42, 1291-1302 (1981)]. To find the free parameters of the latter, an unconstrained optimization problem is defined as a condition of thermodynamic consistency based on the compressibility and solved using Evolutionary Algorithms. For the hard-sphere fluid, the results show good agreement when compared with mean-field equations of state and accurate computer simulation results; at high densities, i.e., close to the freezing transition, expected (small) deviations are seen. In the case of the square-well fluid, a good agreement is observed at low and high densities when compared with event-driven molecular dynamics computer simulations. For intermediate densities, the explored closure relations vary in terms of accuracy. Our findings suggest that a modification of the optimization problem to include, for example, additional thermodynamic consistency criteria could improve the results for the type of fluids here explored.

Related papers

• Neural Galerkin Normalizing Flow for Transition Probability Density Functions of Diffusion Models [0.0]
  We propose a new framework to approximate the transition probability density function of a diffusion process.<n>We look for the solution as a transformation of the transition probability density function of a reference process.<n>We derive a system of ODEs for the time evolution of the Normalizing Flow's parameters.
  arXiv  Detail & Related papers  (2026-03-19T13:43:18Z)
• Estimating Solvation Free Energies with Boltzmann Generators [0.0]
  We introduce a computational framework based on normalizing flows that maps solvent configurations between solutes of different sizes.<n>For a Lennard-Jones solvent, we demonstrate that this approach yields acceptable accuracy in estimating free energy differences.
  arXiv  Detail & Related papers  (2025-12-20T00:08:19Z)
• Solvaformer: an SE(3)-equivariant graph transformer for small molecule solubility prediction [2.274456001127632]
  Solvaformer is a geometry-aware graph transformer that models solutions as multiple molecules with independent SE(3) symmetries.<n>We train Solvaformer to predict both solubility (log S) and solvation free energy, using an alternating-batch regimen that trains on quantum-mechanical data and on experimental measurements.<n>Solvaformer attains the strongest overall performance among the learned models and approaches a DFT-assisted gradient-boosting baseline.
  arXiv  Detail & Related papers  (2025-11-12T22:12:12Z)
• Non-convex entropic mean-field optimization via Best Response flow [0.0]
  We discuss the problem of minimizing non- functionals on the space probability measures, regularized by the relative entropy (KL) with respect to a fixed reference measure.<n>We show how to choose the regularizer, given the non functional, so that the Best Response becomes a contraction with respect to the $L1$Wasserstein distance.
  arXiv  Detail & Related papers  (2025-05-28T18:22:08Z)
• Asymptotically Optimal Change Detection for Unnormalized Pre- and Post-Change Distributions [65.38208224389027]
  This paper addresses the problem of detecting changes when only unnormalized pre- and post-change distributions are accessible. Our approach is based on the estimation of the Cumulative Sum statistics, which is known to produce optimal performance.
  arXiv  Detail & Related papers  (2024-10-18T17:13:29Z)
• DiffFluid: Plain Diffusion Models are Effective Predictors of Flow Dynamics [16.660107496540146]
  We showcase the plain diffusion models with Transformers as effective predictors of fluid dynamics under various working conditions. Our approach formulates the prediction of flow dynamics as the image translation problem and accordingly leverage the plain diffusion model to tackle the problem.
  arXiv  Detail & Related papers  (2024-09-20T17:19:03Z)
• Efficient Pseudomode Representation and Complexity of Quantum Impurity Models [0.7373617024876725]
  Out-of-equilibrium fermionic quantum impurity models (QIM) describe a small interacting system coupled to a continuous fermionic bath. We find efficient bath representations as that of approximating a kernel of the bath's Feynman-Vernon influence functional by a sum of complex exponentials. To relate our findings to QIM, we derive an explicit Liouvillian that describes the time evolution of the combined impurity-pseudomodes system.
  arXiv  Detail & Related papers  (2024-09-13T13:31:53Z)
• Noise-Free Sampling Algorithms via Regularized Wasserstein Proximals [3.4240632942024685]
  We consider the problem of sampling from a distribution governed by a potential function. This work proposes an explicit score based MCMC method that is deterministic, resulting in a deterministic evolution for particles.
  arXiv  Detail & Related papers  (2023-08-28T23:51:33Z)
• Machine learning of hidden variables in multiscale fluid simulation [77.34726150561087]
  Solving fluid dynamics equations often requires the use of closure relations that account for missing microphysics. In our study, a partial differential equation simulator that is end-to-end differentiable is used to train judiciously placed neural networks. We show that this method enables an equation based approach to reproduce non-linear, large Knudsen number plasma physics.
  arXiv  Detail & Related papers  (2023-06-19T06:02:53Z)
• Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance [10.153270126742369]
  We study gradient flows in both probability density space and Gaussian space. The flow in the Gaussian space may be understood as a Gaussian approximation of the flow.
  arXiv  Detail & Related papers  (2023-02-21T21:44:08Z)
• Sampling with Mollified Interaction Energy Descent [57.00583139477843]
  We present a new optimization-based method for sampling called mollified interaction energy descent (MIED) MIED minimizes a new class of energies on probability measures called mollified interaction energies (MIEs) We show experimentally that for unconstrained sampling problems our algorithm performs on par with existing particle-based algorithms like SVGD.
  arXiv  Detail & Related papers  (2022-10-24T16:54:18Z)
• Structural aspects of FRG in quantum tunnelling computations [68.8204255655161]
  We probe both the unidimensional quartic harmonic oscillator and the double well potential. Two partial differential equations for the potential V_k(varphi) and the wave function renormalization Z_k(varphi) are studied.
  arXiv  Detail & Related papers  (2022-06-14T15:23:25Z)
• Using Computational Intelligence for solving the Ornstein-Zernike equation [0.0]
  This thesis provides an exploration of the use of computational intelligence techniques to study the numerical solution of the Ornstein-Zernike equation for simple liquids.
  arXiv  Detail & Related papers  (2021-11-17T20:57:32Z)
• Mean-Square Analysis with An Application to Optimal Dimension Dependence of Langevin Monte Carlo [60.785586069299356]
  This work provides a general framework for the non-asymotic analysis of sampling error in 2-Wasserstein distance. Our theoretical analysis is further validated by numerical experiments.
  arXiv  Detail & Related papers  (2021-09-08T18:00:05Z)
• A Near-Optimal Gradient Flow for Learning Neural Energy-Based Models [93.24030378630175]
  We propose a novel numerical scheme to optimize the gradient flows for learning energy-based models (EBMs) We derive a second-order Wasserstein gradient flow of the global relative entropy from Fokker-Planck equation. Compared with existing schemes, Wasserstein gradient flow is a smoother and near-optimal numerical scheme to approximate real data densities.
  arXiv  Detail & Related papers  (2019-10-31T02:26:20Z)

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.