Isotension Ensemble Research Articles

Implementation of Isotension Ensemble in Deep Learning

The implementation of the isotension ensemble in deep learning is a novel approach that aims to enhance the performance and robustness of deep learning models. This abstract provides a detailed overview of the implementation and its key components, highlighting its significance and potential impact on the field of deep learning. Deep learning has achieved remarkable success in various domains, including computer vision, natural language processing, and pattern recognition. However, deep neural networks are known to suffer from overfitting and lack of generalization when trained on limited datasets or when faced with complex and diverse data distributions. These limitations hinder their performance and reliability in real-world applications.
 The isotension ensemble approach addresses these challenges by integrating the concept of isotension into the training process of deep learning models. Isotension refers to a state in which the tensions between different parts of a model are balanced, promoting overall stability and robustness. By incorporating isotension, the ensemble aims to improve generalization capabilities, reduce overfitting, and enhance the model's ability to handle diverse data distributions. The implementation of the isotension ensemble involves several key components. The ensemble is constructed by training multiple deep neural networks with different initializations or hyperparameter configurations. Each network is designed to capture different aspects of the data and learn diverse representations. Sean isotension constraint is introduced during the training process to balance the tensions between the networks, ensuring that they collectively converge to a stable and robust solution. This constraint can be achieved through various techniques such as isotonic regression or loss function regularization.
 The implementation of the isotension ensemble in deep learning has shown promising results in various applications. Experimental evaluations demonstrate improved generalization capabilities, enhanced model performance, and increased robustness compared to conventional deep learning approaches. The isotension ensemble has been successfully applied in tasks such as image classification, object detection, and natural language processing, achieving state-of-the-art results and demonstrating its potential impact in real-world scenarios.
 The significance of the isotension ensemble lies in its ability to address the limitations of deep learning models, providing a framework for enhanced performance and reliability. By integrating the concept of isotension into the training process, the ensemble promotes stability, robustness, and improved generalization capabilities. This approach opens up new possibilities for tackling complex and diverse datasets, advancing the field of deep learning, and enabling the deployment of more reliable and efficient models in practical applications.
 The implementation of the isotension ensemble in deep learning offers a promising approach to overcome the limitations of conventional deep learning models. By leveraging the concept of isotension, the ensemble enhances generalization capabilities, reduces overfitting, and improves model performance and robustness. The successful application of the isotension ensemble in various tasks demonstrates its potential impact and paves the way for future research and development in the field of deep learning.

Implementation of isotension ensemble in molecular dynamics

The implementation of the new type of ensemble, with constant tension force in the molecular dynamic simulations, is considered. In contrast to the isostress NtT ensemble, in which the stress components act on the surface and the volume elements, the new NfT ensemble is determined by the tension forces acting on each particle in the extended space. Correspondingly, instead of the stress–strain relation used in conventional theory, a new type of constitutive equation in terms of stretch and tension becomes an objective of the molecular dynamics simulations. Comparison with the Parrinello–Rahman method is made for the general external load and the temperature applied. Results for the aluminum lattice show that the suggested approach gives an unbiased sampling of the isostress–isothermal ensemble in the LAMMPS environment. Additionally, the problem of atomistic boundary condition was renovated, due to almost identical tension and traction forces. It was shown on several examples of strains that the tension forces properly represent the type and magnitude of the atomistic external load applied to the surface, despite the absence of any quantities related to the area in the constitutive equations. An analog of Cauchy’s stress theorem in the new setting is formulated and verified by numerical simulations.

Simulating Equilibrium Surface Forces in Polymer Solutions Using a Canonical Grid Method

A new simulation method for nonuniform polymer solutions between planar surfaces at full chemical equilibrium is described. The technique uses a grid of points in a two-dimensional thermodynamic space, labeled by surface area and surface separations. Free energy differences between these points are determined via Bennett's optimized rates method in the canonical ensemble. Subsequently, loci of constant chemical potential are determined within the grid via simple numerical interpolation. In this way, a series of free energy versus separation curves are determined for a number of different chemical potentials. The method is applied to the case of hard sphere polymers between attractive surfaces, and its veracity is confirmed via comparisons with established alternative simulation techniques, namely, the grand canonical ensemble and isotension ensemble methods. The former method is shown to fail when the degree of polymerization is too large. An interesting interplay between repulsive steric interactions and attractive bridging forces occurs as the surface attraction and bulk monomer density are varied. This behavior is further explored using polymer density functional theory, which is shown to be in good agreement with the simulations. Our results are also discussed in light of recent self-consistent field calculations which correct the original deGennes results for infinitely long polymers. In particular, we look at the role of chain ends by investigating the behavior of ring polymers.

Simulations of Surface Forces in Polyelectrolyte Solutions

We have simulated interactions between charged surfaces in the presence of oppositely charged polyelectrolytes by coupling perturbations in the isotension ensemble to a free energy variance minimization scheme. For polymeric systems, this method completely outperforms configurationally biased versions of grand canonical simulations. Proper diffusive equilibrium between bulk and slit has been established for polyelectrolytes with up to 60 monomers per chain. A consequence of imposing diffusive equilibrium conditions, in contrast to previous more restricted models, is the possibility of surface charge inversion; ion-ion correlation and the cooperativity of monomer adsorption drive the formation of a polyion layer close to the surface, that overcompensates the nominal surface charge. This is observed even at modest surface charge densities, and leads to a build up of a long ranged electrostatic barrier. In addition, the onset of charge inversion requires very low bulk polymer densities. Due to screening effects, this leads to a higher and more long-ranged free energy barrier at low, compared to high, bulk densities. Oscillatory forces, reminiscent of those found in simple hard sphere systems, are resolved in the high concentration regime. As a consequence of a second surface charge inversion, the system "stratifies" to form a stable polyelectrolyte layer in the central part of the slit, stabilized by the adsorbed surface layers.

Simulations and density functional calculations of surface forces in the presence of semiflexible polymers

We simulate interactions between adsorbing and nonadsorbing surfaces immersed in solutions containing monodisperse semiflexible chains. Apart from the nature of the surfaces, we investigate responses to changes of the intrinsic chain stiffness, the degree of polymerization, and the bulk concentration. Our simulations display a sufficient accuracy and precision to reveal free-energy barriers that are small on a typical scale of surface force simulations, but still of the same order as the expected van der Waals interactions. Two different approaches have been tested: grand canonical simulations, improved by configurational-biased techniques, and a perturbation method utilizing the isotension ensemble. We find the former to be preferable when the surfaces are nonadsorbing, whereas the isotension approach is superior for calculations of interactions between adsorbing surfaces, especially if the polymers are stiff. We also compare our simulation results with predictions from several versions of polymer density functional theory. We find that a crucial aspect of these theories, in quantitative terms, is that they recognize that end monomers exclude more volume to the surrounding than inner ones do. Those theories provide satisfactorily accurate predictions, particularly when the surfaces are nonadsorbing.

Surface forces in polymer fluids: a comparison between simulations and density functional theory.

A polymer density functional theory is evaluated in terms of its ability to predict interactions between large surfaces in a polymer fluid. Comparisons are made with results from simulations in an expanded isotension ensemble. The variation of the net surface-surface interaction with adsorption strength is examined. Cases where the monomers interact via a pure hard sphere potential are investigated, but we have also studied the effect of attractions between the monomers. In all cases, we obtain an almost quantitative agreement between the simulated results and the predictions from the polymer density functional theory.

Optimizing simulations of confined polymer melts at constant chemical potential

In this article we describe the simulation of a confined polymer fluid at constant chemical potential. The simulation program uses an optimized rate method to establish free energy differences adapted to the Isotension Ensemble. The method is implemented on both uni- and multi-processor platforms. Results and optimizations at all levels of parallel memory hierarchy are discussed.

Simulations of coexistence between layered phases in planar slits

Layering transitions of a simple fluid in a planar pore with structureless attractive surfaces are investigated, using both simulations and density functional theory. The thermodynamic conditions for coexistence between three different layered phases, denoted 1, 2 and 3 in order of increasing average density, are determined, and coexistence curves are presented. The simulations are performed in the isotension ensemble at low temperatures, while the recently developed restricted isotension ensemble was used at elevated temperatures, in order to avoid phase transitions. According to the simulation results, 1–2 and 2–3 coexistences exist between stable phases at low temperatures, but the 2-phase is truncated by a triple point at which all three phases coexist. Above this triple point, 1–3 coexistence is the only stable one. These results are not confirmed by the density functional calculations, according to which 1–3 coexistence at low temperatures is replaced by a simple thin—thick coexistence at higher temperatures. With a slightly increased surface—fluid potential, the density functional calculations do predict the existence of a 1-2-3 triple point. However, in this case the relative stability of the layered phases above and below the triple point is reversed, as compared with the simulation results. Since the differences in the coexistence quantities are small, we have to consider the possibility that this unexpected behaviour is not a true effect, but rather a result of statistical fluctuations. At any rate, the occurrence of 1–3 coexistence together with a triple point is, to the best of our knowledge, a novel observation and is confirmed by density functional theory. Furthermore, the simulations show that the 1–2, 2–3 and 1–3 coexistence curves are very similar.

Improving the Efficiency of a New Infinite Order Perturbation Method to Simulate Surface Forces

Svensson and Woodward [1] have recently developed an infinite order thermodynamic perturbation technique, utilizing free energy differences, with which surface forces and free energies may be simulated without particle insertions. In this Note, we investigate another free energy difference method, in which we employ an isotension ensemble version of the variance minimization scheme, introduced by Bennet [2] for canonical systems. It is shown that this method provides a substantially improved efficiency, as compared with the simple thermodynamic perturbation technique. The applicability is also increased, since fluids with hard cores may be treated without restrictions.

Simulations of phase equilibria in planar slits

Gas-liquid coexistence, free energies and surface forces are investigated for a simple fluid confined by planar walls, which also interact with the fluid. Isotension ensemble simulations and an infinite order thermodynamic perturbation theory are utilized. The free energies are calculated to high accuracy as a function of the separation between the walls. At a particular separation the fluid undergoes a phase transition and both gas and liquid branches are simulated. A new ensemble, the restricted isotension ensemble, is introduced: this prevents interphase crossings between gas and liquid phases, near the critical temperature. This ensemble may prove useful for further studies of wetting phenomena.

Simulations of a confined polymer fluid at constant chemical potential

Monte Carlo simulations are reported of a polymer fluid confined between planar walls using the isotension ensemble, which allows one to perform simulations at constant chemical potential without the necessity of particle exchanges with a bulk polymer fluid. The pressure acting upon the walls and the free energy per unit area of the confined fluid as a function of separation between the walls are obtained, all at constant chemical potential. This is made possible by the use of the so-called free energy difference method. This method appears to be less susceptible to the difficulties that confront the simulation of confined fluids at high density in grand canonical ensemble simulations.

Simulations of a confined polymer fluid at constant chemical potential

Monte Carlo simulations are reported of a polymer fluid confined between planar walls using the isotension ensemble, which allows one to perform simulations at constant chemical potential without the necessity of particle exchanges with a bulk polymer fluid. The pressure acting upon the walls and the free energy per unit area of the confined fluid as a function of separation between the walls are obtained, all at constant chemical potential. This is made possible by the use of the so-called free energy difference method. This method appears to be less susceptible to the difficulties that confront the simulation of confined fluids at high density in grand canonical ensemble simulations.

Computer Simulations of Water between Hydrophobic Surfaces: The Hydrophobic Force

The force between two hydrophobic surfaces enclosing an aqueous solution has been calculated via Monte Carlo simulations using the isotension ensemble. The confined water phase is in equilibrium with a bulk at constant chemical potential, and the average density between the surfaces is gradually decreased as they are brought closer together. The density depression in the slit gives rise to a strong attractive interaction exceeding the standard van der Waals force by an order of magnitude. This force mechanism is consistent with some of the experimental results obtained for the interaction of two hydrophobized surfaces in water. The results cannot, however, be used as a comparison with the very long-range forces extending over several thousand angstroms found in some experiments.

Simulations in planar slits at constant chemical potential

In this work we describe Monte Carlo simulations of a fluid confined between planar walls. We derive a free energy difference method (FEDM) in the isotension ensemble. We illustrate the method by varying the separation between the walls at constant chemical potential. It is shown that the FEDM is a viable alternative to grand canonical ensemble (GCE) simulations. Our method appears to be less susceptible to the difficulties that confront the simulation of confined fluids at high density in the GCE.

Statistical ensembles and molecular dynamics studies of anisotropic solids. II

We have recently discussed how the Parrinello–Rahman theory can be brought into accord with the theory of the elastic and thermodynamic behavior of anisotropic media. This involves the isoenthalpic–isotension ensemble of statistical mechanics. Nosé has developed a canonical ensemble form of molecular dynamics. We combine Nosé’s ideas with the Parrinello–Rahman theory to obtain a canonical form of molecular dynamics appropriate to the study of anisotropic media subjected to arbitrary external stress. We employ this isothermal–isotension ensemble in a study of a fcc→ close-packed structural phase transformation in a Lennard-Jones solid subjected to uniaxial compression. Our interpretation of the Nosé theory does not involve a scaling of the time variable. This latter fact leads to simplifications when studying the time dependence of quantities.