In-layer inhomogeneity of molecular dynamics in quasi-liquid layers of ice.

Quasi-liquid layers (QLLs) are present on the surface of ice and play a significant role in its distinctive chemical and physical properties. These layers exhibit considerable heterogeneity across different scales ranging from nanometers to millimeters. Although the formation of partially ice-like structures has been proposed, the molecular-level understanding of this heterogeneity remains unclear. Here, we examined the heterogeneity of molecular dynamics on QLLs based on molecular dynamics simulations and machine learning analysis of the simulation data. We demonstrated that the molecular dynamics of QLLs do not comprise a mixture of solid- and liquid water molecules. Rather, molecules having similar behaviors form dynamical domains that are associated with the dynamical heterogeneity of supercooled water. Nonetheless, molecules in the domains frequently switch their dynamical state. Furthermore, while there is no observable characteristic domain size, the long-range ordering strongly depends on the temperature and crystal face. Instead of a mixture of static solid- and liquid-like regions, our results indicate the presence of heterogeneous molecular dynamics in QLLs, which offers molecular-level insights into the surface properties of ice.

Hysteresis Elimination for an Anisotropic Liquid-Crystal Model via Molecule Design and Replica-Exchange Optimization.

The phenomenon of hysteresis in simulations, in which a system's current state is correlated to previous states and inhibits the transition to a more stable phase, may often lead to misleading results in physical chemistry. In this study, in addition to the replica exchange method (REM), a novel approach was taken by combining an evolution strategy based on the evolutionary principles of nature to predict phase transitions for the Hess-Su liquid-crystal model. In this model, an anisotropy term is added to the simple 6-12 Lennard-Jones model to intuitively reproduce the behavior of liquid crystals. We first applied the pressure-temperature REM to the Hess-Su model and optimized the replica spacing for the energy distribution to gain the maximum advantage from the REM. We then used the same approach as for the Hamiltonian REM, seeking to optimize the replica spacing in the same way. Based on both results, we attempted to predict this coarse-grained liquid-crystal model's exact phase transition point. In the Hamiltonian REM, replicas were prepared with different molecular aspect ratios corresponding to the values of the anisotropy terms in the potential function. The Hess-Su liquid-crystal model, which undergoes a direct transition from the nematic to the solid phase without going through a smectic phase, is a challenging research target for understanding phase transitions. Despite the tremendous computational difficulty in overcoming the strong hysteresis present in this system, our method could predict the phase transition point clearly and significantly reduce the extent of hysteresis. Our approach is beneficial when simulating more complex systems and, above all, shows great potential for more accurate and efficient phase transition predictions in the field of molecular simulation in the future.

Novel approach for designing order parameters of clathrate hydrate structures by graph neural network.

Clathrate hydrates continue to be the focus of active research efforts due to their use in energy resources, transportation, and storage-related applications. Therefore, it is crucial to define their essential characteristics from a molecular standpoint. Understanding molecular structure in particular is crucial because it aids in understanding the mechanisms that lead to the formation or dissociation of clathrate hydrates. In the past, a wide variety of order parameters have been employed to classify and evaluate hydrate structures. An alternative approach to inventing bespoke order parameters is to apply machine learning techniques to automatically generate effective order parameters. In earlier work, we suggested a method for automatically designing novel parameters for ice and liquid water structures with Graph Neural Networks (GNNs). In this work, we use a GNN to implement our method, which can independently produce feature representations of the molecular structures. By using the TeaNet-type model in our method, it is possible to directly learn the molecular geometry and topology. This enables us to build novel parameters without prior knowledge of suitable order parameters for the structure type, discover structural differences, and classify molecular structures with high accuracy. We use this approach to classify the structures of clathrate hydrate structures: sI, sII, and sH. This innovative approach provides an appealing and highly accurate replacement for the traditional order parameters. Furthermore, our method makes clear the process of automatically designing a universal parameter for liquid water, ice, and clathrate hydrate to analyze their structures and phases.

Graph-Neural-Network-Based Unsupervised Learning of the Temporal Similarity of Structural Features Observed in Molecular Dynamics Simulations.

Classification of molecular structures is a crucial step in molecular dynamics (MD) simulations to detect various structures and phases within systems. Molecular structures, which are commonly identified using order parameters, were recently identified using machine learning (ML), that is, the ML models acquire structural features using labeled crystals or phases via supervised learning. However, these approaches may not identify unlabeled or unknown structures, such as the imperfect crystal structures observed in nonequilibrium systems and interfaces. In this study, we proposed the use of a novel unsupervised learning framework, denoted temporal self-supervised learning (TSSL), to learn structural features and design their parameters. In TSSL, the ML models learn that the structural similarity is learned via contrastive learning based on minor short-term variations caused by perturbations in MD simulations. This learning framework is applied to a sophisticated architecture of graph neural network models that use bond angle and length data of the neighboring atoms. TSSL successfully classifies water and ice crystals based on high local ordering, and furthermore, it detects imperfect structures typical of interfaces such as the water-ice and ice-vapor interfaces.

Unsupervised deep learning for molecular dynamics simulations: a novel analysis of protein-ligand interactions in SARS-CoV-2 Mpro.

Molecular dynamics (MD) simulations, which are central to drug discovery, offer detailed insights into protein-ligand interactions. However, analyzing large MD datasets remains a challenge. Current machine-learning solutions are predominantly supervised and have data labelling and standardisation issues. In this study, we adopted an unsupervised deep-learning framework, previously benchmarked for rigid proteins, to study the more flexible SARS-CoV-2 main protease (Mpro). We ran MD simulations of Mpro with various ligands and refined the data by focusing on binding-site residues and time frames in stable protein conformations. The optimal descriptor chosen was the distance between the residues and the center of the binding pocket. Using this approach, a local dynamic ensemble was generated and fed into our neural network to compute Wasserstein distances across system pairs, revealing ligand-induced conformational differences in Mpro. Dimensionality reduction yielded an embedding map that correlated ligand-induced dynamics and binding affinity. Notably, the high-affinity compounds showed pronounced effects on the protein's conformations. We also identified the key residues that contributed to these differences. Our findings emphasize the potential of combining unsupervised deep learning with MD simulations to extract valuable information and accelerate drug discovery.

Construction of full-atomistic polymer amorphous structures using reverse-mapping from Kremer-Grest models.

We propose a method to build full-atomistic (FA) amorphous polymer structures using reverse-mapping from coarse-grained (CG) models. In this method, three models with different resolutions are utilized, namely the CG1, CG2, and FA models. It is assumed that the CG1 model is more abstract than the CG2 model. The CG1 is utilized to equilibrate the system, and then sequential reverse-mapping procedures from the CG1 to the CG2 models and from the CG2 to the FA models are conducted. A mapping relation between the CG1 and the FA models is necessary to generate a polymer structure with a given density and radius of chains. Actually, we have used the Kremer-Grest (KG) model as the CG1 and the monomer-level CG model as the CG2 model. Utilizing the mapping relation, we have developed a scheme that constructs an FA polymer model from the KG model. In the scheme, the KG model, the monomer level CG model, and the FA model are successively constructed. The scheme is applied to polyethylene (PE), cis 1,4-polybutadiene (PB), and poly(methyl methacrylate) (PMMA). As a validation, the structures of PE and PB constructed by the scheme were carefully checked through comparison with those obtained using long-time FA molecular dynamics (MD) simulations. We found that both short- and long-range chain structures constructed by the scheme reproduced those obtained by the FA MD simulations. Then, as an interesting application, the scheme is applied to generate an entangled PMMA structure. The results showed that the scheme provides an efficient and easy way to construct amorphous structures of FA polymers.

Graph neural networks classify molecular geometry and design novel order parameters of crystal and liquid.

Molecular dynamics simulation produces three-dimensional data on molecular structures. The classification of molecular structure is an important task. Conventionally, various order parameters are used to classify different structures of liquid and crystal. Recently, machine learning (ML) methods have been proposed based on order parameters to find optimal choices or use them as input features of neural networks. Conventional ML methods still require manual operation, such as calculating the conventional order parameters and manipulating data to impose rotational/translational invariance. Conversely, deep learning models that satisfy invariance are useful because they can automatically learn and classify three-dimensional structural features. However, in addition to the difficulty of making the learned features explainable, deep learning models require information on large structures for highly accurate classification, making it difficult to use the obtained parameters for structural analysis. In this work, we apply two types of graph neural network models, the graph convolutional network (GCN) and the tensor embedded atom network (TeaNet), to classify the structures of Lennard-Jones (LJ) systems and water systems. Both models satisfy invariance, while GCN uses only length information between nodes. TeaNet uses length and orientation information between nodes and edges, allowing it to recognize molecular geometry efficiently. TeaNet achieved a highly accurate classification with an extremely small molecular structure, i.e., when the number of input molecules is 17 for the LJ system and 9 for the water system, the accuracy is 98.9% and 99.8%, respectively. This is an advantage of our method over conventional order parameters and ML methods such as GCN, which require a large molecular structure or the information of wider area neighbors. Furthermore, we verified that TeaNet could build novel order parameters without manual operation. Because TeaNet can recognize extremely small local structures with high accuracy, all structures can be mapped to a low-dimensional parameter space that can explain structural features. TeaNet offers an alternative to conventional order parameters because of its novelty.

Pre-Smectic Ordering and the Unwinding Helix in Monte Carlo Simulations of Cholesteric Liquid-Crystals.

In this paper, molecular chirality is studied for liquid-crystal fluids represented by hard rods with the addition of an attractive chiral dispersion term. Chiral forces between molecular pairs are assumed to be long-ranged and are described in terms of the pseudotensor of Goossens [W. J. A. Goossens, Mol. Cryst. Liq. Cryst. 1971, 12, 237-244]. Following Varga and Jackson [S. Varga and G. Jackson, Chem. Phys. Lett. 2003, 377, 6-12], this is combined with a hard-spherocylinder core. We investigate the relationship between molecular chirality and the helical pitch of the system, which occurs in the absence of full three-dimensional periodic boundary conditions. The dependence of the wavenumber of this pitch on the thermodynamic variables, temperature, and density is measured. We also explore the use of a novel surface boundary interaction model. As a result of this approach, we are able to lower the temperature of the system without the occurrence of nematic droplets, which would interfere with the formation of a uniaxial pitch. Regarding the theoretical predictions of Wensink and Jackson [H. H. Wensink and G. Jackson, J. Chem. Phys. 2009, 130, 234911], on the one hand, we have qualitative agreement with the observed non-monotonic density dependence of the wavenumber. Initially increasing with density, the wavenumber reaches a maximum, before falling as the density moves toward the point of phase transition from cholesteric to smectic. However, further analysis for shorter rods, in the presence of novel boundary conditions, reveals some disagreement with the theory, at least in this case; the unwinding of the cholesteric helix in the cholesteric phase occurs simultaneously with subtle increases in smectic ordering. These pre-smectic fluctuations have not been accounted for so far in theories on cholesterics but turn out to play a key role in controlling the pitch of cholesteric phases of rod-shaped mesogens with a small to moderate aspect ratio.

Learned pseudo-random number generator: WGAN-GP for generating statistically robust random numbers.

Pseudo-random number generators (PRNGs) are software algorithms generating a sequence of numbers approximating the properties of random numbers. They are critical components in many information systems that require unpredictable and nonarbitrary behaviors, such as parameter configuration in machine learning, gaming, cryptography, and simulation. A PRNG is commonly validated through a statistical test suite, such as NIST SP 800-22rev1a (NIST test suite), to evaluate its robustness and the randomness of the numbers. In this paper, we propose a Wasserstein distance-based generative adversarial network (WGAN) approach to generating PRNGs that fully satisfy the NIST test suite. In this approach, the existing Mersenne Twister (MT) PRNG is learned without implementing any mathematical programming code. We remove the dropout layers from the conventional WGAN network to learn random numbers distributed in the entire feature space because the nearly infinite amount of data can suppress the overfitting problems that occur without dropout layers. We conduct experimental studies to evaluate our learned pseudo-random number generator (LPRNG) by adopting cosine-function-based numbers with poor random number properties according to the NIST test suite as seed numbers. The experimental results show that our LPRNG successfully converted the sequence of seed numbers to random numbers that fully satisfy the NIST test suite. This study opens the way for the "democratization" of PRNGs through the end-to-end learning of conventional PRNGs, which means that PRNGs can be generated without deep mathematical know-how. Such tailor-made PRNGs will effectively enhance the unpredictability and nonarbitrariness of a wide range of information systems, even if the seed numbers can be revealed by reverse engineering. The experimental results also show that overfitting was observed after about 450,000 trials of learning, suggesting that there is an upper limit to the number of learning counts for a fixed-size neural network, even when learning with unlimited data.

Wetting hysteresis induces effective unidirectional water transport through a fluctuating nanochannel.

We propose a water pump that actively transports water molecules through nanochannels. Spatially asymmetric noise fluctuations imposed on the channel radius cause unidirectional water flow without osmotic pressure, which can be attributed to hysteresis in the cyclic transition between the wetting/drying states. We show that the water transport depends on fluctuations, such as white, Brownian, and pink noises. Because of the high-frequency components in white noise, fast switching of open and closed states inhibits channel wetting. Conversely, pink and Brownian noises generate high-pass filtered net flow. Brownian fluctuation leads to a faster water transport rate, whereas pink noise has a higher capability to overcome pressure differences in the opposite direction. A trade-off relationship exists between the resonant frequency of the fluctuation and the flow amplification. The proposed pump can be considered as an analogy for the reversed Carnot cycle, which is the upper limit of the energy conversion efficiency.

Combining Molecular Dynamics and Machine Learning to Analyze Shear Thinning for Alkane and Globular Lubricants in the Low Shear Regime.

Lubricants with desirable frictional properties are important in achieving an energy-saving society. Lubricants at the interfaces of mechanical components are confined under high shear rates and pressures and behave quite differently from the bulk material. Computational approaches such as nonequilibrium molecular dynamics (NEMD) simulations have been performed to probe the molecular behavior of lubricants. However, the low-shear-velocity regions of the materials have rarely been simulated owing to the expensive calculations necessary to do so, and the molecular dynamics under shear velocities comparable with that in the experiments are not clearly understood. In this study, we performed NEMD simulations of extremely confined lubricants, i.e., two molecular layers for four types of lubricants confined in mica walls, under shear velocities from 0.001 to 1 m/s. While we confirmed shear thinning, the velocity profiles could not show the flow behavior when the shear velocity was much slower than thermal fluctuations. Therefore, we used an unsupervised machine learning approach to detect molecular movements that contribute to shear thinning. First, we extracted the simple features of molecular movements from large amounts of MD data, which were found to correlate with the effective viscosity. Subsequently, the extracted features were interpreted by examining the trajectories contributing to these features. The magnitude of diffusion corresponded to the viscosity, and the location of slips that varied depending on the spherical and chain lubricants was irrelevant. Finally, we attempted to apply a modified Stokes-Einstein relation at equilibrium to the nonequilibrium and confined systems. While systems with low shear rates obeyed the relation sufficiently, large deviations were observed under large shear rates.

Prediction of Water Diffusion in Wide Varieties of Polymers with All-Atom Molecular Dynamics Simulations and Deep Generative Models.

Permeation through polymer membranes is an important technology in the chemical industry, and in its design, the self-diffusion coefficient is one of the physical quantities that determine permeability. Since the self-diffusion coefficient sensitively reflects intra- and intermolecular interactions, analysis using an all-atom model is required. However, all-atom simulations are computationally expensive and require long simulation times for the diffusion of small molecules dissolved in polymers. MD-GAN, a machine learning model, is effective in accelerating simulations and reducing computational costs. The target systems for MD-GAN prediction were limited to polyethylene melts in previous studies; therefore, this study extended MD-GAN to systems containing copolymers with branches and successfully predicted water diffusion in various polymers. The correlation coefficient between the predicted self-diffusion coefficient and that of the long-time simulation was 1.00. Additionally, we found that incorporating statistical domain knowledge into MD-GAN improved accuracy, reducing the mean-square displacement prediction outliers from 14.6% to 5.3%. Lastly, the distribution of latent variables with embedded dynamics information within the model was found to be strongly related to accuracy. We believe that these findings can be useful for the practical applications of MD-GAN.

MD-GAN with multi-particle input: the machine learning of long-time molecular behavior from short-time MD data.

Molecular dynamics simulation is a method of investigating the behavior of molecules, which is useful for analyzing a variety of structural and dynamic properties and mechanisms of phenomena. However, the huge computational cost of large-scale and long-time simulations is an enduring problem that must be addressed. MD-GAN is a machine learning-based method that can evolve part of the system at any time step, accelerating the generation of molecular dynamics data [Endo et al., Proceedings of the AAAI Conference on Artificial Intelligence, 2018, 32]. For the accurate prediction of MD-GAN, sufficient information on the dynamics of a part of the system should be included with the training data. Therefore, the selection of the part of the system is important for efficient learning. In a previous study, only one particle (or vector) of each molecule was extracted as part of the system. The effectiveness of adding information from other particles to the learning process is investigated in this study. When the dynamics of three particles of each molecule were used in the polyethylene experiment, the diffusion was successfully predicted using the training data with a time length of approximately 40%, compared to the single-particle input. Surprisingly, the unobserved transition of diffusion in the training data was also predicted using this method. The reduced cost for the generation of training MD data achieved in this study is useful for accelerating MD-GAN.

Correlation between ordering and shear thinning in confined OMCTS liquids.

Despite decades of extensive research, the behavior of confined liquids, particularly in the mixed/boundary lubrication regime, remains unelucidated. This can be attributed to several factors, including the difficulty to make direct experimental observations of the behavior of lubricant molecules under nonequilibrium conditions, the high computational cost of molecular simulations to reach steady state, and the low signal-to-noise ratio at extremely low shear rates corresponding to actual operating conditions. In this regard, we studied the correlation between the structure formation and shear viscosity of octamethylcyclotetrasiloxane confined between two mica surfaces in a mixed/boundary lubrication regime. Three different surface separations-corresponding to two-, three-, and five-layered structures-were considered to analyze the effect of confinement. The orientational distributions with one specific peak for n = 2 and two distributions, including a parallel orientation with the surface normal for n > 2, were observed at rest. The confined liquids exhibited a distinct shear-thinning behavior independent of surface separations for a relatively low shear rate, γ̇≲108s-1. However, the shear viscosities at γ̇≲108s-1 depended on the number of layered structures. Newtonian behavior was observed with further increase in the shear rate. Furthermore, we found a strong correlation between the degree of molecular orientation and the shear viscosity of the confined liquids. The magnitude of the shear viscosity of the confined liquids can primarily be determined by the degree of molecular orientation, and shear thinning originates from the vanishing of specific orientational distributions with increasing shear rate.

Optimal Replica-Exchange Molecular Simulations in Combination with Evolution Strategies.

We have incorporated Evolution Strategies into the Replica-Exchange Monte Carlo simulation method to predict the phase behavior of several example fluids. The replica-exchange method allows one system to exchange temperatures with its neighbors to search for the most stable structure relatively efficiently in a single simulation. However, if the temperature intervals of the replicas are not positioned carefully, there is an issue that local exchange does not occur. Our results for a simple Lennard-Jones fluid and the liquid-crystal Yukawa model demonstrate the utility of the approach when compared to conventional methods. When Evolution Strategies were applied to the Replica-Exchange Monte Carlo simulation, the problem of a significant localized decrease in exchange probability near the phase transition was avoided. By obtaining the optimal temperature intervals, the system efficiently traverses a broader parameter space with a small number of replicas. This is equivalent to accelerating molecular simulations with limited computational resources and can be useful when attempting to predict the phase behavior of complex systems.

Impact of free energy of polymers on polymorphism of polymer-grafted nanoparticles.

Colloidal crystals have gathered wide attention as a model material for optical applications because of their feasibility in controlling the propagation of light by their crystal structure and lattice spacing as well as the simplicity of their fabrication. However, due to the simple interaction between colloids, the colloidal crystal structures that can be formed are limited. It is also difficult to adjust the lattice spacing. Furthermore, colloidal crystals are fragile compared to other crystals. In this study, we focused on polymer-grafted nanoparticles (PGNP) as a possible solution to these unresolved issues. We expected that PGNPs, composed of two distinct layers (the hard core of a nanoparticle and the soft corona of grafted polymers on the surface), will demonstrate similar behaviors as star polymers and hard spheres. We also predicted that PGNPs may exhibit polymorphism because the interaction between PGNPs strongly depends upon their grafting density and the length of the grafted polymer chains. Moreover, we expected that crystals made from PGNPs will be structurally tough due to the entanglement of grafted polymers. From exploration of crystal polymorphs of PGNPs by molecular dynamics simulations, we found face-centered cubic (FCC)/hexagonal close-packed (HCP) and body-centered cubic (BCC) crystals, depending on the length of the grafted polymer chains. When the chains were short, PGNPs behaved like hard spheres and crystals were arranged in FCC/HCP structure, much like the phase transition observed in an Alder transition. When the chains were long enough, the increase in the free energy of grafted polymers was no longer negligible and crystals were arranged in BCC structure, which has a lower density than FCC/HCP. When the chains were not too short or long, FCC/HCP structures were first observed when the volume fraction of system was small, but a phase transition occurred when the system was further compressed and the crystals arranged themselves in a BCC structure. These results most likely have laid strong foundations for future simulations and experimental studies of PGNP crystals.

Differences in ligand-induced protein dynamics extracted from an unsupervised deep learning approach correlate with protein-ligand binding affinities.

Prediction of protein-ligand binding affinity is a major goal in drug discovery. Generally, free energy gap is calculated between two states (e.g., ligand binding and unbinding). The energy gap implicitly includes the effects of changes in protein dynamics induced by ligand binding. However, the relationship between protein dynamics and binding affinity remains unclear. Here, we propose a method that represents ligand-binding-induced protein behavioral change with a simple feature that can be used to predict protein-ligand affinity. From unbiased molecular simulation data, an unsupervised deep learning method measures the differences in protein dynamics at a ligand-binding site depending on the bound ligands. A dimension reduction method extracts a dynamic feature that strongly correlates to the binding affinities. Moreover, the residues that play important roles in protein-ligand interactions are specified based on their contribution to the differences. These results indicate the potential for binding dynamics-based drug discovery.

Efficient Monte Carlo Sampling for Molecular Systems Using Continuous Normalizing Flow.

Monte Carlo molecular simulation is a powerful computational method for simulating molecular behavior. It generates samples of the possible states of molecular systems. To generate a sample efficiently, it is advantageous to avoid suggesting extremely high-energy states that would never become possible states. In this study, we propose a new sampling method for Monte Carlo molecular simulation, that is, a continuous normalizing molecular flow (CNMF) method, which can create various probabilistic distributions of molecular states from some initial distribution. The CNMF method generates samples by solving a first-order differential equation with two-body intermolecular interaction terms. We also develop specific probabilistic distributions using CNMF called inverse square flow, which yields distributions with zero probability density when molecule pairs are in close proximity, whereas probability densities are compressed uniformly from the initial distribution in all other cases. Using inverse square flow, we demonstrate that Monte Carlo molecular simulation is more efficient than the standard simulation. Although the increased computational costs of the CNMF method are non-negligible, this method is feasible for parallel computation and has the potential for expansion.

Natural quantum reservoir computing for temporal information processing.

Reservoir computing is a temporal information processing system that exploits artificial or physical dissipative dynamics to learn a dynamical system and generate the target time-series. This paper proposes the use of real superconducting quantum computing devices as the reservoir, where the dissipative property is served by the natural noise added to the quantum bits. The performance of this natural quantum reservoir is demonstrated in a benchmark time-series regression problem and a practical problem classifying different objects based on temporal sensor data. In both cases the proposed reservoir computer shows a higher performance than a linear regression or classification model. The results indicate that a noisy quantum device potentially functions as a reservoir computer, and notably, the quantum noise, which is undesirable in the conventional quantum computation, can be used as a rich computation resource.

An Efficient Random Number Generation Method for Molecular Simulation.

We propose a new random number generation method, which is the fastest and the simplest of its kind, for use with molecular simulation. We also discuss the possibility of using this method with various other numerical calculations. To demonstrate the significant increases in calculation speeds that can be gained by using our method, we present a comparison with prior methods for dissipative particle dynamics (DPD) simulations. The DPD method uses random numbers to reproduce thermal fluctuations of molecules. As such, an efficient method to generate random numbers in parallel computing environments has been widely sought after. Several random number generation methods have been developed that use encryption. In this study, we establish for the first time that random numbers with desirable properties exist in the particle coordinates used in DPD calculations. We propose a method for generating random numbers without encryption that utilizes this source of randomness. This is an innovative method with minimal computational cost, since it is not dependent on a complicated random number generation algorithm or an encryption process. Furthermore, our method may lead to faster random number generation for many other physical and chemical simulations.