Machine learning coarse grained models for water

Liquid-liquid transition and ice crystallization in a machine-learned coarse-grained water model

Mounting experimental evidence supports the existence of a liquid-liquid transition (LLT) in high-pressure supercooled water. However, fast crystallization of supercooled water has impeded identification of the LLT line TLL(p) in experiments. While the most accurate all-atom (AA) water models display a LLT, their computational cost limits investigations of its interplay with ice formation. Coarse-grained (CG) models provide over 100-fold computational efficiency gain over AA models, enabling the study of water crystallization, but have not yet shown to have a LLT. Here, we demonstrate that the CG machine-learned water model Machine-Learned Bond-Order Potential (ML-BOP) has a LLT that ends in a critical point at pc = 170 ± 10 MPa and Tc = 181 ± 3 K. The TLL(p) of ML-BOP is almost identical to the one of TIP4P/2005, adding to the similarity in the equation of state of liquid water in both models. Cooling simulations reveal that ice crystallization is fastest at the LLT and its supercritical continuation of maximum heat capacity, supporting a mechanistic relationship between the structural transformation of water to a low-density liquid (LDL) and ice formation. We find no signature of liquid-liquid criticality in the ice crystallization temperatures. ML-BOP replicates the competition between formation of LDL and ice observed in ultrafast experiments of decompression of the high-density liquid (HDL) into the region of stability of LDL. The simulations reveal that crystallization occurs prior to the coarsening of the HDL and LDL domains, obscuring the distinction between the highly metastable first-order LLT and pronounced structural fluctuations along its supercritical continuation.

Synthetic Force-Field Database for Training Machine Learning Models to Predict Mobility-Preserving Coarse-Grained Molecular-Simulation Potentials

Balancing accuracy and efficiency is a common problem in molecular simulation. This tradeoff is evident in coarse-grained molecular dynamics simulation, which prioritizes efficiency, and all-atom molecular simulation, which prioritizes accuracy. Despite continuous efforts, creating a coarse-grained model that accurately captures both the system's structure and dynamics remains elusive. In this article, we present a data-driven approach for constructing coarse-grained models that aim to describe both the structure and dynamics of the system equally well. While the development of machine learning models is well-received in the scientific community, the significance of dataset creation for these models is often overlooked. However, data-driven approaches cannot progress without a robust dataset. To address this, we construct a database of synthetic coarse-grained potentials generated from unphysical all-atom models. A neural network is trained with the generated database to predict the coarse-grained potentials of real liquids. We evaluate their quality by calculating the combined loss of structural and dynamical accuracy upon coarse-graining. When we compare our machine learning-based coarse-grained potential with the one from iterative Boltzmann inversion, the machine learning prediction turns out better for all eight hydrocarbon liquids we studied. As all-atom surfaces turn more nonspherical, both ways of coarse-graining degrade. Still, the neural network outperforms iterative Boltzmann inversion in constructing good quality coarse-grained models for such cases. The synthetic database and the developed machine learning models are freely available to the community, and we believe that our approach will generate interest in efficiently deriving accurate coarse-grained models for liquids.

Resolving the dynamic properties of entangled linear polymers in non-equilibrium coarse grain simulation with a priori scaling factors

The molecular weight of polymers can influence the material properties, but the molecular weight at the experiment level sometimes can be a huge burden for property prediction with full-atomic simulations. The traditional bottom-up coarse grain (CG) simulation can reduce the computation cost. However, the dynamic properties predicted by the CG simulation can deviate from the full-atomic simulation result. Usually, in CG simulations, the diffusion is faster and the viscosity and modulus are much lower. The fast dynamics in CG are usually solved by a posteriori scaling on time, temperature, or potential modifications, which usually have poor transferability to other non-fitted physical properties because of a lack of fundamental physics. In this work, a priori scaling factors were calculated by the loss of degrees of freedom and implemented in the iterative Boltzmann inversion. According to the simulation results on 3 different CG levels at different temperatures and loading rates, such a priori scaling factors can help in reproducing some dynamic properties of polycaprolactone in CG simulation more accurately, such as heat capacity, Young's modulus, and viscosity, while maintaining the accuracy in the structural distribution prediction. The transferability of entropy-enthalpy compensation and a dissipative particle dynamics thermostat is also presented for comparison. The proposed method reveals the huge potential for developing customized CG thermostats and offers a simple way to rebuild multiphysics CG models for polymers with good transferability.

Maximum Entropy Theory of Multiscale Coarse-Graining via Matching Thermodynamic Forces: Application to a Molecular Crystal (TATB)

The MSCG/FM (multiscale coarse-graining via force-matching) approach is an efficient supervised machine learning method to develop microscopically informed coarse-grained (CG) models. We present a theory based on the principle of maximum entropy (PME) enveloping the existing MSCG/FM approaches. This theory views the MSCG/FM method as a special case of matching the thermodynamic forces from the extended ensemble described by the set of thermodynamic (relevant) system coordinates. This set may include CG coordinates, the stress tensor, applied external fields, and so forth, and may be characterized by nonequilibrium conditions. Following the presentation of the theory, we discuss the consistent matching of both bonded and nonbonded interactions. The proposed PME formulation is used as a starting point to extend the MSCG/FM method to the constant strain ensemble, which together with the explicit matching of the bonded forces is better suited for coarse-graining anisotropic media at a submolecular resolution. The theory is demonstrated by performing the fine coarse-graining of crystalline 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), a well-known insensitive molecular energetic material, which exhibits highly anisotropic mechanical properties.

Coupling at the molecular scale between the graphene nanosheet and water and its effect on the thermal conductivity of the nanofluid

Graphene nanofluid is a promising way to improve heat transfer in many situations. As a two-dimensional material, graphene's anisotropic thermal conductivity influences the heat transfer of nanofluids. In the present study, a nonequilibrium molecular dynamics (MD) simulation is adopted to study the interaction between graphene nanosheets (GNSs) and liquid water in water-based graphene nanofluids. Consequently, the coupling interaction between the orientation and length of GNSs and the thermal conductivity of nanofluids is then investigated. We discover that the molecular thermal coupling between GNSs and water can effectively influence the orientation angle of the GNSs. A preferential orientation angle of the GNSs inside the nanofluid is then observed during heat transfer. The preferential orientation angle decreases with the GNS length and has no apparent relation with the size of heat flux in this study. The overall thermal conductivity of the nanofluid decreases as the orientation angle of the GNS rises. Increasing the GNS length not only reduces the preferential orientation angle but also improves the thermal conductivity along the graphene length direction. The thermal conductivity of the nanofluid along the graphene length direction increases from 0.414 to 4.085 W m K-1 as the length increases from 103 to 3274 A. Our results provide the fundamental knowledge of the heat transfer performance of graphene nanofluids.

Efficient characterization of double-cross-linked networks in hydrogels using data-inspired coarse-grained molecular dynamics model

The network structure within polymers significantly influences their mechanical properties, including their strength, toughness, and fatigue resistance. All-atom molecular dynamics (AAMD) simulations offer a method to investigate the energy dissipation mechanism within polymers during deformation and fracture; Such an approach is, however, computationally inefficient when used to analyze polymers with complex network structures, such as the common chemically double-networked hydrogels. Alternatively, coarse-grained molecular dynamics (CGMD) models, which reduce the computational degrees of freedom by concentrating a set of adjacent atoms into a coarse-grained bead, can be employed. In CGMD simulations, a coarse-grained force field (CGFF) is a critical factor affecting the simulation accuracy. In this paper, we proposed a data-based method for predicting the CGFF parameters to improve the simulation efficiency of complex cross-linked network in polymers. Here, we utilized a typical chemically double-networked hydrogel as an example. An artificial neural network was selected, and it was trained with the tensile stress-strain data from the CGMD simulations using different CGFF parameters. The CGMD simulations using the predicted CGFF parameters show good agreement with the AAMD simulations and are almost fifty times faster. The data-inspired CGMD model presented here broadens the applicability of molecular dynamics simulations to cross-linked polymers and has the potential to provide insights that will aid the design of polymers with desirable mechanical properties.

Coarse-Graining with Equivariant Neural Networks: A Path Toward Accurate and Data-Efficient Models

Machine learning has recently entered into the mainstream of coarse-grained (CG) molecular modeling and simulation. While a variety of methods for incorporating deep learning into these models exist, many of them involve training neural networks to act directly as the CG force field. This has several benefits of which the most significant is accuracy. Neural networks can inherently incorporate multibody effects during the calculation of CG forces, and a well-trained neural network force field outperforms pairwise basis sets generated from essentially any methodology. However, this comes at a significant cost. First, these models are typically slower than pairwise force fields, even when accounting for specialized hardware, which accelerates the training and integration of such networks. The second and the focus of this paper is the need for a considerable amount of data to train such force fields. It is common to use 10s of microseconds of molecular dynamics data to train a single CG model, which approaches the point of eliminating the CG model's usefulness in the first place. As we investigate in this work, this "data-hunger" trap from neural networks for predicting molecular energies and forces can be remediated in part by incorporating equivariant convolutional operations. We demonstrate that, for CG water, networks that incorporate equivariant convolutional operations can produce functional models using data sets as small as a single frame of reference data, while networks without these operations cannot.

Lessons Learned from Multiobjective Automatic Optimizations of Classical Three-Site Rigid Water Models Using Microscopic and Macroscopic Target Experimental Observables

The development of accurate water models is of primary importance for molecular simulations. Despite their intrinsic approximations, three-site rigid water models are still ubiquitously used to simulate a variety of molecular systems. Automatic optimization approaches have been recently used to iteratively refine three-site water models to fit macroscopic (average) thermodynamic properties, providing state-of-the-art three-site models that still present some deviations from the liquid water properties. Here, we show the results obtained by automatically optimizing three-site rigid water models to fit a combination of microscopic and macroscopic experimental observables. We use Swarm-CG, a multiobjective particle-swarm-optimization algorithm, for training the models to reproduce the experimental radial distribution functions of liquid water at various temperatures (rich in microscopic-level information on, e.g., the local orientation and interactions of the water molecules). We systematically analyze the agreement of these models with experimental observables and the effect of adding macroscopic information to the training set. Our results demonstrate how adding microscopic-rich information in the training of water models allows one to achieve state-of-the-art accuracy in an efficient way. Limitations in the approach and in the approximated description of water in these three-site models are also discussed, providing a demonstrative case useful for the optimization of approximated molecular models, in general.

Factorization in molecular modeling and belief propagation algorithms

Factorization reduces computational complexity, and is therefore an important tool in statistical machine learning of high dimensional systems. Conventional molecular modeling, including molecular dynamics and Monte Carlo simulations of molecular systems, is a large research field based on approximate factorization of molecular interactions. Recently, the local distribution theory was proposed to factorize joint distribution of a given molecular system into trainable local distributions. Belief propagation algorithms are a family of exact factorization algorithms for (junction) trees, and are extended to approximate loopy belief propagation algorithms for graphs with loops. Despite the fact that factorization of probability distribution is the common foundation, computational research in molecular systems and machine learning studies utilizing belief propagation algorithms have been carried out independently with respective track of algorithm development. The connection and differences among these factorization algorithms are briefly presented in this perspective, with the hope to intrigue further development of factorization algorithms for physical modeling of complex molecular systems.

Atomic-Level Insights into Hollow Silica-Based Materials for Drug Delivery: Effects of Wettability and Porosity

Experimental evidence has demonstrated that the drug carrier capacity can be significantly enhanced through the use of hollow silica particles. Nevertheless, the effects of varying functional drug carrier surfaces and porous structures remain ambiguous. This study employs molecular dynamics simulations to examine the effects of varying the surface wettability, pore size, and flow velocity on the transfer process. The different levels of wettability of the silica surface with the coarse-grained water model is illustrated by adjusted interaction parameters. The effect of wettability is investigated. With weak interactions, the flow molecules form a nanodroplet to transfer through the porous structure. A strong interaction will lead to molecules flowing as a liquid film to transfer through the structure. Interestingly, the "contradiction effect" is observed when the flow molecules fail to penetrate the porous structure with weak interactions, during which surface tension dominates their flow behavior. Moreover, different porous structures are considered. The flow behaviors are divided into three processes: (1) fast flowing, (2) transient point, and (3) penetration flowing. Furthermore, the concept of surface molecules is defined to quantitatively measure the effect of porosity. A recommended contact angle is proposed. The results will pave the way for more carrier structures in medical engineering.

Explicit solvent machine-learned coarse-grained model of sodium polystyrene sulfonate to capture polymer structure and dynamics

Strongly charged polyelectrolytes (PEs) demonstrate complex solution behavior as a function of chain length, concentrations, and ionic strength. The viscosity behavior is important to understand and is a core quantity for many applications, but aspects remain a challenge. Molecular dynamics simulations using implicit solvent coarse-grained (CG) models successfully reproduce structure, but are often inappropriate for calculating viscosities. To address the need for CG models which reproduce viscoelastic properties of one of the most studied PEs, sodium polystyrene sulfonate (NaPSS), we report our recent efforts in using Bayesian optimization to develop CG models of NaPSS which capture both polymer structure and dynamics in aqueous solutions with explicit solvent. We demonstrate that our explicit solvent CG NaPSS model with the ML-BOP water model [Chan et al. Nat Commun 10, 379 (2019)] quantitatively reproduces NaPSS chain statistics and solution structure. The new explicit solvent CG model is benchmarked against diffusivities from atomistic simulations and experimental specific viscosities for short chains. We also show that our Bayesian-optimized CG model is transferable to larger chain lengths across a range of concentrations. Overall, this work provides a machine-learned model to probe the structural, dynamic, and rheological properties of polyelectrolytes such as NaPSS and aids in the design of novel, strongly charged polymers with tunable structural and viscoelastic properties.

Coarse-grained versus fully atomistic machine learning for zeolitic imidazolate frameworks

Zeolitic imidazolate frameworks are widely thought of as being analogous to inorganic AB2 phases. We test the validity of this assumption by comparing simplified and fully atomistic machine-learning models for local environments in ZIFs. Our work addresses the central question to what extent chemical information can be "coarse-grained" in hybrid framework materials.

Complex Oxides for Brain-Inspired Computing: A Review

The fields of brain-inspired computing, robotics, and, more broadly, artificial intelligence (AI) seek to implement knowledge gleaned from the natural world into human-designed electronics and machines. In this review, the opportunities presented by complex oxides, a class of electronic ceramic materials whose properties can be elegantly tuned by doping, electron interactions, and a variety of external stimuli near room temperature, are discussed. The review begins with a discussion of natural intelligence at the elementary level in the nervous system, followed by collective intelligence and learning at the animal colony level mediated by social interactions. An important aspect highlighted is the vast spatial and temporal scales involved in learning and memory. The focus then turns to collective phenomena, such as metal-to-insulator transitions (MITs), ferroelectricity, and related examples, to highlight recent demonstrations of artificial neurons, synapses, and circuits and their learning. First-principles theoretical treatments of the electronic structure, and in situ synchrotron spectroscopy of operating devices are then discussed. The implementation of the experimental characteristics into neural networks and algorithm design is then revewed. Finally, outstanding materials challenges that require a microscopic understanding of the physical mechanisms, which will be essential for advancing the frontiers of neuromorphic computing, are highlighted.

Hierarchical Machine Learning of Low-Resolution Coarse-Grained Free Energy Potentials

A force-matching-based method for supervised machine learning (ML) of coarse-grained (CG) free energy (FE) potentials─known as multiscale coarse-graining via force-matching (MSCG/FM)─is an efficient method to develop microscopically informed CG models that are thermodynamically and statistically equivalent to the reference microscopic models. For low-resolution models, when the coarse-graining is at supramolecular scales, objective-oriented clustering of nonbonded particles is required and the reduced description becomes a function of the clustering algorithm. In the present work, we explore the dependence of the ML of the CG Helmholtz FE potential on the clustering algorithm. We consider coarse-graining based on partitional (k-means, leading to Voronoi diagram) and hierarchical agglomerative (bottom-up) clustering algorithms common in unsupervised ML and develop theory connecting the MSCG/FM learned CG Helmholtz potential and the clustering statistics. By combining the agglomerative clustering and the MSCG/FM learning in a recursive manner, we propose an efficient ML methodology to develop the fine-to-low resolution hierarchies of the CG models. The methodology does not suffer from degrading accuracy or increased computational cost to construct larger hierarchies and as such does not impose an upper size limitation of the CG particles resulting from the extended hierarchies. The utility of the methodology is demonstrated by obtaining the bottom-up agglomerative hierarchy for liquid nitromethane from all-atom molecular dynamics (MD) simulations. For agglomerative hierarchies, we prove the existence of renormalization group transformations that indicate self-similarity and allow for learning the low-resolution MSCG/FM potentials at low computational cost by rescaling and renormalizing the certain finer-resolution members of the hierarchy. The hierarchies of the CG models can be used to carry out simulations under constant-pressure conditions.

Performance efficient macromolecular mechanics via sub-nanometer shape based coarse graining

Dimensionality reduction via coarse grain modeling is a valuable tool in biomolecular research. For large assemblies, ultra coarse models are often knowledge-based, relying on a priori information to parameterize models thus hindering general predictive capability. Here, we present substantial advances to the shape based coarse graining (SBCG) method, which we refer to as SBCG2. SBCG2 utilizes a revitalized formulation of the topology representing network which makes high-granularity modeling possible, preserving atomistic details that maintain assembly characteristics. Further, we present a method of granularity selection based on charge density Fourier Shell Correlation and have additionally developed a refinement method to optimize, adjust and validate high-granularity models. We demonstrate our approach with the conical HIV-1 capsid and heteromultimeric cofilin-2 bound actin filaments. Our approach is available in the Visual Molecular Dynamics (VMD) software suite, and employs a CHARMM-compatible Hamiltonian that enables high-performance simulation in the GPU-resident NAMD3 molecular dynamics engine.

Kinetics and Mechanisms of Pressure-Induced Ice Amorphization and Polyamorphic Transitions in a Machine-Learned Coarse-Grained Water Model

Water glasses have attracted considerable attention due to their potential connection to a liquid-liquid transition in supercooled water. Here we use molecular simulations to investigate the formation and phase behavior of water glasses using the machine-learned bond-order parameter (ML-BOP) water model. We produce glasses through hyperquenching of water, pressure-induced amorphization (PIA) of ice, and pressure-induced polyamorphic transformations. We find that PIA of polycrystalline ice occurs at a lower pressure than that of monocrystalline ice and through a different mechanism. The temperature dependence of the amorphization pressure of polycrystalline ice for ML-BOP agrees with that in experiments. We also find that ML-BOP accurately reproduces the density, coordination number, and structural features of low-density (LDA), high-density (HDA), and very high-density (VHDA) amorphous water glasses. ML-BOP accurately reproduces the experimental radial distribution function of LDA but overpredicts the minimum between the first two shells in high-density glasses. We examine the kinetics and mechanism of the transformation between low-density and high-density glasses and find that the sharp nature of these transitions in ML-BOP is similar to that in experiments and all-atom water models with a liquid-liquid transition. Transitions between ML-BOP glasses occur through a spinodal-like mechanism, similar to ice crystallization from LDA. Both glass-to-glass and glass-to-ice transformations have Avrami-Kolmogorov kinetics with exponent n = 1.5 ± 0.2 in experiments and simulations. Importantly, ML-BOP reproduces the competition between crystallization and HDA→LDA transition above the glass transition temperature T_g, and separation of their time scales below T_g, observed also in experiments. These findings demonstrate the ability of ML-BOP to accurately reproduce water properties across various regimes, making it a promising model for addressing the competition between polyamorphic transitions and crystallization in water and solutions.

Machine learning assisted coarse-grained molecular dynamics modeling of meso-scale interfacial fluids

A hallmark of meso-scale interfacial fluids is the multi-faceted, scale-dependent interfacial energy, which often manifests different characteristics across the molecular and continuum scale. The multi-scale nature imposes a challenge to construct reliable coarse-grained (CG) models, where the CG potential function needs to faithfully encode the many-body interactions arising from the unresolved atomistic interactions and account for the heterogeneous density distributions across the interface. We construct the CG models of both single- and two-component polymeric fluid systems based on the recently developed deep coarse-grained potential [Zhang et al., J. Chem. Phys. 149, 034101 (2018)] scheme, where each polymer molecule is modeled as a CG particle. By only using the training samples of the instantaneous force under the thermal equilibrium state, the constructed CG models can accurately reproduce both the probability density function of the void formation in bulk and the spectrum of the capillary wave across the fluid interface. More importantly, the CG models accurately predict the volume-to-area scaling transition for the apolar solvation energy, illustrating the effectiveness to probe the meso-scale collective behaviors encoded with molecular-level fidelity.

Stability and Metastability of Liquid Water in a Machine-Learned Coarse-Grained Model with Short-Range Interactions

Coarse-grained water models are ∼100 times more efficient than all-atom models, enabling simulations of supercooled water and crystallization. The machine-learned monatomic model ML-BOP reproduces the experimental equation of state (EOS) and ice-liquid thermodynamics at 0.1 MPa on par with the all-atom TIP4P/2005 and TIP4P/Ice models. These all-atom models were parametrized using high-pressure experimental data and are either accurate for water's EOS (TIP4P/2005) or ice-liquid equilibrium (TIP4P/Ice). ML-BOP was parametrized from temperature-dependent ice and liquid experimental densities and melting data at 0.1 MPa; its only pressure training is from compression of TIP4P/2005 ice at 0 K. Here we investigate whether ML-BOP replicates the experimental EOS and ice-water thermodynamics along all pressures of ice I. We find that ML-BOP reproduces the temperature, enthalpy, entropy, and volume of melting of hexagonal ice up to 400 MPa and the EOS of water along the melting line with an accuracy that rivals that of both TIP4P/2005 and TIP4P/Ice. We interpret that the accuracy of ML-BOP originates from its ability to capture the shift between compact and open local structures to changes in pressure and temperature. ML-BOP reproduces the sharpening of the tetrahedral peak of the pair distribution function of water upon supercooling, and its pressure dependence. We characterize the region of metastability of liquid ML-BOP with respect to crystallization and cavitation. The accessibility of ice crystallization to simulations of ML-BOP, together with its accurate representation of the thermodynamics of water, makes it promising for investigating the interplay between anomalies, glass transition, and crystallization under conditions challenging to access through experiments.

Transferable and Polarizable Coarse Grained Model for Proteins─ProMPT

The application of classical molecular dynamics (MD) simulations at atomic resolution (fine-grained level, FG), to most biomolecular processes, remains limited because of the associated computational complexity of representing all the atoms. This problem is magnified in the presence of protein-based biomolecular systems that have a very large conformational space, and MD simulations with fine-grained resolution have slow dynamics to explore this space. Current transferable coarse grained (CG) force fields in literature are either limited to only peptides with the environment encoded in an implicit form or cannot capture transitions into secondary/tertiary peptide structures from a primary sequence of amino acids. In this work, we present a transferable CG force field with an explicit representation of the environment for accurate simulations with proteins. The force field consists of a set of pseudoatoms representing different chemical groups that can be joined/associated together to create different biomolecular systems. This preserves the transferability of the force field to multiple environments and simulation conditions. We have added electronic polarization that can respond to environmental heterogeneity/fluctuations and couple it to protein's structural transitions. The nonbonded interactions are parametrized with physics-based features such as solvation and partitioning free energies determined by thermodynamic calculations and matched with experiments and/or atomistic simulations. The bonded potentials are inferred from corresponding distributions in nonredundant protein structure databases. We present validations of the CG model with simulations of well-studied aqueous protein systems with specific protein fold types─Trp-cage, Trpzip4, villin, WW-domain, and β-α-β. We also explore the applications of the force field to study aqueous aggregation of Aβ 16-22 peptides.

Melting points of water models: Current situation

By using the direct coexistence method, we have calculated the melting points of ice I h at normal pressure for three recently proposed water models, namely, TIP3P-FB, TIP4P-FB, and TIP4P-D. We obtained T m = 216 K for TIP3P-FB, T m = 242 K for TIP4P-FB, and T m = 247 K for TIP4P-D. We revisited the melting point of TIP4P/2005 and TIP5P obtaining T m = 250 and 274 K, respectively. We summarize the current situation of the melting point of ice I h for a number of water models and conclude that no model is yet able to simultaneously reproduce the melting temperature of ice I h and the temperature of the maximum in density at room pressure. This probably points toward our both still incomplete knowledge of the potential energy surface of water and the necessity of incorporating nuclear quantum effects to describe both properties simultaneously.

The Critical Diameter for Continuous Evaporation Is between 3 and 4 nm for Hydrophilic Nanopores

Evaporation studies of water using classical molecular dynamics simulations are largely limited due to their high computational expense. This study addresses that issue by developing coarse-grained molecular dynamics models based on Morse potential. Models are optimized based on multi-temperature and at room temperature using machine learning techniques like Genetic Algorithm, Nelder-Mead algorithm, and Strength Pareto Evolutionary Algorithm. The multi-temperature-based model named as Morse-D is found to be more accurate than the single temperature model in representing the water properties at higher temperatures. Using this Morse-D water model, evaporation from hydrophilic nanopores with pore diameter varying from 2 to 5 nm is studied. Our results show that the critical diameter to initiate continuous evaporation at nanopores lies between 3 and 4 nm. A maximum heat flux of 21.3 kW/cm² is observed for a pore diameter of 4.5 nm and a maximum mass flow rate of 16.2 ng/s for a pore diameter of 5 nm. The observed heat flux is an order of magnitude times larger than the currently reported values from experiments in the literature for water, which indicates that we need to focus on nanoscale evaporation to enhance the critical heat flux.

A neural network-assisted open boundary molecular dynamics simulation method

A neural network-assisted molecular dynamics method is developed to reduce the computational cost of open boundary simulations. Particle influxes and neural network-derived forces are applied at the boundaries of an open domain consisting of explicitly modeled Lennard-Jones atoms in order to represent the effects of the unmodeled surrounding fluid. Canonical ensemble simulations with periodic boundaries are used to train the neural network and to sample boundary fluxes. The method, as implemented in the LAMMPS, yields temperature, kinetic energy, potential energy, and pressure values within 2.5% of those calculated using periodic molecular dynamics and runs two orders of magnitude faster than a comparable grand canonical molecular dynamics system.

Many-Body Neural Network-Based Force Field for Structure-Based Coarse-Graining of Water

High-fidelity results from atomistic simulations can only be obtained by using accurate force-field (FF) parameters. Although empirical FFs are commonly used in the modeling of atomistic systems due to their simplicity, they have many limitations inherent in the crude approximations associated with their analytical form. Recent advances in neural network-based FFs have led to more accurate FFs by using symmetry functions or full many-body expansions. However, this approach leads to several issues including the arbitrariness of the symmetry functions, and the intangible and uninterpretable interactions which are only known once the positions of all atoms are set. More importantly, training is another bottleneck, as high-quality force and energy information is required, which is usually not accessible from experimental data. To solve these issues within the context of structure-based coarse-graining methods, we switch in this work to a local-search method to target the reference structure instead of using conventional backpropagation algorithms used to target the forces and energies of the reference structure. Our FF is decomposed into two-, three-, and higher-order terms, where each term is modeled with a separate neural network. To show the versatility of our method, we study four different systems, namely, Stillinger-Weber particles as an atomistic case and three water models, namely SPC/E, MB-pol, and ab initio, as coarse-graining cases. We show the successful application of our approach, by reproducing structural properties of different water models, followed by providing insight into the role of two-and three-body interactions. The results of all models indicate that the double-well isotropic pair potential, the signature of water-like behavior in an isotropic system, vanishes upon inclusion of the three-body interaction, showing dominance of the three-body interaction over the two-body interaction in water-like behavior with the single-well isotropic pair potential.

Microstructure of the fluid particles around the rigid body at the shear-thickening state toward understanding of the fluid mechanics

We studied the shear-thickening behavior of systems containing rigid spherical bodies immersed in smaller particles using non-equilibrium molecular dynamics simulations. We generated shear-thickening states through particle mass modulation of the systems. From the microstructures, i.e., two-dimensional pair distribution functions, we found anisotropic structures resulting from shear thickening, that are explained by the difference between the velocities of rigid bodies and fluid particles. The increasing viscosity in our system originated from collisions between fluid particles and rigid bodies. The lubrication forces defined in macroscale physics are then briefly discussed.

Advances in the study of supercooled water

In this review, we report recent progress in the field of supercooled water. Due to its uniqueness, water presents numerous anomalies with respect to most simple liquids, showing polyamorphism both in the liquid and in the glassy state. We first describe the thermodynamic scenarios hypothesized for the supercooled region and in particular among them the liquid-liquid critical point scenario that has so far received more experimental evidence. We then review the most recent structural indicators, the two-state model picture of water, and the importance of cooperative effects related to the fact that water is a hydrogen-bonded network liquid. We show throughout the review that water's peculiar properties come into play also when water is in solution, confined, and close to biological molecules. Concerning dynamics, upon mild supercooling water behaves as a fragile glass former following the mode coupling theory, and it turns into a strong glass former upon further cooling. Connections between the slow dynamics and the thermodynamics are discussed. The translational relaxation times of density fluctuations show in fact the fragile-to-strong crossover connected to the thermodynamics arising from the existence of two liquids. When considering also rotations, additional crossovers come to play. Mobility-viscosity decoupling is also discussed in supercooled water and aqueous solutions. Finally, the polyamorphism of glassy water is considered through experimental and simulation results both in bulk and in salty aqueous solutions. Grains and grain boundaries are also discussed.

Learning neural network potentials from experimental data via Differentiable Trajectory Reweighting

In molecular dynamics (MD), neural network (NN) potentials trained bottom-up on quantum mechanical data have seen tremendous success recently. Top-down approaches that learn NN potentials directly from experimental data have received less attention, typically facing numerical and computational challenges when backpropagating through MD simulations. We present the Differentiable Trajectory Reweighting (DiffTRe) method, which bypasses differentiation through the MD simulation for time-independent observables. Leveraging thermodynamic perturbation theory, we avoid exploding gradients and achieve around 2 orders of magnitude speed-up in gradient computation for top-down learning. We show effectiveness of DiffTRe in learning NN potentials for an atomistic model of diamond and a coarse-grained model of water based on diverse experimental observables including thermodynamic, structural and mechanical properties. Importantly, DiffTRe also generalizes bottom-up structural coarse-graining methods such as iterative Boltzmann inversion to arbitrary potentials. The presented method constitutes an important milestone towards enriching NN potentials with experimental data, particularly when accurate bottom-up data is unavailable.

On-the-Fly Training of Atomistic Potentials for Flexible and Mechanically Interlocked Molecules

Mechanically interlocked molecules have gained significant attention because of their unique ability to perform well-defined motions originating from their entanglement, which is important for the design of artificial molecular machines. Atomistic simulations based on force fields (FFs) provide detailed insights into such architectures at the molecular level enabling one to predict the resulting functionalities. However, the development of reliable FFs is still challenging and time-consuming, in particular for highly dynamic and interlocked structures such as rotaxanes, which exhibit a large number of different conformers. In the present work, we present an on-the-fly training (OTFT) algorithm. By a guided and nonguided phase space sampling, relevant reference data are automatically and continuously generated and included for the on-the-fly parametrization of the FF based on a population swapping genetic algorithm (psGA). The OTFT approach provides a fast and automated FF parametrization scheme and tackles problems caused by missing phase space information or the need for big data. We demonstrate the high accuracy of the developed FF for flexible molecules with respect to equilibrium and out-of-equilibrium properties. Finally, by applying the ab initio parametrized FF, molecular dynamic simulations were performed up to experimentally relevant time scales (ca. 1 μs) enabling capture in detail of the structural evaluation and mapping out of the free-energy topology. The on-the-fly training approach thus provides a strong foundation toward automated FF developments and large-scale investigations of phenomena in and out of thermal equilibrium.

Recent developments in multiscale free energy simulations

Physics-based free energy simulations enable the rigorous calculation of properties, such as conformational equilibria, solvation or binding free energies. While historically most applications have occurred at the atomistic level of resolution, a range of advances in the past years make it possible now to reliably cross the temporal, spatial and theory scales for the modeling of complex systems or the efficient prediction of results at the accuracy level of expensive quantum-mechanical calculations. In this mini-review, we discuss recent methodological advances as well as opportunities opened up by the introduction of machine learning approaches, which tackle the diverse challenges across the different scales, improve the accuracy and feasibility, and push the boundaries of multiscale free energy simulations.

Machine learning implicit solvation for molecular dynamics

Accurate modeling of the solvent environment for biological molecules is crucial for computational biology and drug design. A popular approach to achieve long simulation time scales for large system sizes is to incorporate the effect of the solvent in a mean-field fashion with implicit solvent models. However, a challenge with existing implicit solvent models is that they often lack accuracy or certain physical properties compared to explicit solvent models as the many-body effects of the neglected solvent molecules are difficult to model as a mean field. Here, we leverage machine learning (ML) and multi-scale coarse graining (CG) in order to learn implicit solvent models that can approximate the energetic and thermodynamic properties of a given explicit solvent model with arbitrary accuracy, given enough training data. Following the previous ML-CG models CGnet and CGSchnet, we introduce ISSNet, a graph neural network, to model the implicit solvent potential of mean force. ISSNet can learn from explicit solvent simulation data and be readily applied to molecular dynamics simulations. We compare the solute conformational distributions under different solvation treatments for two peptide systems. The results indicate that ISSNet models can outperform widely used generalized Born and surface area models in reproducing the thermodynamics of small protein systems with respect to explicit solvent. The success of this novel method demonstrates the potential benefit of applying machine learning methods in accurate modeling of solvent effects for in silico research and biomedical applications.

Ultra-coarse-graining modeling of liquid water

It is a great challenge to develop ultra-coarse-grained models in simulations of biological macromolecules. In this study, the original coarse-graining strategy proposed in our previous work [M. Li and J. Z. H. Zhang, Phys. Chem. Chem. Phys. 23, 8926 (2021)] is first extended to the ultra-coarse-graining (UCG) modeling of liquid water, with the N_C increasing from 4-10 to 20-500. The UCG force field is parameterized by the top-down strategy and subsequently refined on important properties of liquid water by the trial-and-error scheme. The optimal cutoffs for non-bonded interactions in the N_C = 20/100/500 UCG simulations are, respectively, determined on energy convergence. The results show that the average density at 300 K can be accurately reproduced from the well-refined UCG models while it is largely different in describing compressibility, self-diffusion coefficient, etc. The density-temperature relationships predicted by these UCG models are in good agreement with the experiment result. Besides, two polarizable states of the UCG molecules are observed after simulated systems are equilibrated. The ion-water RDFs from the ion-involved N_C = 100 UCG simulation are nearly in accord with the scaled AA ones. Furthermore, the concentration of ions can influence the ratio of two polarizable states in the N_C = 100 simulation. Finally, it is illustrated that the proposed UCG models can accelerate liquid water simulation by 114-135 times, compared with the TIP3P force field. The proposed UCG force field is simple, generic, and transferable, potentially providing valuable information for UCG simulations of large biomolecules.

"Dividing and Conquering" and "Caching" in Molecular Modeling

Molecular modeling is widely utilized in subjects including but not limited to physics, chemistry, biology, materials science and engineering. Impressive progress has been made in development of theories, algorithms and software packages. To divide and conquer, and to cache intermediate results have been long standing principles in development of algorithms. Not surprisingly, most important methodological advancements in more than half century of molecular modeling are various implementations of these two fundamental principles. In the mainstream classical computational molecular science, tremendous efforts have been invested on two lines of algorithm development. The first is coarse graining, which is to represent multiple basic particles in higher resolution modeling as a single larger and softer particle in lower resolution counterpart, with resulting force fields of partial transferability at the expense of some information loss. The second is enhanced sampling, which realizes "dividing and conquering" and/or "caching" in configurational space with focus either on reaction coordinates and collective variables as in metadynamics and related algorithms, or on the transition matrix and state discretization as in Markov state models. For this line of algorithms, spatial resolution is maintained but results are not transferable. Deep learning has been utilized to realize more efficient and accurate ways of "dividing and conquering" and "caching" along these two lines of algorithmic research. We proposed and demonstrated the local free energy landscape approach, a new framework for classical computational molecular science. This framework is based on a third class of algorithm that facilitates molecular modeling through partially transferable in resolution "caching" of distributions for local clusters of molecular degrees of freedom. Differences, connections and potential interactions among these three algorithmic directions are discussed, with the hope to stimulate development of more elegant, efficient and reliable formulations and algorithms for "dividing and conquering" and "caching" in complex molecular systems.

Dynamical properties across different coarse-grained models for ionic liquids

Room-temperature ionic liquids (RTILs) stand out among molecular liquids for their rich physicochemical characteristics, including structural and dynamic heterogeneity. The significance of electrostatic interactions in RTILs results in long characteristic length- and timescales, and has motivated the development of a number of coarse-grained (CG) simulation models. In this study, we aim to better understand the connection between certain CG parameterization strategies and the dynamical properties and transferability of the resulting models. We systematically compare five CG models: a model largely parameterized from experimental thermodynamic observables; a refinement of this model to increase its structural accuracy; and three models that reproduce a given set of structural distribution functions by construction, with varying intramolecular parameterizations and reference temperatures. All five CG models display limited structural transferability over temperature, and also result in various effective dynamical speedup factors, relative to a reference atomistic model. On the other hand, the structure-based CG models tend to result in more consistent cation-anion relative diffusion than the thermodynamic-based models, for a single thermodynamic state point. By linking short- and long-timescale dynamical behaviors, we demonstrate that the varying dynamical properties of the different CG models can be largely collapsed onto a single curve, which provides evidence for a route to constructing dynamically-consistent CG models of RTILs.

Machine learning for reparameterization of four-site water models: TIP4P-BG and TIP4P-BGT

Parameterizing an effective water model is a challenging issue because of the difficulty in maintaining a comprehensive balance among the diverse physical properties of water with a limited number of parameters. The advancement in machine learning provides a promising path to search for a reliable set of parameters. Based on the TIP4P water model, hence, about 6000 molecular dynamics (MD) simulations for pure water at 1 atm and in the range of 273-373 K are conducted here as the training data. The back-propagation (BP) neural network is then utilized to construct an efficient mapping between the model parameters and four crucial physical properties of water, including the density, vaporization enthalpy, self-diffusion coefficient and viscosity. Without additional time-consuming MD simulations, this mapping operation could result in sufficient and accurate data for high-population genetic algorithm (GA) to optimize the model parameters as much as possible. Based on the proposed parameterizing strategy, TIP4P-BG (a conventional four-site water model) and TIP4P-BGT (an advanced model with temperature-dependent parameters) are established. Both the water models exhibit excellent performance with a reasonable balance among the four crucial physical properties. The relevant mean absolute percentage errors are 3.53% and 3.08%, respectively. Further calculations on the temperature of maximum density, isothermal compressibility, thermal expansion coefficient, radial distribution function and surface tension are also performed and the resulting values are in good agreement with the experimental values. Through this water modeling example, the potential of the proposed data-driven machine learning procedure has been demonstrated for parameterizing a MD-based material model.

Bond order redefinition needed to reduce inherent noise in molecular dynamics simulations

In this work, we present the bond order redefinition needed to reduce the inherent noise in order to enhance the accuracy of molecular dynamics simulations. We propose defining the bond order as a fraction of energy distribution. It happens due to the character of the material in nature, which tries to maintain its environment. To show the necessity, we developed a factory empirical interatomic potential (FEIP) for carbon that implements the redefinition with a short-range interaction approach. FEIP has been shown to enhance the accuracy of the calculation of lattice constants, cohesive energy, elastic properties, and phonons compared to experimental data, and can even be compared to other potentials with the long-range interaction approach. The enhancements due to FEIP can reduce the inherent noise, then provide a better prediction of the energy based on the behaviour of the atomic environment. FEIP can also transform simple two-body interactions into many-body interactions, which is useful for enhancing accuracy. Due to implementing the bond order redefinition, FEIP offers faster calculations than other complex interatomic potentials.

Machine Learning of Coarse-Grained Models for Organic Molecules and Polymers: Progress, Opportunities, and Challenges

Machine learning (ML) has emerged as one of the most powerful tools transforming all areas of science and engineering. The nature of molecular dynamics (MD) simulations, complex and time-consuming calculations, makes them particularly suitable for ML research. This review article focuses on recent advancements in developing efficient and accurate coarse-grained (CG) models using various ML methods, in terms of regulating the coarse-graining process, constructing adequate descriptors/features, generating representative training data sets, and optimization of the loss function. Two classes of the CG models are introduced: bottom-up and top-down CG methods. To illustrate these methods and demonstrate the open methodological questions, we survey several important principles in constructing CG models and how these are incorporated into ML methods and improved with specific learning techniques. Finally, we discuss some key aspects of developing machine-learned CG models with high accuracy and efficiency. Besides, we describe how these aspects are tackled in state-of-the-art methods and which remain to be addressed in the near future. We expect that these machine-learned CG models can address thermodynamic consistent, transferable, and representative issues in classical CG models.

Recent Open Issues in Coarse Grained Force Fields

This viewpoint intends to show recent open issues of using coarse grained models in molecular dynamics simulation. It reviews the current knowledge of the comparison between experimental and simulation data of structural and physical chemical properties that depend on the hydrophilic and hydrophobic behavior of the molecule.