DeePCG: Constructing coarse-grained models via deep neural networks

Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems

Machine learning models are poised to make a transformative impact on chemical sciences by dramatically accelerating computational algorithms and amplifying insights available from computational chemistry methods. However, achieving this requires a confluence and coaction of expertise in computer science and physical sciences. This Review is written for new and experienced researchers working at the intersection of both fields. We first provide concise tutorials of computational chemistry and machine learning methods, showing how insights involving both can be achieved. We follow with a critical review of noteworthy applications that demonstrate how computational chemistry and machine learning can be used together to provide insightful (and useful) predictions in molecular and materials modeling, retrosyntheses, catalysis, and drug design.

Multi-body effects in a coarse-grained protein force field

The use of coarse-grained (CG) models is a popular approach to study complex biomolecular systems. By reducing the number of degrees of freedom, a CG model can explore long time- and length-scales inaccessible to computational models at higher resolution. If a CG model is designed by formally integrating out some of the system's degrees of freedom, one expects multi-body interactions to emerge in the effective CG model's energy function. In practice, it has been shown that the inclusion of multi-body terms indeed improves the accuracy of a CG model. However, no general approach has been proposed to systematically construct a CG effective energy that includes arbitrary orders of multi-body terms. In this work, we propose a neural network based approach to address this point and construct a CG model as a multi-body expansion. By applying this approach to a small protein, we evaluate the relative importance of the different multi-body terms in the definition of an accurate model. We observe a slow convergence in the multi-body expansion, where up to five-body interactions are needed to reproduce the free energy of an atomistic model.

Conservative Potentials for a Lattice-Mapped Coarse-Grained Scheme

The conservative potential, arising from a coarse-grain (CG) mapping scheme for nonbonded atomistic particles, is studied. This is a bottom-up approach from first-principles that maps atomistic particles to fluid element-like subcells whose centers lie on a regular, cubic lattice. Unlike standard CG mapping schemes, the current one uses dynamic labeling which on-the-fly changes the CG labels of the particles. The subcells can also be different sizes and shapes, in principle. Equilibrium atomistic molecular dynamics trajectories for different Lennard-Jones fluids are calculated and converted to CG ones, from which CG probability distribution functions are calculated. Correlation studies show position and mass CG variables are uncoupled in a given subcell, as are different vector components of position. Furthermore, the strongest coupling occurs with neighboring cells in specific directions, and the resulting distribution is well described by a multivariate Gaussian. This implies the CG potential has a generalized quadratic form, whose derivative can be determined analytically. A microscopic rationalization is provided for the signs and relative magnitudes of different correlation coefficients, and in some cases, a connection is made with bulk properties of the fluid. We argue the generalized quadratic form should be robust to changes in the particulars of the CG scheme, as well as the nature of the atomistic intermolecular potential. Only a few potential parameters need to be calculated from the underlying atomistic system. This is significant because it indicates the transferability of this form to other, more complex systems. This transferability will be tested in future work, where mapping schemes with fuzzy boundaries will be considered.

Transfer learning of memory kernels for transferable coarse-graining of polymer dynamics

The present work concerns the transferability of coarse-grained (CG) modeling in reproducing the dynamic properties of the reference atomistic systems across a range of parameters. In particular, we focus on implicit-solvent CG modeling of polymer solutions. The CG model is based on the generalized Langevin equation, where the memory kernel plays the critical role in determining the dynamics in all time scales. Thus, we propose methods for transfer learning of memory kernels. The key ingredient of our methods is Gaussian process regression. By integration with the model order reduction via proper orthogonal decomposition and the active learning technique, the transfer learning can be practically efficient and requires minimum training data. Through two example polymer solution systems, we demonstrate the accuracy and efficiency of the proposed transfer learning methods in the construction of transferable memory kernels. The transferability allows for out-of-sample predictions, even in the extrapolated domain of parameters. Built on the transferable memory kernels, the CG models can reproduce the dynamic properties of polymers in all time scales at different thermodynamic conditions (such as temperature and solvent viscosity) and for different systems with varying concentrations and lengths of polymers.

Semi-supervised learning for the study of structural formation in colloidal systems via image recognition

The analysis of the structural formation of colloidal systems using machine learning techniques has recently attracted much attention. In many of these studies, local bond-order parameters (LBOPs) were employed as descriptors, where such LBOPs are suitable mainly for the detection of crystal structures. On the other hand, image-based convolutional neural networks (CNNs) are quite effective in detecting not only crystals but also random structures, and the author demonstrated their efficiency in a previous paper. However, in supervised learning, it is difficult to obtain a correct result when there is an unexpected new phase that was unknown when training the CNN. In this paper, we propose a hybrid scheme that consists of supervised and unsupervised learning techniques, employing two different approaches: image-based CNN and generalized LBOP. The proposed method was applied to two-dimensional colloidal systems, and its efficiency was demonstrated.

Perspective on integrating machine learning into computational chemistry and materials science

Machine learning (ML) methods are being used in almost every conceivable area of electronic structure theory and molecular simulation. In particular, ML has become firmly established in the construction of high-dimensional interatomic potentials. Not a day goes by without another proof of principle being published on how ML methods can represent and predict quantum mechanical properties-be they observable, such as molecular polarizabilities, or not, such as atomic charges. As ML is becoming pervasive in electronic structure theory and molecular simulation, we provide an overview of how atomistic computational modeling is being transformed by the incorporation of ML approaches. From the perspective of the practitioner in the field, we assess how common workflows to predict structure, dynamics, and spectroscopy are affected by ML. Finally, we discuss how a tighter and lasting integration of ML methods with computational chemistry and materials science can be achieved and what it will mean for research practice, software development, and postgraduate training.

From System Modeling to System Analysis: The Impact of Resolution Level and Resolution Distribution in the Computer-Aided Investigation of Biomolecules

The ever increasing computer power, together with the improved accuracy of atomistic force fields, enables researchers to investigate biological systems at the molecular level with remarkable detail. However, the relevant length and time scales of many processes of interest are still hardly within reach even for state-of-the-art hardware, thus leaving important questions often unanswered. The computer-aided investigation of many biological physics problems thus largely benefits from the usage of coarse-grained models, that is, simplified representations of a molecule at a level of resolution that is lower than atomistic. A plethora of coarse-grained models have been developed, which differ most notably in their granularity; this latter aspect determines one of the crucial open issues in the field, i.e. the identification of an optimal degree of coarsening, which enables the greatest simplification at the expenses of the smallest information loss. In this review, we present the problem of coarse-grained modeling in biophysics from the viewpoint of system representation and information content. In particular, we discuss two distinct yet complementary aspects of protein modeling: on the one hand, the relationship between the resolution of a model and its capacity of accurately reproducing the properties of interest; on the other hand, the possibility of employing a lower resolution description of a detailed model to extract simple, useful, and intelligible information from the latter.

Machine-learned potentials for next-generation matter simulations

The choice of simulation methods in computational materials science is driven by a fundamental trade-off: bridging large time- and length-scales with highly accurate simulations at an affordable computational cost. Venturing the investigation of complex phenomena on large scales requires fast yet accurate computational methods. We review the emerging field of machine-learned potentials, which promises to reach the accuracy of quantum mechanical computations at a substantially reduced computational cost. This Review will summarize the basic principles of the underlying machine learning methods, the data acquisition process and active learning procedures. We highlight multiple recent applications of machine-learned potentials in various fields, ranging from organic chemistry and biomolecules to inorganic crystal structure predictions and surface science. We furthermore discuss the developments required to promote a broader use of ML potentials, and the possibility of using them to help solve open questions in materials science and facilitate fully computational materials design.

"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.

A Review of Cellulose Coarse-Grained Models and Their Applications

Cellulose is the most common biopolymer and widely used in our daily life. Due to its unique properties and biodegradability, it has been attracting increased attention in the recent years and various new applications of cellulose and its derivatives are constantly being found. The development of new materials with improved properties, however, is not always an easy task, and theoretical models and computer simulations can often help in this process. In this review, we give an overview of different coarse-grained models of cellulose and their applications to various systems. Various coarse-grained models with different mapping schemes are presented, which can efficiently simulate systems from the single cellulose fibril/crystal to the assembly of many fibrils/crystals. We also discuss relevant applications of these models with a focus on the mechanical properties, self-assembly, chiral nematic phases, conversion between cellulose allomorphs, composite materials and interactions with other molecules.

Bottom-Up Coarse-Grained Modeling of DNA

Recent advances in methodology enable effective coarse-grained modeling of deoxyribonucleic acid (DNA) based on underlying atomistic force field simulations. The so-called bottom-up coarse-graining practice separates fast and slow dynamic processes in molecular systems by averaging out fast degrees of freedom represented by the underlying fine-grained model. The resulting effective potential of interaction includes the contribution from fast degrees of freedom effectively in the form of potential of mean force. The pair-wise additive potential is usually adopted to construct the coarse-grained Hamiltonian for its efficiency in a computer simulation. In this review, we present a few well-developed bottom-up coarse-graining methods, discussing their application in modeling DNA properties such as DNA flexibility (persistence length), conformation, "melting," and DNA condensation.

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.

Coarse-Graining Organic Semiconductors: The Path to Multiscale Design

Four decades of molecular theory and computation have helped form the modern understanding of the physical chemistry of organic semiconductors. Whereas these efforts have historically centered around characterizations of electronic structure at the single-molecule or dimer scale, emerging trends in noncrystalline molecular and polymeric semiconductors are motivating the need for modeling techniques capable of morphological and electronic structure predictions at the mesoscale. Provided the challenges associated with these prediction tasks, the community has begun to evolve a computational toolkit for organic semiconductors incorporating techniques from the fields of soft matter, coarse-graining, and machine learning. Here, we highlight recent advances in coarse-grained methodologies aimed at the multiscale characterization of noncrystalline organic semiconductors. As organic semiconductor performance is dependent on the interplay of mesoscale morphology and molecular electronic structure, specific emphasis is placed on coarse-grained modeling approaches capable of both structural and electronic predictions without recourse to all-atom representations.

Artificial intelligence techniques for integrative structural biology of intrinsically disordered proteins

We outline recent developments in artificial intelligence (AI) and machine learning (ML) techniques for integrative structural biology of intrinsically disordered proteins (IDP) ensembles. IDPs challenge the traditional protein structure-function paradigm by adapting their conformations in response to specific binding partners leading them to mediate diverse, and often complex cellular functions such as biological signaling, self-organization and compartmentalization. Obtaining mechanistic insights into their function can therefore be challenging for traditional structural determination techniques. Often, scientists have to rely on piecemeal evidence drawn from diverse experimental techniques to characterize their functional mechanisms. Multiscale simulations can help bridge critical knowledge gaps about IDP structure-function relationships-however, these techniques also face challenges in resolving emergent phenomena within IDP conformational ensembles. We posit that scalable statistical inference techniques can effectively integrate information gleaned from multiple experimental techniques as well as from simulations, thus providing access to atomistic details of these emergent phenomena.

Deep Learning in Protein Structural Modeling and Design

Deep learning is catalyzing a scientific revolution fueled by big data, accessible toolkits, and powerful computational resources, impacting many fields, including protein structural modeling. Protein structural modeling, such as predicting structure from amino acid sequence and evolutionary information, designing proteins toward desirable functionality, or predicting properties or behavior of a protein, is critical to understand and engineer biological systems at the molecular level. In this review, we summarize the recent advances in applying deep learning techniques to tackle problems in protein structural modeling and design. We dissect the emerging approaches using deep learning techniques for protein structural modeling and discuss advances and challenges that must be addressed. We argue for the central importance of structure, following the "sequence → structure → function" paradigm. This review is directed to help both computational biologists to gain familiarity with the deep learning methods applied in protein modeling, and computer scientists to gain perspective on the biologically meaningful problems that may benefit from deep learning techniques.

Coarse graining molecular dynamics with graph neural networks

Coarse graining enables the investigation of molecular dynamics for larger systems and at longer timescales than is possible at an atomic resolution. However, a coarse graining model must be formulated such that the conclusions we draw from it are consistent with the conclusions we would draw from a model at a finer level of detail. It has been proved that a force matching scheme defines a thermodynamically consistent coarse-grained model for an atomistic system in the variational limit. Wang et al. [ACS Cent. Sci. 5, 755 (2019)] demonstrated that the existence of such a variational limit enables the use of a supervised machine learning framework to generate a coarse-grained force field, which can then be used for simulation in the coarse-grained space. Their framework, however, requires the manual input of molecular features to machine learn the force field. In the present contribution, we build upon the advance of Wang et al. and introduce a hybrid architecture for the machine learning of coarse-grained force fields that learn their own features via a subnetwork that leverages continuous filter convolutions on a graph neural network architecture. We demonstrate that this framework succeeds at reproducing the thermodynamics for small biomolecular systems. Since the learned molecular representations are inherently transferable, the architecture presented here sets the stage for the development of machine-learned, coarse-grained force fields that are transferable across molecular systems.

DNN-assisted statistical analysis of a model of local cortical circuits

In neuroscience, computational modeling is an effective way to gain insight into cortical mechanisms, yet the construction and analysis of large-scale network models—not to mention the extraction of underlying principles—are themselves challenging tasks, due to the absence of suitable analytical tools and the prohibitive costs of systematic numerical exploration of high-dimensional parameter spaces. In this paper, we propose a data-driven approach assisted by deep neural networks (DNN). The idea is to first discover certain input-output relations, and then to leverage this information and the superior computation speeds of the well-trained DNN to guide parameter searches and to deduce theoretical understanding. To illustrate this novel approach, we used as a test case a medium-size network of integrate-and-fire neurons intended to model local cortical circuits. With the help of an accurate yet extremely efficient DNN surrogate, we revealed the statistics of model responses, providing a detailed picture of model behavior. The information obtained is both general and of a fundamental nature, with direct application to neuroscience. Our results suggest that the methodology proposed can be scaled up to larger and more complex biological networks when used in conjunction with other techniques of biological modeling.

Synthesis of computer simulation and machine learning for achieving the best material properties of filled rubber

Molecular dynamics (MD) simulation is used to analyze the mechanical properties of polymerized and nanoscale filled rubber. Unfortunately, the computation time for a simulation can require several months’ computing power, because the interactions of thousands of filler particles must be calculated. To alleviate this problem, we introduce a surrogate convolutional neural network model to achieve faster and more accurate predictions. The major difficulty when employing machine-learning-based surrogate models is the shortage of training data, contributing to the huge simulation costs. To derive a highly accurate surrogate model using only a small amount of training data, we increase the number of training instances by dividing the large-scale simulation results into 3D images of middle-scale filler morphologies and corresponding regional stresses. The images include fringe regions to reflect the influence of the filler constituents outside the core regions. The resultant surrogate model provides higher prediction accuracy than that trained only by images of the entire region. Afterwards, we extract the fillers that dominate the mechanical properties using the surrogate model and we confirm their validity using MD.

Understanding the geometric diversity of inorganic and hybrid frameworks through structural coarse-graining

Much of our understanding of complex structures is based on simplification: for example, metal-organic frameworks are often discussed in the context of "nodes" and "linkers", allowing for a qualitative comparison with simpler inorganic structures. Here we show how such an understanding can be obtained in a systematic and quantitative framework, combining atom-density based similarity (kernel) functions and unsupervised machine learning with the long-standing idea of "coarse-graining" atomic structure. We demonstrate how the latter enables a comparison of vastly different chemical systems, and we use it to create a unified, two-dimensional structure map of experimentally known tetrahedral AB2 networks - including clathrate hydrates, zeolitic imidazolate frameworks (ZIFs), and diverse inorganic phases. The structural relationships that emerge can then be linked to microscopic properties of interest, which we exemplify for structural heterogeneity and tetrahedral density.

Targeted sequence design within the coarse-grained polymer genome

The chemical design of polymers with target structural and/or functional properties represents a grand challenge in materials science. While data-driven design approaches are promising, success with polymers has been limited, largely due to limitations in data availability. Here, we demonstrate the targeted sequence design of single-chain structure in polymers by combining coarse-grained modeling, machine learning, and model optimization. Nearly 2000 unique coarse-grained polymers are simulated to construct and analyze machine learning models. We find that deep neural networks inexpensively and reliably predict structural properties with limited sequence information as input. By coupling trained ML models with sequential model-based optimization, polymer sequences are proposed to exhibit globular, swollen, or rod-like behaviors, which are verified by explicit simulations. This work highlights the promising integration of coarse-grained modeling with data-driven design and represents a necessary and crucial step toward more complex polymer design efforts.

Data-driven coarse-grained modeling of polymers in solution with structural and dynamic properties conserved

We present data-driven coarse-grained (CG) modeling for polymers in solution, which conserves the dynamic as well as structural properties of the underlying atomistic system. The CG modeling is built upon the framework of the generalized Langevin equation (GLE). The key is to determine each term in the GLE by directly linking it to atomistic data. In particular, we propose a two-stage Gaussian process-based Bayesian optimization method to infer the non-Markovian memory kernel from the data of the velocity autocorrelation function (VACF). Considering that the long-time behaviors of the VACF and memory kernel for polymer solutions can exhibit hydrodynamic scaling (algebraic decay with time), we further develop an active learning method to determine the emergence of hydrodynamic scaling, which can accelerate the inference process of the memory kernel. The proposed methods do not rely on how the mean force or CG potential in the GLE is constructed. Thus, we also compare two methods for constructing the CG potential: a deep learning method and the iterative Boltzmann inversion method. With the memory kernel and CG potential determined, the GLE is mapped onto an extended Markovian process to circumvent the expensive cost of directly solving the GLE. The accuracy and computational efficiency of the proposed CG modeling are assessed in a model star-polymer solution system at three representative concentrations. By comparing with the reference atomistic simulation results, we demonstrate that the proposed CG modeling can robustly and accurately reproduce the dynamic and structural properties of polymers in solution.

Generalized Born radii computation using linear models and neural networks

MOTIVATION

Implicit solvent models play an important role in describing the thermodynamics and the dynamics of biomolecular systems. Key to an efficient use of these models is the computation of generalized Born (GB) radii, which is accomplished by algorithms based on the electrostatics of inhomogeneous dielectric media. The speed and accuracy of such computations are still an issue especially for their intensive use in classical molecular dynamics. Here, we propose an alternative approach that encodes the physics of the phenomena and the chemical structure of the molecules in model parameters which are learned from examples.

RESULTS

GB radii have been computed using (i) a linear model and (ii) a neural network. The input is the element, the histogram of counts of neighbouring atoms, divided by atom element, within 16 Å. Linear models are ca. 8 times faster than the most widely used reference method and the accuracy is higher with correlation coefficient with the inverse of 'perfect' GB radii of 0.94 versus 0.80 of the reference method. Neural networks further improve the accuracy of the predictions with correlation coefficient with 'perfect' GB radii of 0.97 and ca. 20% smaller root mean square error.

AVAILABILITY AND IMPLEMENTATION

We provide a C program implementing the computation using the linear model, including the coefficients appropriate for the set of Bondi radii, as Supplementary Material. We also provide a Python implementation of the neural network model with parameter and example files in the Supplementary Material as well.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Machine Learning Force Fields and Coarse-Grained Variables in Molecular Dynamics: Application to Materials and Biological Systems

Machine learning encompasses tools and algorithms that are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems. We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling.

Kernel-Based Machine Learning for Efficient Simulations of Molecular Liquids

Current machine learning (ML) models aimed at learning force fields are plagued by their high computational cost at every integration time step. We describe a number of practical and computationally efficient strategies to parametrize traditional force fields for molecular liquids from ML: the particle decomposition ansatz to two- and three-body force fields, the use of kernel-based ML models that incorporate physical symmetries, the incorporation of switching functions close to the cutoff, and the use of covariant meshing to boost the training set size. Results are presented for model molecular liquids: pairwise Lennard-Jones, three-body Stillinger-Weber, and bottom-up coarse-graining of water. Here, covariant meshing proves to be an efficient strategy to learn canonically averaged instantaneous forces. We show that molecular dynamics simulations with tabulated two- and three-body ML potentials are computationally efficient and recover two- and three-body distribution functions. Many-body representations, decomposition, and kernel regression schemes are all implemented in the open-source software package VOTCA.

Machine Learning for Molecular Simulation

Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for an ML revolution and have already been profoundly affected by the application of existing ML methods. Here we review recent ML methods for molecular simulation, with particular focus on (deep) neural networks for the prediction of quantum-mechanical energies and forces, on coarse-grained molecular dynamics, on the extraction of free energy surfaces and kinetics, and on generative network approaches to sample molecular equilibrium structures and compute thermodynamics. To explain these methods and illustrate open methodological problems, we review some important principles of molecular physics and describe how they can be incorporated into ML structures. Finally, we identify and describe a list of open challenges for the interface between ML and molecular simulation.

Discovery and design of soft polymeric bio-inspired materials with multiscale simulations and artificial intelligence

Establishing the “Materials 4.0” paradigm requires intimate knowledge of the virtual space in materials design.

Adversarial-residual-coarse-graining: Applying machine learning theory to systematic molecular coarse-graining

We utilize connections between molecular coarse-graining (CG) approaches and implicit generative models in machine learning to describe a new framework for systematic molecular CG. Focus is placed on the formalism encompassing generative adversarial networks. The resulting method enables a variety of model parameterization strategies, some of which show similarity to previous CG methods. We demonstrate that the resulting framework can rigorously parameterize CG models containing CG sites with no prescribed connection to the reference atomistic system (termed virtual sites); however, this advantage is offset by the lack of a closed-form expression for the CG Hamiltonian at the resolution obtained after integration over the virtual CG sites. Computational examples are provided for cases in which these methods ideally return identical parameters as relative entropy minimization CG but where traditional relative entropy minimization CG optimization equations are not applicable.

Molecular Modeling Investigations of Sorption and Diffusion of Small Molecules in Glassy Polymers

With a wide range of applications, from energy and environmental engineering, such as in gas separations and water purification, to biomedical engineering and packaging, glassy polymeric materials remain in the core of novel membrane and state-of the art barrier technologies. This review focuses on molecular simulation methodologies implemented for the study of sorption and diffusion of small molecules in dense glassy polymeric systems. Basic concepts are introduced and systematic methods for the generation of realistic polymer configurations are briefly presented. Challenges related to the long length and time scale phenomena that govern the permeation process in the glassy polymer matrix are described and molecular simulation approaches developed to address the multiscale problem at hand are discussed.

Machine Learning of Coarse-Grained Molecular Dynamics Force Fields

Atomistic or ab initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such computationally expensive simulations is the definition of coarse-grained molecular models. Existing coarse-graining approaches define an effective interaction potential to match defined properties of high-resolution models or experimental data. In this paper, we reformulate coarse-graining as a supervised machine learning problem. We use statistical learning theory to decompose the coarse-graining error and cross-validation to select and compare the performance of different models. We introduce CGnets, a deep learning approach, that learns coarse-grained free energy functions and can be trained by a force-matching scheme. CGnets maintain all physically relevant invariances and allow one to incorporate prior physics knowledge to avoid sampling of unphysical structures. We show that CGnets can capture all-atom explicit-solvent free energy surfaces with models using only a few coarse-grained beads and no solvent, while classical coarse-graining methods fail to capture crucial features of the free energy surface. Thus, CGnets are able to capture multibody terms that emerge from the dimensionality reduction.

Computational Modeling of Realistic Cell Membranes

Cell membranes contain a large variety of lipid types and are crowded with proteins, endowing them with the plasticity needed to fulfill their key roles in cell functioning. The compositional complexity of cellular membranes gives rise to a heterogeneous lateral organization, which is still poorly understood. Computational models, in particular molecular dynamics simulations and related techniques, have provided important insight into the organizational principles of cell membranes over the past decades. Now, we are witnessing a transition from simulations of simpler membrane models to multicomponent systems, culminating in realistic models of an increasing variety of cell types and organelles. Here, we review the state of the art in the field of realistic membrane simulations and discuss the current limitations and challenges ahead.

A deep learning approach to the structural analysis of proteins

Deep learning (DL) algorithms hold great promise for applications in the field of computational biophysics. In fact, the vast amount of available molecular structures, as well as their notable complexity, constitutes an ideal context in which DL-based approaches can be profitably employed. To express the full potential of these techniques, though, it is a prerequisite to express the information contained in a molecule’s atomic positions and distances in a set of input quantities that the network can process. Many of the molecular descriptors devised so far are effective and manageable for relatively small structures, but become complex and cumbersome for larger ones. Furthermore, most of them are defined locally, a feature that could represent a limit for those applications where global properties are of interest. Here, we build a DL architecture capable of predicting non-trivial and intrinsically global quantities, that is, the eigenvalues of a protein’s lowest-energy fluctuation modes. This application represents a first, relatively simple test bed for the development of a neural network approach to the quantitative analysis of protein structures, and demonstrates unexpected use in the identification of mechanically relevant regions of the molecule.

Transfer-Learning-Based Coarse-Graining Method for Simple Fluids: Toward Deep Inverse Liquid-State Theory

Machine learning is an attractive paradigm to circumvent difficulties associated with the development and optimization of force-field parameters. In this study, a deep neural network (DNN) is used to study the inverse problem of the liquid-state theory, in particular, to obtain the relation between the radial distribution function (RDF) and the Lennard-Jones (LJ) potential parameters at various thermodynamic states. Using molecular dynamics (MD), many observables, including RDF, are determined once the interatomic potential is specified. However, the inverse problem (parametrization of the potential for a specific RDF) is not straightforward. Here we present a framework integrating DNN with big data from 1.5 TB of MD trajectories with a cumulative simulation time of 52 μs for 26 000 distinct systems to predict LJ potential parameters. Our results show that DNN is successful not only in the parametrization of the atomic LJ liquids but also in parametrizing the LJ potential for coarse-grained models of simple multiatom molecules.

Deep Learning for Nonadiabatic Excited-State Dynamics

In this work we show that deep learning (DL) can be used for exploring complex and highly nonlinear multistate potential energy surfaces of polyatomic molecules and related nonadiabatic dynamics. Our DL is based on deep neural networks (DNNs), which are used as accurate representations of the CASSCF ground- and excited-state potential energy surfaces (PESs) of CH₂NH. After geometries near conical intersection are included in the training set, the DNN models accurately reproduce excited-state topological structures; photoisomerization paths; and, importantly, conical intersections. We have also demonstrated that the results from nonadiabatic dynamics run with the DNN models are very close to those from the dynamics run with the pure ab initio method. The present work should encourage further studies of using machine learning methods to explore excited-state potential energy surfaces and nonadiabatic dynamics of polyatomic molecules.