Active and Transfer Learning of High-Dimensional Neural Network Potentials for Transition Metals.

Classical molecular dynamics (MD) simulations represent a very popular and powerful tool for materials modeling and design. The predictive power of MD hinges on the ability of the interatomic potential to capture the underlying physics and chemistry. There have been decades of seminal work on developing interatomic potentials, albeit with a focus predominantly on capturing the properties of bulk materials. Such physics-based models, while extensively deployed for predicting the dynamics and properties of nanoscale systems over the past two decades, tend to perform poorly in predicting nanoscale potential energy surfaces (PESs) when compared to high-fidelity first-principles calculations. These limitations stem from the lack of flexibility in such models, which rely on a predefined functional form. Machine learning (ML) models and approaches have emerged as a viable alternative to capture the diverse size-dependent cluster geometries, nanoscale dynamics, and the complex nanoscale PESs, without sacrificing the bulk properties. Here, we introduce an ML workflow that combines transfer and active learning strategies to develop high-dimensional neural networks (NNs) for capturing the cluster and bulk properties for several different transition metals with applications in catalysis, microelectronics, and energy storage, to name a few. Our NN first learns the bulk PES from the high-quality physics-based models in literature and subsequently augments this learning via retraining with a higher-fidelity first-principles training data set to concurrently capture both the nanoscale and bulk PES. Our workflow departs from status-quo in its ability to learn from a sparsely sampled data set that nonetheless covers a diverse range of cluster configurations from near-equilibrium to highly nonequilibrium as well as learning strategies that iteratively improve the fingerprinting depending on model fidelity. All the developed models are rigorously tested against an extensive first-principles data set of energies and forces of cluster configurations as well as several properties of bulk configurations for 10 different transition metals. Our approach is material agnostic and provides a methodology to transfer and build upon the learnings from decades of seminal work in molecular simulations on to a new generation of ML-trained potentials to accelerate materials discovery and design.

Correction: Accelerating copolymer inverse design using monte carlo tree search.

Correction for 'Accelerating copolymer inverse design using monte carlo tree search' by Tarak K. Patra et al., Nanoscale, 2020, 12, 23653-23662, https://doi.org/10.1039/D0NR06091G.

Machine learning overcomes human bias in the discovery of self-assembling peptides.

Peptide materials have a wide array of functions, from tissue engineering and surface coatings to catalysis and sensing. Tuning the sequence of amino acids that comprise the peptide modulates peptide functionality, but a small increase in sequence length leads to a dramatic increase in the number of peptide candidates. Traditionally, peptide design is guided by human expertise and intuition and typically yields fewer than ten peptides per study, but these approaches are not easily scalable and are susceptible to human bias. Here we introduce a machine learning workflow-AI-expert-that combines Monte Carlo tree search and random forest with molecular dynamics simulations to develop a fully autonomous computational search engine to discover peptide sequences with high potential for self-assembly. We demonstrate the efficacy of the AI-expert to efficiently search large spaces of tripeptides and pentapeptides. The predictability of AI-expert performs on par or better than our human experts and suggests several non-intuitive sequences with high self-assembly propensity, outlining its potential to overcome human bias and accelerate peptide discovery.

Multi-reward Reinforcement Learning Based Bond-Order Potential to Study Strain-Assisted Phase Transitions in Phosphorene.

We introduce a multi-reward reinforcement learning (RL) approach to train a flexible bond-order potential (BOP) for 2D phosphorene based on ab initio training data sets. Our approach is based on a continuous action space Monte Carlo tree search algorithm that is general and scalable and presents an efficient multiobjective optimization scheme for high-dimensional materials design problems. As a proof-of-concept, we deploy this scheme to parametrize multiple structural and dynamical properties of 2D phosphorene polymorphs. Our RL-trained BOP model adequately captures the structure, energetics, transformation barriers, equation of state, elastic constants, and phonon dispersions of various 2D P polymorphs. We use this model to probe the impact of temperature and strain rate on the phase transition from black (α-P) to blue phosphorene (ß-P) through molecular dynamics simulations. A decrease in critical strain for this phase transition with increase in temperature is observed, and the underlying atomistic mechanisms are discussed.

Learning in continuous action space for developing high dimensional potential energy models.

Reinforcement learning (RL) approaches that combine a tree search with deep learning have found remarkable success in searching exorbitantly large, albeit discrete action spaces, as in chess, Shogi and Go. Many real-world materials discovery and design applications, however, involve multi-dimensional search problems and learning domains that have continuous action spaces. Exploring high-dimensional potential energy models of materials is an example. Traditionally, these searches are time consuming (often several years for a single bulk system) and driven by human intuition and/or expertise and more recently by global/local optimization searches that have issues with convergence and/or do not scale well with the search dimensionality. Here, in a departure from discrete action and other gradient-based approaches, we introduce a RL strategy based on decision trees that incorporates modified rewards for improved exploration, efficient sampling during playouts and a "window scaling scheme" for enhanced exploitation, to enable efficient and scalable search for continuous action space problems. Using high-dimensional artificial landscapes and control RL problems, we successfully benchmark our approach against popular global optimization schemes and state of the art policy gradient methods, respectively. We demonstrate its efficacy to parameterize potential models (physics based and high-dimensional neural networks) for 54 different elemental systems across the periodic table as well as alloys. We analyze error trends across different elements in the latent space and trace their origin to elemental structural diversity and the smoothness of the element energy surface. Broadly, our RL strategy will be applicable to many other physical science problems involving search over continuous action spaces.

Accelerating copolymer inverse design using monte carlo tree search.

There exists a broad class of sequencing problems in soft materials such as proteins and polymers that can be formulated as a heuristic search that involves decision making akin to a computer game. AI gaming algorithms such as Monte Carlo tree search (MCTS) gained prominence after their exemplary performance in the computer Go game and are decision trees aimed at identifying the path (moves) that should be taken by the policy to reach the final winning or optimal solution. Major challenges in inverse sequencing problems are that the materials search space is extremely vast and property evaluation for each sequence is computationally demanding. Reaching an optimal solution by minimizing the total number of evaluations in a given design cycle is therefore highly desirable. We demonstrate that one can adopt this approach for solving the sequencing problem by developing and growing a decision tree, where each node in the tree is a candidate sequence whose fitness is directly evaluated by molecular simulations. We interface MCTS with MD simulations and use a representative example of designing a copolymer compatibilizer, where the goal is to identify sequence specific copolymers that lead to zero interfacial energy between two immiscible homopolymers. We apply the MCTS algorithm to polymer chain lengths varying from 10-mer to 30-mer, wherein the overall search space varies from 210 (1024) to 230 (∼1 billion). In each case, we identify a target sequence that leads to zero interfacial energy within a few hundred evaluations demonstrating the scalability and efficiency of MCTS in exploring practical materials design problems with exceedingly vast chemical/material search space. Our MCTS-MD framework can be easily extended to several other polymer and protein inverse design problems, in particular, for cases where sequence-property data is either unavailable and/or is resource intensive.

Promoting Noncovalent Intermolecular Interactions Using a C60 Core Particle in Aqueous PC60s-Covered Colloids for Ultraefficient Photoinduced Particle Activity.

Noncovalent intermolecular interactions in nanomaterials, such as van der Waals effects, allow adjustment of the nanoscopic size of compounds and their conformation in molecular crystal regimes. These strong interactions permit small particle sizes to be maintained as the crystals grow. In particular, these effects can be leveraged in the confined/reinforcing phase of molecules. With this in mind, we used C60 molecules as a core particle in single-PC60 surfactant-covered colloid in a water-processable system. Compared with our previous results based on a PC61BM core-PC60 shell particle, the PC60-C60 colloid had a considerably smaller spherical structure due to the increased intermolecular interactions between C60 (fullerene) molecules. Interestingly, the conformation of C60 aggregates was altered depending on the mixed solvents and their volume fraction in the organic phase, which strongly affected the structural properties of the PC60-C60 colloids. The particle facilitated strong interactions with a p-type core sphere when it was introduced as the shell part of a p-n heterojunction particle. This direct interaction provided effective electronic communication between p- and n-type particles, resulting in ultraefficient photonic properties, particularly in charge separation in aqueous heterostructured colloids. This enabled the development of an extremely efficient photovoltaic device with a 6.74% efficiency, which could provide the basis for creating high-performance water-processable solar cells based on p-n heterostructured NPs.

"Teamwork Makes the Dream Work": Tribal Competition Evolutionary Search as a Surrogate for Free-Energy-Based Structural Predictions.

Crystal structure prediction has been a grand challenge in material science owing to the large configurational space that one must explore. Evolutionary (genetic) algorithms coupled with first principles calculations are commonly used in crystal structure prediction to sample the ground and metastable states of materials based on configurational energies. However, crystal structure predictions at finite temperature ( T), pressure ( P), and composition ( X) require a free-energy-based search that is often computationally expensive and tedious. Here, we introduce a new machine-learning workflow for structure prediction that is based on a concept inspired by the evolution of human tribes in primitive society. Our tribal genetic algorithm (GA) combines configurational sampling with evolutionary optimization to accurately predict entropically stabilized phases at finite ( T, P, X), at a computational cost that is an order of magnitude smaller than that required for a free-energy-based search. In a departure from standard GA techniques, the populations of individuals are divided into multiple tribes based on a bond-order fingerprint, and genetic operations are modified to ensure that cluster configurations are sampled adequately to capture entropic contributions. Team competition introduced into the evolutionary process allows winning teams (representing a better set of individuals) to expand their sizes; this translates into a more expanded search of the phase space allowing us to explore solutions near possible global minimum. Each team explores a specific section of the structural phase space and avoids bias on solutions arising from the use of individual populations in a purely energy-based search. We demonstrate the efficacy of our approach by performing the structural prediction of a representative two-dimensional two-body system as well as Lennard-Jones clusters over a range of temperatures up to its melting point. Our approach outperforms the standard GA approaches and enables structural search under "real nonambient conditions" on both bulk systems and finite-sized clusters.

Machine learning coarse grained models for water.

An accurate and computationally efficient molecular level description of mesoscopic behavior of ice-water systems remains a major challenge. Here, we introduce a set of machine-learned coarse-grained (CG) models (ML-BOP, ML-BOPdih, and ML-mW) that accurately describe the structure and thermodynamic anomalies of both water and ice at mesoscopic scales, all at two orders of magnitude cheaper computational cost than existing atomistic models. In a significant departure from conventional force-field fitting, we use a multilevel evolutionary strategy that trains CG models against not just energetics from first-principles and experiments but also temperature-dependent properties inferred from on-the-fly molecular dynamics (~ 10's of milliseconds of overall trajectories). Our ML BOP models predict both the correct experimental melting point of ice and the temperature of maximum density of liquid water that remained elusive to-date. Our ML workflow navigates efficiently through the high-dimensional parameter space to even improve upon existing high-quality CG models (e.g. mW model).

Configurational-Bias Monte Carlo Back-Mapping Algorithm for Efficient and Rapid Conversion of Coarse-Grained Water Structures into Atomistic Models.

Coarse-grained molecular dynamics (MD) simulations represent a powerful approach to simulate longer time scale and larger length scale phenomena than those accessible to all-atom models. The gain in efficiency, however, comes at the cost of atomistic details. The reverse transformation, also known as back mapping, of coarse-grained beads into their atomistic constituents represents a major challenge. Most existing approaches are limited to specific molecules or specific force fields and often rely on running a long-time atomistic MD of the back-mapped configuration to arrive at an optimal solution. Such approaches are problematic when dealing with systems with high diffusion barriers. Here, we introduce a new extension of the configurational-bias Monte Carlo (CBMC) algorithm, which we term the crystalline-configurational-bias Monte Carlo (C-CBMC) algorithm, which allows rapid and efficient conversion of a coarse-grained model back into its atomistic representation. Although the method is generic, we use a coarse-grained water model as a representative example and demonstrate the back mapping or reverse transformation for model systems ranging from the ice-liquid water interface to amorphous and crystalline ice configurations. A series of simulations using the TIP4P/Ice model are performed to compare the new CBMC method to several other standard Monte Carlo and molecular dynamics-based back-mapping techniques. In all of the cases, the C-CBMC algorithm is able to find optimal hydrogen-bonded configuration many thousand evaluations/steps sooner than the other methods compared within this paper. For crystalline ice structures, such as a hexagonal, cubic, and cubic-hexagonal stacking disorder structures, the C-CBMC was able to find structures that were between 0.05 and 0.1 eV/water molecule lower in energy than the ground-state energies predicted by the other methods. Detailed analysis of the atomistic structures shows a significantly better global hydrogen positioning when contrasted with the existing simpler back-mapping methods. The errors in the radial distribution functions (RDFs) of back-mapped configuration relative to reference configuration for the C-CBMC, MD, and MC were found to be 6.9, 8.7, and 12.9, respectively, for the hexagonal system. For the cubic system, the relative errors of the RDFs for the C-CBMC, MD, and MC were found to be 18.2, 34.6, and 39.0, respectively. Our results demonstrate the efficiency and efficacy of our new back-mapping approach, especially for crystalline systems where simple force-field-based relaxations have a tendency to get trapped in local minima.

Improving the Efficiency of Configurational-Bias Monte Carlo: Extension of the Jacobian-Gaussian Scheme to Interior Sections of Cyclic and Polymeric Molecules.

The Jacobian-Gaussian method, which has recently been developed for generating bending angle trials, is extended to the conformational sampling of inner segments of a long chain or cyclic molecule where regular configurational-bias Monte Carlo was found to be very inefficient or simply incapable (i.e., for the cyclic case). For these molecules, a new conformational move would be required where one interior section is relocated while the rest of the molecule, before and after this section, is fixed. Techniques have been developed to extend the regular configurational-bias Monte Carlo to such a fixed-end points case by introducing a biasing probability function. Each trial is weighted by this function to ensure the closure of the molecule by selecting appropriate growth direction. However, the acceptance rate might be reduced significantly due to the incongruity of this weight and the energy weight. In addition, the last steps of closing the molecule include several bending and torsional energies that are coupled to each other. Thus, generating a trial that is acceptable for all energetic terms becomes a difficult problem. The Jacobian-Gaussian method can overcome these two problems with the following two principles: First, basic geometrical constraints must be fulfilled to guarantee molecular closure, which avoids the need of the biasing probability function. Second, the growth variables are transformed into those used explicitly in expressing the various intramolecular energies between fixed points to allow for the trials to be generated directly according to the Boltzmann distributions of these energetic terms, which improves the acceptance rates dramatically. This method has been examined on the growth of inner segments of linear and cyclic alkanes, which proves its higher efficiency over that of traditional methods.

Improving the Efficiency of Configurational-Bias Monte Carlo: A Jacobian-Gaussian Scheme for Generating Bending Angle Trials for Linear and Branched Molecules.

A new method, called Jacobian-Gaussian scheme, has been developed to overcome the challenge of bending angle generation for linear and branched molecules in configurational-bias Monte Carlo. This method is simple, general, fast, and robust which can yield high acceptance rates. Since there are several bending angles in a branched point and their energies are coupled to each other, generating one trial that is acceptable for all energetic terms is a difficult problem. In order to reach reasonable acceptance rates, traditional methods either generate many trials uniformly or use prepared tables to generate trials according to the expected distribution. While the former consumes a considerable amount of simulation time, the later needs a modest amount of memory to store the tabulated distribution information. In contrast, this Jacobian-Gaussian scheme decouples the energetic terms through simple variable transformations and then generates each bending angle according to its Boltzmann distribution. Thus, high acceptance rates can be obtained using only a few trials without requirement for generation and storage of distribution data. This method has been shown to be efficient for various molecular types including propane, 2-methylpropane, 2,2-dimethylpropane, and acetone.

Improved Monte Carlo Scheme for Efficient Particle Transfer in Heterogeneous Systems in the Grand Canonical Ensemble: Application to Vapor-Liquid Nucleation.

Reformulation of existing Monte Carlo algorithms used in the study of grand canonical systems has yielded massive improvements in efficiency. Here we present an energy biasing scheme designed to address targeting issues encountered in particle swap moves using sophisticated algorithms such as the Aggregation-Volume-Bias and Unbonding-Bonding methods. Specifically, this energy biasing scheme allows a particle to be inserted to (or removed from) a region that is more acceptable. As a result, this new method showed a several-fold increase in insertion/removal efficiency in addition to an accelerated rate of convergence for the thermodynamic properties of the system.

Improving the efficiency of configurational-bias Monte Carlo: a density-guided method for generating bending angle trials for linear and branched molecules.

A new method has been developed to generate bending angle trials to improve the acceptance rate and the speed of configurational-bias Monte Carlo. Whereas traditionally the trial geometries are generated from a uniform distribution, in this method we attempt to use the exact probability density function so that each geometry generated is likely to be accepted. In actual practice, due to the complexity of this probability density function, a numerical representation of this distribution function would be required. This numerical table can be generated a priori from the distribution function. This method has been tested on a united-atom model of alkanes including propane, 2-methylpropane, and 2,2-dimethylpropane, that are good representatives of both linear and branched molecules. It has been shown from these test cases that reasonable approximations can be made especially for the highly branched molecules to reduce drastically the dimensionality and correspondingly the amount of the tabulated data that is needed to be stored. Despite these approximations, the dependencies between the various geometrical variables can be still well considered, as evident from a nearly perfect acceptance rate achieved. For all cases, the bending angles were shown to be sampled correctly by this method with an acceptance rate of at least 96% for 2,2-dimethylpropane to more than 99% for propane. Since only one trial is required to be generated for each bending angle (instead of thousands of trials required by the conventional algorithm), this method can dramatically reduce the simulation time. The profiling results of our Monte Carlo simulation code show that trial generation, which used to be the most time consuming process, is no longer the time dominating component of the simulation.

Surface induced nucleation of a Lennard-Jones system on an implicit surface at sub-freezing temperatures: a comparison with the classical nucleation theory.

The aggregation-volume-bias Monte Carlo method was employed to study surface-induced nucleation of Lennard-Jonesium on an implicit surface below the melting point. It was found that surfaces catalyze not only the formation of the droplets (where the nucleation free energy barriers were shown to decrease with increasing surface interaction strength), but also the transition of these droplets into crystal structures due to the surface-induced layering effects. However, this only occurs under suitable interaction strength. When surface attraction is too strong, crystallization is actually inhibited due to the spread of the particles across the surface and corresponding formation of two-dimensional clusters. The simulation results were also used to examine the bulk-droplet based classical nucleation theory for surface-induced nucleation, particularly the additional contact angle term used to describe both the nucleation free energy barrier heights and the critical cluster sizes compared to its homogeneous nucleation formalism. Similar to what has been found previously for homogeneous nucleation, the theory does poorly toward the high-supersaturation region when the critical clusters are small and fractal, but the theoretical predictions on both barrier heights and critical cluster sizes improve rapidly with the decrease of the supersaturation.

Vapor-liquid nucleation in two dimensions: on the intriguing sign switch of the errors of the classical nucleation theory.

A nucleation study of a two-dimensional (2D) Lennard-Jones (LJ) system is done using the aggregation-volume-bias Monte Carlo with umbrella sampling method. The results obtained from this simulation study was compared to those predicted by the classical nucleation theory (CNT). It was found that the nucleation free energy obtained for this 2D LJ system was underestimated by CNT; however, this result is significantly different from that found for the 3D LJ system where CNT overestimates the free energy. These results are generally in agreement with previous studies on these systems. While both errors can be traced to the incorrect description of the smallest clusters by the theory, structural analysis reveals striking differences between 2D and 3D clusters, leading to a possible source for this observed sign switch. In particular, the radius of gyration data indicates that for the 3D LJ system, clusters formed at the beginning are fractal and the cluster growth is accompanied by an increase of the dimensionality, whereas clusters in 2D show little sign of this dimensionality transition.