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Speckle patterns produced by coherent X-ray have a close relationship with the internal structure of materials but quantitative inversion of the relationship to determine structure from speckle patterns is challenging. Here, we investigate the link between coherent X-ray speckle patterns and sample structures using a model 2D disk system and explore the ability of machine learning to learn aspects of the relationship. Specifically, we train a deep neural network to classify the coherent X-ray speckle patterns according to the disk number density in the corresponding structure. It is demonstrated that the classification system is accurate for both non-disperse and disperse size distributions.

Defect dynamics in materials are of central importance to a broad range of technologies from catalysis to energy storage systems to microelectronics. Material functionality depends strongly on the nature and organization of defects, their arrangements often involve intermediate or transient states that present a high barrier for transformation. The lack of knowledge of these intermediate states and the presence of this energy barrier presents a serious challenge for inverse defect design, especially for gradient-based approaches. Here, we present a reinforcement learning (Monte Carlo Tree Search) based on delayed rewards that allow for efficient search of the defect configurational space and allows us to identify optimal defect arrangements in low dimensional materials. Using a representative case of 2D MoS2, we demonstrate that the use of delayed rewards allows us to efficiently sample the defect configurational space and overcome the energy barrier for a wide range of defect concentrations (from 1.5% to 8% S vacancies), the system evolves from an initial randomly distributed S vacancies to one with extended S line defects consistent with previous experimental studies. Detailed analysis in the feature space allows us to identify the optimal pathways for this defect transformation and arrangement. Comparison with other global optimization schemes like genetic algorithms suggests that the MCTS with delayed rewards takes fewer evaluations and arrives at a better quality of the solution. The implications of the various sampled defect configurations on the 2H to 1T phase transitions in MoS2 are discussed. Overall, we introduce a Reinforcement Learning (RL) strategy employing delayed rewards that can accelerate the inverse design of defects in materials for achieving targeted functionality.

We consider the problem of black-box function optimization over the boolean hypercube. Despite the vast literature on black-box function optimization over continuous domains, not much attention has been paid to learning models for optimization over combinatorial domains until recently. However, the computational complexity of the recently devised algorithms are prohibitive even for moderate numbers of variables; drawing one sample using the existing algorithms is more expensive than a function evaluation for many black-box functions of interest. To address this problem, we propose a computationally efficient model learning algorithm based on multilinear polynomials and exponential weight updates. In the proposed algorithm, we alternate between simulated annealing with respect to the current polynomial representation and updating the weights using monomial experts' advice. Numerical experiments on various datasets in both unconstrained and sum-constrained boolean optimization indicate the competitive performance of the proposed algorithm, while improving the computational time up to several orders of magnitude compared to state-of-the-art algorithms in the literature.

Small metal clusters are of fundamental scientific interest and of tremendous significance in catalysis. These nanoscale clusters display diverse geometries and structural motifs depending on the cluster size; a knowledge of this size-dependent structural motifs and their dynamical evolution has been of longstanding interest. Classical MD typically employ predefined functional forms which limits their ability to capture such complex size-dependent structural and dynamical transformation. Neural Network (NN) based potentials represent flexible alternatives and in principle, well-trained NN potentials can provide high level of flexibility, transferability and accuracy on-par with the reference model used for training. A major challenge, however, is that NN models are interpolative and requires large quantities of training data to ensure that the model adequately samples the energy landscape both near and far-from-equilibrium. Here, we introduce an active learning (AL) scheme that trains a NN model on-the-fly with minimal amount of first-principles based training data. Our AL workflow is initiated with a sparse training dataset (1 to 5 data points) and is updated on-the-fly via a Nested Ensemble Monte Carlo scheme that iteratively queries the energy landscape in regions of failure and updates the training pool to improve the network performance. Using a representative system of gold clusters, we demonstrate that our AL workflow can train a NN with ~500 total reference calculations. Our NN predictions are within 30 meV/atom and 40 meV/\AA of the reference DFT calculations. Moreover, our AL-NN model also adequately captures the various size-dependent structural and dynamical properties of gold clusters in excellent agreement with DFT calculations and available experiments.

There exists a broad class of sequencing problems, for example, in proteins and polymers that can be formulated as a heuristic search algorithm that involve 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.

Phase diagrams are an invaluable tool for material synthesis and provide information on the phases of the material at any given thermodynamic condition. Conventional phase diagram generation involves experimentation to provide an initial estimate of thermodynamically accessible phases, followed by use of phenomenological models to interpolate between the available experimental data points and extrapolate to inaccessible regions. Such an approach, combined with first-principles calculations and data-mining techniques, has led to exhaustive thermodynamic databases albeit at distinct thermodynamic equilibria. In contrast, materials during their synthesis, operation, or processing, may not reach their thermodynamic equilibrium state but, instead, remain trapped in a local free energy minimum, that may exhibit desirable properties. Mapping these metastable phases and their thermodynamic behavior is highly desirable but currently lacking. Here, we introduce an automated workflow that integrates first principles physics and atomistic simulations with machine learning (ML), and high-performance computing to allow rapid exploration of the metastable phases of a given elemental composition. Using a representative material, carbon, with a vast number of metastable phases without parent in equilibrium, we demonstrate automatic mapping of hundreds of metastable states ranging from near equilibrium to those far-from-equilibrium. Moreover, we incorporate the free energy calculations into a neural-network-based learning of the equations of state that allows for construction of metastable phase diagrams. High temperature high pressure experiments using a diamond anvil cell on graphite sample coupled with high-resolution transmission electron microscopy are used to validate our metastable phase predictions. Our introduced approach is general and broadly applicable to single and multi-component systems., Comment: 32 pages 16 figures; v3: Added acknowledgments and removed affiliations from author metadata

Due to the absence of matching carbon atoms at honeycomb centers with carbon atoms in adjacent graphene sheets, theorists predicted that a sliding process is needed to form AA, AB, or ABC stacking when directly converting graphite into sp3 bonded diamond. Here, using twisted bilayer graphene, which naturally provides AA and AB stacking configurations, we report the ultrafast formation of a transient 2D diamond-like structure (which is not observed in aligned graphene) under femtosecond laser irradiation. This photo-induced phase transition is evidenced by the appearance of new bond lengths of 1.94A and 3.14A in the time-dependent differential pair distribution function using MeV ultrafast electron diffraction. Molecular dynamics and first principles calculation indicate that sp3 bonds nucleate at AA and AB stacked areas in moire pattern. This work sheds light on the direct graphite-to-diamond transformation mechanism, which has not been fully understood for more than 60 years.

The ever-increasing power of supercomputers coupled with highly scalable simulation codes have made molecular dynamics an indispensable tool in applications ranging from predictive modeling of materials to computational design and discovery of new materials for a broad range of applications. Multi-fidelity scale bridging between the various flavors of molecular dynamics i.e. ab-initio, classical and coarse-grained models has remained a long-standing challenge. Here, we introduce our framework BLAST (Bridging Length/time scales via Atomistic Simulation Toolkit) that leverages machine learning principles to address this challenge. BLAST is a multi-fidelity scale bridging framework that provide users with the capabilities to train and develop their own classical atomistic and coarse-grained interatomic potentials (force fields) for molecular simulations. BLAST is designed to address several long-standing problems in the molecular simulations community, such as unintended misuse of existing force fields due to knowledge gap between developers and users, bottlenecks in traditional force field development approaches, and other issues relating to the accuracy, efficiency, and transferability of force fields. Here, we discuss several important aspects in force field development and highlight features in BLAST that enable its functionalities and ease of use.

We introduce a coarse-grained deep neural network model (CG-DNN) for liquid water that utilizes 50 rotational and translational invariant coordinates, and is trained exclusively against energies of ~30,000 bulk water configurations. Our CG-DNN potential accurately predicts both the energies and molecular forces of water; within 0.9 meV/molecule and 54 meV/angstrom of a reference (coarse-grained bond-order potential) model. The CG-DNN water model also provides good prediction of several structural, thermodynamic, and temperature dependent properties of liquid water, with values close to that obtained from the reference model. More importantly, CG-DNN captures the well-known density anomaly of liquid water observed in experiments. Our work lays the groundwork for a scheme where existing empirical water models can be utilized to develop fully flexible neural network framework that can subsequently be trained against sparse data from high-fidelity albeit expensive beyond-DFT calculations.

ANNs are currently trained by generating large quantities (On the order of $10^{4}$ or greater) of structural data in hopes that the ANN has adequately sampled the energy landscape both near and far-from-equilibrium. This can, however, be a bit prohibitive when it comes to more accurate levels of quantum theory. As such it is desirable to train a model using the absolute minimal data set possible, especially when costs of high-fidelity calculations such as CCSD and QMC are high. Here, we present an Active Learning approach that iteratively trains an ANN model to faithfully replicate the coarse-grained energy surface of water clusters using only 426 total structures in its training data. Our active learning workflow starts with a sparse training dataset which is continually updated via a Monte Carlo scheme that sparsely queries the energy landscape and tests the network performance. Next, the network is retrained with an updated training set that includes failed configurations/energies from previous iteration until convergence is attained. Once trained, we generate an extensive test set of ~100,000 configurations sampled across clusters ranging from 1 to 200 molecules and demonstrate that the trained network adequately reproduces the energies (within mean absolute error (MAE) of ~ 2 meV/molecule) and forces (MAE ~ 40 meV/{\r{A}}) compared to the reference model. More importantly, the trained ANN model also accurately captures both the structure as well as the free energy as a function of the various cluster sizes. Overall, this study reports a new active learning scheme with promising strategy to develop accurate force-fields for molecular simulations using extremely sparse training data sets.

Atom-probe tomography (APT) facilitates nano- and atomic-scale characterization and analysis of microstructural features. Specifically, APT is well suited to study the interfacial properties of granular or heterophase systems. Traditionally, the identification of the interface between, for precipitate and matrix phases, in APT data has been obtained either by extracting iso-concentration surfaces based on a user-supplied concentration value or by manually perturbing the concentration value until the iso-concentration surface qualitatively matches the interface. These approaches are subjective, not scalable, and may lead to inconsistencies due to local composition inhomogeneities. We propose a digital image segmentation approach based on deep neural networks that transfer learned knowledge from natural images to automatically segment the data obtained from APT into different phases. This approach not only provides an efficient way to segment the data and extract interfacial properties but does so without the need for expensive interface labeling for training the segmentation model. We consider here a system with a precipitate phase in a matrix and with three different interface modalities---layered, isolated, and interconnected---that are obtained for different relative geometries of the precipitate phase. We demonstrate the accuracy of our segmentation approach through qualitative visualization of the interfaces, as well as through quantitative comparisons with proximity histograms obtained by using more traditional approaches., Comment: 23 pages, 6 figures