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The slow microstructural evolution of materials often plays a key role in determining material properties. When the unit steps of the evolution process are slow, direct simulation approaches such as molecular dynamics become prohibitive and Kinetic Monte-Carlo (kMC) algorithms, where the state-to-state evolution of the system is represented in terms of a continuous-time Markov chain, are instead frequently relied upon to efficiently predict long-time evolution. The accuracy of kMC simulations however relies on the complete and accurate knowledge of reaction pathways and corresponding kinetics. This requirement becomes extremely stringent in complex systems such as concentrated alloys where the astronomical number of local atomic configurations makes the a priori tabulation of all possible transitions impractical. Machine learning models of transition kinetics have been used to mitigate this problem by enabling the efficient on-the-fly prediction of kinetic parameters. In this study, we show how physics-informed ML architectures can exactly enforce the detailed balance condition, by construction. Using the diffusion of a vacancy in a concentrated alloy as an example, we show that such ML architectures also exhibit superior performance in terms of prediction accuracy, demonstrating that the imposition of physical constraints can facilitate the accurate learning of barriers at no increase in computational cost., Comment: 20 pages, 11 figures

The development of multifunctional devices calls for the discovery of new layered materials with novel electronic properties. f-electron systems naturally host a rich set of competing and intertwining phases owning to the presence of strong spin-orbit coupling, electron-electron interactions, and hybridization between itinerant and local electrons. However, very little attention has been devoted to exploring the f-electron family of compounds for new promising layered material candidates. Here, we identify 295 rare earth compounds from across the lanthanide series of elements that exhibit a spectrum of lattice symmetries and electronic properties. In particular, we find metallic compounds and insulating systems with band gaps covering a 0.1 eV to 5.3 eV range which opens new possibilities in infrared quantum sensors, designer photocatalysts, and tunable transistors. The inclusion of 4f-states in a layered system also suggests the possibility of 2D confined heavy-fermion superconductivity and topological semimetals. Our study serves as a springboard to further systematic theoretical investigation of correlation-driven properties of the 4f and other 2D materials composed of heavy elements., Comment: 6 pages main text, 3 figures, 7 pages supplementary material

We propose a novel model-centric evaluation framework, OmniInput, to evaluate the quality of an AI/ML model's predictions on all possible inputs (including human-unrecognizable ones), which is crucial for AI safety and reliability. Unlike traditional data-centric evaluation based on pre-defined test sets, the test set in OmniInput is self-constructed by the model itself and the model quality is evaluated by investigating its output distribution. We employ an efficient sampler to obtain representative inputs and the output distribution of the trained model, which, after selective annotation, can be used to estimate the model's precision and recall at different output values and a comprehensive precision-recall curve. Our experiments demonstrate that OmniInput enables a more fine-grained comparison between models, especially when their performance is almost the same on pre-defined datasets, leading to new findings and insights for how to train more robust, generalizable models.

Methodologies for training machine learning potentials (MLPs) to quantum-mechanical simulation data have recently seen tremendous progress. Experimental data has a very different character than simulated data, and most MLP training procedures cannot be easily adapted to incorporate both types of data into the training process. We investigate a training procedure based on Iterative Boltzmann Inversion that produces a pair potential correction to an existing MLP, using equilibrium radial distribution function data. By applying these corrections to a MLP for pure aluminum based on Density Functional Theory, we observe that the resulting model largely addresses previous overstructuring in the melt phase. Interestingly, the corrected MLP also exhibits improved performance in predicting experimental diffusion constants, which are not included in the training procedure. The presented method does not require auto-differentiating through a molecular dynamics solver, and does not make assumptions about the MLP architecture. The results suggest a practical framework of incorporating experimental data into machine learning models to improve accuracy of molecular dynamics simulations.

The output distribution of a neural network (NN) over the entire input space captures the complete input-output mapping relationship, offering insights toward a more comprehensive NN understanding. Exhaustive enumeration or traditional Monte Carlo methods for the entire input space can exhibit impractical sampling time, especially for high-dimensional inputs. To make such difficult sampling computationally feasible, in this paper, we propose a novel Gradient-based Wang-Landau (GWL) sampler. We first draw the connection between the output distribution of a NN and the density of states (DOS) of a physical system. Then, we renovate the classic sampler for the DOS problem, the Wang-Landau algorithm, by replacing its random proposals with gradient-based Monte Carlo proposals. This way, our GWL sampler investigates the under-explored subsets of the input space much more efficiently. Extensive experiments have verified the accuracy of the output distribution generated by GWL and also showcased several interesting findings - for example, in a binary image classification task, both CNN and ResNet mapped the majority of human unrecognizable images to very negative logit values.

In Monte Carlo simulations, proposed configurations are accepted or rejected according to an acceptance ratio, which depends on an underlying probability distribution and an a priori sampling probability. By carefully selecting the probability distribution from which random variates are sampled, simulations can be made more efficient, by virtue of an autocorrelation time reduction. In this paper, we illustrate how to directly sample random variates from a two dimensional truncated exponential distribution. We show that our direct sampling approach converges faster to the target distribution compared to rejection sampling. The direct sampling of one and two dimensional truncated exponential distributions is then applied to a recent Path Integral Monte Carlo (PIMC) algorithm for the simulation of Bose-Hubbard lattice models at zero temperature. The new sampling method results in improved acceptance ratios and reduced autocorrelation times of estimators, providing an effective speed up of the simulation., Comment: ~8 pages, 8 figures. For associated data and code repository see: https://github.com/DelMaestroGroup/papers-code-truncExponSampling

We identify configurational phases and structural transitions in a polymer nanotube composite by means of machine learning. We employ various unsupervised dimensionality reduction methods, conventional neural networks, as well as the confusion method, an unsupervised neural-network-based approach. We find neural networks are able to reliably recognize all configurational phases that have been found previously in experiment and simulation. Furthermore, we locate the boundaries between configurational phases in a way that removes human intuition or bias. This could be done before only by relying on preconceived, ad-hoc order parameters.

Using a realistic molecular catalyst system, we conduct scaling studies of ab initio molecular dynamics simulations using the CP2K code on both Intel Xeon CPU and NVIDIA V100 GPU architectures. We explore using process placement and affinity to gain additional performance improvements. We also use statistical methods to understand performance changes in spite of the variability in runtime for each molecular dynamics timestep. We found ideal conditions for CPU runs included at least four MPI ranks per node, bound evenly across each socket, and fully utilizing processing cores with one OpenMP thread per core, no benefit was shown from reserving cores for the system. The CPU-only simulations scaled at 70% or more of the ideal scaling up to 10 compute nodes, after which the returns began to diminish more quickly. Simulations on a single 40-core node with two NVIDIA V100 GPUs for acceleration achieved over 3.7x speedup compared to the fastest single 36-core node CPU-only version, and showed 13% speedup over the fastest time we achieved across five CPU-only nodes., Comment: 8 pages, 8 figures

We present a novel deep learning (DL) approach to produce highly accurate predictions of macroscopic physical properties of solid solution binary alloys and magnetic systems. The major idea is to make use of the correlations between different physical properties in alloy systems to improve the prediction accuracy of neural network (NN) models. We use multitasking NN models to simultaneously predict the total energy, charge density and magnetic moment. These physical properties mutually serve as constraints during the training of the multitasking NN, resulting in more reliable DL models because multiple physics properties are correctly learned by a single model. Two binary alloys, copper-gold (CuAu) and iron-platinum (FePt), were studied. Our results show that once the multitasking NN's are trained, they can estimate the material properties for a specific configuration hundreds of times faster than first-principles density functional theory calculations while retaining comparable accuracy. We used a simple measure based on the root-mean-squared errors (RMSE) to quantify the quality of the NN models, and found that the inclusion of charge density and magnetic moment as physical constraints leads to more stable models that exhibit improved accuracy and reduced uncertainty for the energy predictions., Comment: 17 pages, 8 figures, 3 tables

We propose a new scalable method to optimize the architecture of an artificial neural network. The proposed algorithm, called Greedy Search for Neural Network Architecture, aims to determine a neural network with minimal number of layers that is at least as performant as neural networks of the same structure identified by other hyperparameter search algorithms in terms of accuracy and computational cost. Numerical results performed on benchmark datasets show that, for these datasets, our method outperforms state-of-the-art hyperparameter optimization algorithms in terms of attainable predictive performance by the selected neural network architecture, and time-to-solution for the hyperparameter optimization to complete., Comment: 12 pages, 15 figures, 3 table

Complex behavior poses challenges in extracting models from experiment. An example is spin liquid formation in frustrated magnets like Dy$_2$Ti$_2$O$_7$. Understanding has been hindered by issues including disorder, glass formation, and interpretation of scattering data. Here, we use a novel automated capability to extract model Hamiltonians from data, and to identify different magnetic regimes. This involves training an autoencoder to learn a compressed representation of three-dimensional diffuse scattering, over a wide range of spin Hamiltonians. The autoencoder finds optimal matches according to scattering and heat capacity data and provides confidence intervals. Validation tests indicate that our optimal Hamiltonian accurately predicts temperature and field dependence of both magnetic structure and magnetization, as well as glass formation and irreversibility in Dy$_2$Ti$_2$O$_7$. The autoencoder can also categorize different magnetic behaviors and eliminate background noise and artifacts in raw data. Our methodology is readily applicable to other materials and types of scattering problems., Comment: 18 pages, 6 figures

We report a new multicanonical Monte Carlo algorithm to obtain the density of states for physical systems with continuous state variables in statistical mechanics. Our algorithm is able to obtain a closed-form expression for the density of states expressed in a chosen basis set, instead of a numerical array of finite resolution as in previous variants of this class of MC methods such as the multicanonical sampling and Wang-Landau sampling. This is enabled by storing the visited states directly and avoiding the explicit collection of a histogram. This practice also has the advantage of avoiding undesirable artificial errors caused by the discretization and binning of continuous state variables. Our results show that this scheme is capable of obtaining converged results with a much reduced number of Monte Carlo steps, leading to a significant speedup over existing algorithms., Comment: 11 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:1707.07049

QMCPACK is an open source quantum Monte Carlo package for ab-initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wave functions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit (CPU) and graphical processing unit (GPU) systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://www.qmcpack.org .

We report a new multicanonical Monte Carlo (MC) algorithm to obtain the density of states (DOS) for physical systems with continuous state variables in statistical mechanics. Our algorithm is able to obtain an analytical form for the DOS expressed in a chosen basis set, instead of a numerical array of finite resolution as in previous variants of this class of MC methods such as the multicanonical (MUCA) sampling and Wang-Landau (WL) sampling. This is enabled by storing the visited states directly in a data set and avoiding the explicit collection of a histogram. This practice also has the advantage of avoiding undesirable artificial errors caused by the discretization and binning of continuous state variables. Our results show that this scheme is capable of obtaining converged results with a much reduced number of Monte Carlo steps, leading to a significant speedup over existing algorithms., Comment: 8 pages, 6 figures. Paper accepted in the Platform for Advanced Scientific Computing Conference (PASC '17), June 26 to 28, 2017, Lugano, Switzerland

We considered a higher-dimensional extension for the replica-exchange Wang-Landau algorithm to perform a random walk in the energy and magnetization space of the two-dimensional Ising model. This hybrid scheme combines the advantages of Wang-Landau and Replica-Exchange algorithms, and the one-dimensional version of this approach has been shown to be very efficient and to scale well, up to several thousands of computing cores. This approach allows us to split the parameter space of the system to be simulated into several pieces and still perform a random walk over the entire parameter range, ensuring the ergodicity of the simulation. Previous work, in which a similar scheme of parallel simulation was implemented without using replica exchange and with a different way to combine the result from the pieces, led to discontinuities in the final density of states over the entire range of parameters. From our simulations, it appears that the replica-exchange Wang-Landau algorithm is able to overcome this difficulty, allowing exploration of higher parameter phase space by keeping track of the joint density of states., Comment: Proceedings of CCP2014 will appear in Journal of Physics: Conference Series (JPCS), published by the IOP

We describe the study of thermodynamics of materials using replica-exchange Wang-Landau (REWL) sampling, a generic framework for massively parallel implementations of the Wang-Landau Monte Carlo method. To evaluate the performance and scalability of the method, we investigate the magnetic phase transition in body-centered cubic (bcc) iron using the classical Heisenberg model parametrized with first principles calculations. We demonstrate that our framework leads to a significant speedup without compromising the accuracy and precision and facilitates the study of much larger systems than is possible with its serial counterpart., Comment: Supplemental UE: TMS 2015 Conference Proceedings

We investigate a generic, parallel replica-exchange framework for Monte Carlo simulations based on the Wang-Landau method. To demonstrate its advantages and general applicability for massively parallel simulations of complex systems, we apply it to lattice spin models, the self-assembly process in amphiphilic solutions, and the adsorption of molecules on surfaces. While of general, current interest, the latter phenomena are challenging to study computationally because of multiple structural transitions occurring over a broad temperature range. We show how the parallel framework facilitates simulations of such processes and, without any loss of accuracy or precision, gives a significant speedup and allows for the study of much larger systems and much wider temperature ranges than possible with single-walker methods.

We introduce a generic, parallel Wang-Landau method that is naturally suited to implementation on massively parallel, petaflop supercomputers. The approach introduces a replica-exchange framework in which densities of states for overlapping sub-windows in energy space are determined iteratively by traditional Wang-Landau sampling. The advantages and general applicability of the method are demonstrated for several distinct systems that possess discrete or continuous degrees of freedom, including those with complex free energy landscapes and topological constraints., Comment: Conference on Computational Physics 2013 - CCP 2013

Combining traditional Wang-Landau sampling for multiple replica systems with an exchange of densities of states between replicas, we describe a general framework for simulations on massively parallel Petaflop supercomputers. The advantages and general applicability of the method for simulations of complex systems are demonstrated for the classical 2D Potts spin model featuring a strong first-order transition and the self-assembly of lipid bilayers in amphiphilic solutions in a continuous model., Comment: VIIth Brazilian Meeting on Simulational Physics (BMSP) 2013

We introduce a parallel Wang-Landau method based on the replica-exchange framework for Monte Carlo simulations. To demonstrate its advantages and general applicability for simulations of complex systems, we apply it to different spin models including spin glasses, the Ising model and the Potts model, lattice protein adsorption, and the self-assembly process in amphiphilic solutions. Without loss of accuracy, the method gives significant speed-up and potentially scales up to petaflop machines.

The thermodynamic behavior and structural properties of hydrophobic-polar (HP) lattice proteins interacting with attractive surfaces are studied by means of Wang-Landau sampling. Three benchmark HP sequences (48mer, 67mer, and 103mer) are considered with different types of surfaces, each of which attract either all monomers, only hydrophobic (H) monomers, or only polar (P) monomers, respectively. The diversity of folding behavior in dependence of surface strength is discussed. Analyzing the combined patterns of various structural observables, such as, e.g., the derivatives of the numbers of surface contacts, together with the specific heat, we are able to identify generic categories of folding and transition hierarchies. We also infer a connection between these transition categories and the relative surface strengths, i.e., the ratio of the surface attractive strength to the interchain attraction among H monomers. The validity of our proposed classification scheme is reinforced by the analysis of additional benchmark sequences. We thus believe that the folding hierarchies and identification scheme are generic for HP proteins interacting with attractive surfaces, regardless of chain length, sequence, or surface attraction., Comment: 12 pages, 5 figures, 3 tables

We describe a class of "bare bones" models of homopolymers which undergo coil-globule collapse and proteins which fold into their native states in free space or into denatured states when captured by an attractive substrate as the temperature is lowered. We then show how, with the use of a properly chosen trial move set, Wang-Landau Monte Carlo sampling can be used to study the rough free energy landscape and ground (native) states of these intriguingly simple systems and thus elucidate their thermodynamic complexity., Comment: 22 pages, 6 figures

Wang-Landau sampling has been applied to investigate the thermodynamics and structural properties of a lattice hydrophobic-polar heteropolymer (the HP protein model) interacting with an attractive substrate. For simplicity, we consider a short HP sequence consisting of only 36 monomers interacting with a substrate which attracts all monomers in the sequence. The conformational "phase transitions" have been identified by a canonical analysis of the specific heat and suitable structural observables. Three major "transitions", namely, adsorption, hydrophobic core formation and "flattening" of adsorbed structures, are observed. Depending on the surface attractive strength relative to the intra-protein attraction among the H monomers, these processes take place in different sequences upon cooling., Comment: 11 pages, 5 figures. Conference on Computational Physics (CCP 2011) Proceedings

Using Wang-Landau sampling with suitable Monte Carlo trial moves (pull moves and bond-rebridging moves combined) we have determined the density of states and thermodynamic properties for a short sequence of the HP protein model. For free chains these proteins are known to first undergo a collapse "transition" to a globule state followed by a second "transition" into a native state. When placed in the proximity of an attractive surface, there is a competition between surface adsorption and folding that leads to an intriguing sequence of "transitions". These transitions depend upon the relative interaction strengths and are largely inaccessible to "standard" Monte Carlo methods., Comment: 6 pages, 6 figures. Article in press. To be published in Computer Physics Communications (2011)

Motivated by the growing importance of fidelity in quantum critical phenomena, we establish a general relation between fidelity and structure factor of the driving term in a Hamiltonian through a newly introduced concept: fidelity susceptibility. Our discovery, as shown by some examples, facilitates the evaluation of fidelity in terms of susceptibility using well developed techniques such as density matrix renormalization group for the ground state, or Monte Carlo simulations for the states in thermal equilibrium., Comment: 4 pages, 2 figures, final version accepted by PRE