Score Dynamics: Scaling Molecular Dynamics with Picoseconds Time Steps via Conditional Diffusion Model.

We propose score dynamics (SD), a general framework for learning accelerated evolution operators with large timesteps from molecular dynamics (MD) simulations. SD is centered around scores or derivatives of the transition log-probability with respect to the dynamical degrees of freedom. The latter play the same role as force fields in MD but are used in denoising diffusion probability models to generate discrete transitions of the dynamical variables in an SD time step, which can be orders of magnitude larger than a typical MD time step. In this work, we construct graph neural network-based SD models of realistic molecular systems that are evolved with 10 ps timesteps. We demonstrate the efficacy of SD with case studies of the alanine dipeptide and short alkanes in aqueous solution. Both equilibrium predictions derived from the stationary distributions of the conditional probability and kinetic predictions for the transition rates and transition paths are in good agreement with MD. Our current SD implementation is about 2 orders of magnitude faster than the MD counterpart for the systems studied in this work. Open challenges and possible future remedies to improve SD are also discussed.

Accurate parameterization of the kinetic energy functional for calculations using exact-exchange.

Electronic structure calculations based on Kohn-Sham density functional theory (KSDFT) that incorporate exact-exchange or hybrid functionals are associated with a large computational expense, a consequence of the inherent cubic scaling bottleneck and large associated prefactor, which limits the length and time scales that can be accessed. Although orbital-free density functional theory (OFDFT) calculations scale linearly with system size and are associated with a significantly smaller prefactor, they are limited by the absence of accurate density-dependent kinetic energy functionals. Therefore, the development of accurate density-dependent kinetic energy functionals is important for OFDFT calculations of large realistic systems. To this end, we propose a method to train kinetic energy functional models at the exact-exchange level of theory by using a dictionary of physically relevant terms that have been proposed in the literature in conjunction with linear or nonlinear regression methods to obtain the fitting coefficients. For our dictionary, we use a gradient expansion of the kinetic energy nonlocal models proposed in the literature and their nonlinear combinations, such as a model that incorporates spatial correlations between higher order derivatives of electron density at two points. The predictive capabilities of these models are assessed by using a variety of model one-dimensional (1D) systems that exhibit diverse bonding characteristics, such as a chain of eight hydrogens, LiF, LiH, C4H2, C4N2, and C3O2. We show that by using the data from model 1D KSDFT calculations performed using the exact-exchange functional for only a few neutral structures, it is possible to generate models with high accuracy for charged systems and electron and kinetic energy densities during self-consistent field iterations. In addition, we show that it is possible to learn both the orbital dependent terms, i.e., the kinetic energy and the exact-exchange energy, and models that incorporate additional nonlinearities in spatial correlations, such as a quadratic model, are needed to capture subtle features of the kinetic energy density that are present in exact-exchange-based KSDFT calculations.

Accurate parameterization of the kinetic energy functional.

The absence of a reliable formulation of the kinetic energy density functional has hindered the development of orbital free density functional theory. Using the data-aided learning paradigm, we propose a simple prescription to accurately model the kinetic energy density of any system. Our method relies on a dictionary of functional forms for local and nonlocal contributions, which have been proposed in the literature, and the appropriate coefficients are calculated via a linear regression framework. To model the nonlocal contributions, we explore two new nonlocal functionals-a functional that captures fluctuations in electronic density and a functional that incorporates gradient information. Since the analytical functional forms of the kernels present in these nonlocal terms are not known from theory, we propose a basis function expansion to model these seemingly difficult nonlocal quantities. This allows us to easily reconstruct kernels for any system using only a few structures. The proposed method is able to learn kinetic energy densities and total kinetic energies of molecular and periodic systems, such as H2, LiH, LiF, and a one-dimensional chain of eight hydrogens using data from Kohn-Sham density functional theory calculations for only a few structures.

Atomistic insights into metal hardening.

For millennia, humans have exploited the natural property of metals to get stronger or harden when mechanically deformed. Ultimately rooted in the motion of dislocations, mechanisms of metal hardening have remained in the cross-hairs of physical metallurgists for over a century. Here, we performed atomistic simulations at the limits of supercomputing that are sufficiently large to be statistically representative of macroscopic crystal plasticity yet fully resolved to examine the origins of metal hardening at its most fundamental level of atomic motion. We demonstrate that the notorious staged (inflection) hardening of metals is a direct consequence of crystal rotation under uniaxial straining. At odds with widely divergent and contradictory views in the literature, we observe that basic mechanisms of dislocation behaviour are the same across all stages of metal hardening.

Probing the limits of metal plasticity with molecular dynamics simulations.

Ordinarily, the strength and plasticity properties of a metal are defined by dislocations-line defects in the crystal lattice whose motion results in material slippage along lattice planes. Dislocation dynamics models are usually used as mesoscale proxies for true atomistic dynamics, which are computationally expensive to perform routinely. However, atomistic simulations accurately capture every possible mechanism of material response, resolving every "jiggle and wiggle" of atomic motion, whereas dislocation dynamics models do not. Here we present fully dynamic atomistic simulations of bulk single-crystal plasticity in the body-centred-cubic metal tantalum. Our goal is to quantify the conditions under which the limits of dislocation-mediated plasticity are reached and to understand what happens to the metal beyond any such limit. In our simulations, the metal is compressed at ultrahigh strain rates along its [001] crystal axis under conditions of constant pressure, temperature and strain rate. To address the complexity of crystal plasticity processes on the length scales (85-340 nm) and timescales (1 ns-1µs) that we examine, we use recently developed methods of in situ computational microscopy to recast the enormous amount of transient trajectory data generated in our simulations into a form that can be analysed by a human. Our simulations predict that, on reaching certain limiting conditions of strain, dislocations alone can no longer relieve mechanical loads; instead, another mechanism, known as deformation twinning (the sudden re-orientation of the crystal lattice), takes over as the dominant mode of dynamic response. Below this limit, the metal assumes a strain-path-independent steady state of plastic flow in which the flow stress and the dislocation density remain constant as long as the conditions of straining thereafter remain unchanged. In this distinct state, tantalum flows like a viscous fluid while retaining its crystal lattice and remaining a strong and stiff metal.

Radiofrequency ablation or stripping of large-diameter incompetent great saphenous varicose veins with C2 or C3 disease.

OBJECTIVE: The objectives of this study were to compare the results of radiofrequency ablation (RFA) and stripping for large-diameter varicose target veins for the period of 1 year, based on a composite end point; to analyze the pain severity on a digital rating scale for 7 days after RFA and stripping; and to detect the factors affecting the level of postoperative pain using the cluster analysis. METHODS: This was a multicenter retrospective cohort study. Two groups, stripping ≥14 mm and RFA ≥14 mm, of 129 varicose vein disease patients underwent surgical treatment in three specialized clinics. We eliminated symptomatic pathologic reflux with RFA in 64 patients and with stripping in 65 patients. In the postoperative phase, we evaluated the pain level, subcutaneous hemorrhage, and paresthesia. A composite end point with four components was used to analyze the results. These were three clinical adverse effects of the intervention (pain, hemorrhage, and paresthesia) and the technical outcome 1 year after the surgical intervention. RESULTS: The frequency of favorable outcomes was 20 (30.8%) in the stripping ≥14 mm group and 61 (95.3%) in the RFA ≥14 mm group (P < .0001). The odds ratio for a favorable outcome between the RFA and the stripping groups was 45.8 (95% confidence interval, 44.5-47.0). The pain clusters that were moderate were created by patients after stripping. These clusters show a link between the pain level on the one hand and an increased body mass index and large vein diameter on the other hand. CONCLUSIONS: For large-diameter veins, RFA is superior to stripping in terms of favorable outcomes according to the composite end point chosen. Significant pain after stripping was linked to a large vein diameter and excess weight or adiposis.

Path factorization approach to stochastic simulations.

The computational efficiency of stochastic simulation algorithms is notoriously limited by the kinetic trapping of the simulated trajectories within low energy basins. Here we present a new method that overcomes kinetic trapping while still preserving exact statistics of escape paths from the trapping basins. The method is based on path factorization of the evolution operator and requires no prior knowledge of the underlying energy landscape. The efficiency of the new method is demonstrated in simulations of anomalous diffusion and phase separation in a binary alloy, two stochastic models presenting severe kinetic trapping.

Singular orientations and faceted motion of dislocations in body-centered cubic crystals.

Dislocation mobility is a fundamental material property that controls strength and ductility of crystals. An important measure of dislocation mobility is its Peierls stress, i.e., the minimal stress required to move a dislocation at zero temperature. Here we report that, in the body-centered cubic metal tantalum, the Peierls stress as a function of dislocation orientation exhibits fine structure with several singular orientations of high Peierls stress-stress spikes-surrounded by vicinal plateau regions. While the classical Peierls-Nabarro model captures the high Peierls stress of singular orientations, an extension that allows dislocations to bend is necessary to account for the plateau regions. Our results clarify the notion of dislocation kinks as meaningful only for orientations within the plateau regions vicinal to the Peierls stress spikes. These observations lead us to propose a Read-Shockley type classification of dislocation orientations into three distinct classes-special, vicinal, and general-with respect to their Peierls stress and motion mechanisms. We predict that dislocation loops expanding under stress at sufficiently low temperatures, should develop well defined facets corresponding to two special orientations of highest Peierls stress, the screw and the M111 orientations, both moving by kink mechanism. We propose that both the screw and the M111 dislocations are jointly responsible for the yield behavior of BCC metals at low temperatures.

First-passage kinetic Monte Carlo method.

We present an efficient method for Monte Carlo simulations of diffusion-reaction processes. Introduced by us in a previous paper [Phys. Rev. Lett. 97, 230602 (2006)], our algorithm skips the traditional small diffusion hops and propagates the diffusing particles over long distances through a sequence of superhops, one particle at a time. By partitioning the simulation space into nonoverlapping protecting domains each containing only one or two particles, the algorithm factorizes the N -body problem of collisions among multiple Brownian particles into a set of much simpler single-body and two-body problems. Efficient propagation of particles inside their protective domains is enabled through the use of time-dependent Green's functions (propagators) obtained as solutions for the first-passage statistics of random walks. The resulting Monte Carlo algorithm is event-driven and asynchronous; each Brownian particle propagates inside its own protective domain and on its own time clock. The algorithm reproduces the statistics of the underlying Monte Carlo model exactly. Extensive numerical examples demonstrate that for an important class of diffusion-reaction models the algorithm is efficient at low particle densities, where other existing algorithms slow down severely.

Dislocation multi-junctions and strain hardening.

At the microscopic scale, the strength of a crystal derives from the motion, multiplication and interaction of distinctive line defects called dislocations. First proposed theoretically in 1934 (refs 1-3) to explain low magnitudes of crystal strength observed experimentally, the existence of dislocations was confirmed two decades later. Much of the research in dislocation physics has since focused on dislocation interactions and their role in strain hardening, a common phenomenon in which continued deformation increases a crystal's strength. The existing theory relates strain hardening to pair-wise dislocation reactions in which two intersecting dislocations form junctions that tie the dislocations together. Here we report that interactions among three dislocations result in the formation of unusual elements of dislocation network topology, termed 'multi-junctions'. We first predict the existence of multi-junctions using dislocation dynamics and atomistic simulations and then confirm their existence by transmission electron microscopy experiments in single-crystal molybdenum. In large-scale dislocation dynamics simulations, multi-junctions present very strong, nearly indestructible, obstacles to dislocation motion and furnish new sources for dislocation multiplication, thereby playing an essential role in the evolution of dislocation microstructure and strength of deforming crystals. Simulation analyses conclude that multi-junctions are responsible for the strong orientation dependence of strain hardening in body-centred cubic crystals.

First-passage Monte Carlo algorithm: diffusion without all the hops.

We present a novel Monte Carlo algorithm for N diffusing finite particles that react on collisions. Using the theory of first-passage processes and time dependent Green's functions, we break the difficult N-body problem into independent single- and two-body propagations circumventing numerous diffusion hops used in standard Monte Carlo simulations. The new algorithm is exact, extremely efficient, and applicable to many important physical situations in arbitrary integer dimensions.

Adaptive importance sampling Monte Carlo simulation of rare transition events.

We develop a general theoretical framework for the recently proposed importance sampling method for enhancing the efficiency of rare-event simulations [W. Cai, M. H. Kalos, M. de Koning, and V. V. Bulatov, Phys. Rev. E 66, 046703 (2002)], and discuss practical aspects of its application. We define the success/fail ensemble of all possible successful and failed transition paths of any duration and demonstrate that in this formulation the rare-event problem can be interpreted as a "hit-or-miss" Monte Carlo quadrature calculation of a path integral. The fact that the integrand contributes significantly only for a very tiny fraction of all possible paths then naturally leads to a "standard" importance sampling approach to Monte Carlo (MC) quadrature and the existence of an optimal importance function. In addition to showing that the approach is general and expected to be applicable beyond the realm of Markovian path simulations, for which the method was originally proposed, the formulation reveals a conceptual analogy with the variational MC (VMC) method. The search for the optimal importance function in the former is analogous to finding the ground-state wave function in the latter. In two model problems we discuss practical aspects of finding a suitable approximation for the optimal importance function. For this purpose we follow the strategy that is typically adopted in VMC calculations: the selection of a trial functional form for the optimal importance function, followed by the optimization of its adjustable parameters. The latter is accomplished by means of an adaptive optimization procedure based on a combination of steepest-descent and genetic algorithms.

Dynamic transitions from smooth to rough to twinning in dislocation motion.

The motion of dislocations in response to stress dictates the mechanical behaviour of materials. However, it is not yet possible to directly observe dislocation motion experimentally at the atomic level. Here, we present the first observations of the long-hypothesized kink-pair mechanism in action using atomistic simulations of dislocation motion in iron. In a striking deviation from the classical picture, dislocation motion at high strain rates becomes rough, resulting in spontaneous self-pinning and production of large quantities of debris. Then, at still higher strain rates, the dislocation stops abruptly and emits a twin plate that immediately takes over as the dominant mode of plastic deformation. These observations challenge the applicability of the Peierls threshold concept to the three-dimensional motion of screw dislocations at high strain rates, and suggest a new interpretation of plastic strength and microstructure of shocked metals.

Anomalous dislocation multiplication in FCC metals.

Direct atomistic simulations of dislocation multiplication in fcc aluminum reveal an unexpected mechanism, in which a Frank-Read source emits dislocations with Burgers vectors different from that of the source itself. The mechanism is traced to a spontaneous nucleation of partial dislocation loops within the stacking fault. Understanding and a quantitative description of this unusual process are achieved through the development of a continuum model for dislocation nucleation based on the coarse-grained dislocation dynamics approach and a minimal amount of atomistic input.

Importance sampling of rare transition events in Markov processes.

We present an importance sampling technique for enhancing the efficiency of sampling rare transition events in Markov processes. Our approach is based on the design of an importance function by which the absolute probability of sampling a successful transition event is significantly enhanced, while preserving the relative probabilities among different successful transition paths. The method features an iterative stochastic algorithm for determining the optimal importance function. Given that the probability of sampling a successful transition event is enhanced by a known amount, transition rates can be readily computed. The method is illustrated in one- and two-dimensional systems.

Nodal effects in dislocation mobility.

We show that, contrary to the prevailing perception, dislocations can become more mobile by zipping together to form junctions. In a series of direct atomistic simulations, the critical stress to move a junction network in a [110] plane of bcc molybdenum is found to be always smaller ( approximately 50%) than that required to move isolated dislocations. Our data support a previously proposed hypothesis about the nature of anomalous slip in bcc transition metals, yet offer a different atomistic mechanism for conservative motion of screw dislocation networks. The same data suggest a hierarchy of motion mechanisms in which lower-dimensional crystal imperfections control the rate of sliding along the low-angle twist boundaries.