We present a computational study on the solid–solid phase transition of a model two-dimensional system between hexagonal and square phases under pressure. The atomistic mechanism of phase nucleation and propagation are determined using solid-state Dimer and nudged elastic band (NEB) methods. The Dimer is applied to identify the saddle configurations and NEB is applied to generate the transition minimum energy path (MEP) using the outputs of Dimer. Both the atomic and cell degrees of freedom are used in saddle search, allowing us to capture the critical nuclei with relatively small supercells. It is found that the phase nucleation in the model material is triggered by the localized shear deformation that comes from the relative shift between two adjacent atomic layers. In addition to the conventional layer-by-layer phase propagation, an interesting defect-assisted low barrier propagation path is identified in the hexagonal to square phase transition. The study demonstrates the significance of using the Dimer method in exploring unknown transition paths without a priori assumption. The results of this study also shed light on phase transition mechanisms of other solid-state and colloidal systems.
more »
« less
This content will become publicly available on January 24, 2025
Improving ab initio diffusion calculations in materials through Gaussian process regression
Saddle point search schemes are widely used to identify the transition state of different processes, like chemical reactions, surface and bulk diffusion, surface adsorption, and many more. In solid-state materials with relatively large numbers of atoms, the minimum mode following schemes such as dimer are commonly used because they alleviate the calculation of the Hessian on the high-dimensional potential energy surface. Here, we show that the dimer search can be further accelerated by leveraging Gaussian process regression (GPR). The GPR serves as a surrogate model to feed the dimer with the required energy and force input. We test the GPR-accelerated dimer method for predicting the diffusion coefficient of vacancy-mediated self-diffusion in body-centered cubic molybdenum and sulfur diffusion in hexagonal molybdenum disulfide. We use a multitask learning approach that utilizes a shared covariance function between energy and force input, and we show that the multitask learning significantly improves the performance of the GPR surrogate model compared to previously used learning approaches. Additionally, we demonstrate that a translation-hop sampling approach is necessary to avoid overfitting the GPR surrogate model to the minimum-mode-following pathway and thus succeeding in locating the saddle point. We show that our method reduces the number of evaluations compared to a conventional dimer method.
more »
« less
- Award ID(s):
- 1954621
- NSF-PAR ID:
- 10491718
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review Materials
- Volume:
- 8
- Issue:
- 1
- ISSN:
- 2475-9953
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
A key aspect of the neural coding problem is understanding how representations of afferent stimuli are built through the dynamics of learning and adaptation within neural networks. The infomax paradigm is built on the premise that such learning attempts to maximize the mutual information between input stimuli and neural activities. In this letter, we tackle the problem of such information-based neural coding with an eye toward two conceptual hurdles. Specifically, we examine and then show how this form of coding can be achieved with online input processing. Our framework thus obviates the biological incompatibility of optimization methods that rely on global network awareness and batch processing of sensory signals. Central to our result is the use of variational bounds as a surrogate objective function, an established technique that has not previously been shown to yield online policies. We obtain learning dynamics for both linear-continuous and discrete spiking neural encoding models under the umbrella of linear gaussian decoders. This result is enabled by approximating certain information quantities in terms of neuronal activity via pairwise feedback mechanisms. Furthermore, we tackle the problem of how such learning dynamics can be realized with strict energetic constraints. We show that endowing networks with auxiliary variables that evolve on a slower timescale can allow for the realization of saddle-point optimization within the neural dynamics, leading to neural codes with favorable properties in terms of both information and energy.more » « less
-
more » « less
Abstract We present in this Letter the first global comparison between traditional line-tied steady-state magnetohydrodynamic models and a new, fully time-dependent thermodynamic magnetohydrodynamic simulation of the global corona. To approximate surface magnetic field distributions and magnitudes around solar minimum, we use the Lockheed Evolving Surface-Flux Assimilation Model to obtain input maps that incorporate flux emergence and surface flows over a full solar rotation, including differential rotation and meridional flows. Each time step evolves the previous state of the plasma with a new magnetic field input boundary condition, mimicking photospheric driving on the Sun. We find that this method produces a qualitatively different corona compared to steady-state models. The magnetic energy levels are higher in the time-dependent model, and coronal holes evolve more along the following edge than they do in steady-state models. Coronal changes, as illustrated with forward-modeled emission maps, evolve on longer timescales with time-dependent driving. We discuss implications for active and quiet Sun scenarios, solar wind formation, and widely used steady-state assumptions like potential field source surface calculations.
-
null (Ed.)Due to increasing volume of measurements in smart grids, surrogate based learning approaches for modeling the power grids are becoming popular. This paper uses regression based models to find the unknown state variables on power systems. Generally, to determine these states, nonlinear systems of power flow equations are solved iteratively. This study considers that the power flow problem can be modeled as an data driven type of a model. Then, the state variables, i.e., voltage magnitudes and phase angles are obtained using machine learning based approaches, namely, Extreme Learning Machine (ELM), Gaussian Process Regression (GPR), and Support Vector Regression (SVR). Several simulations are performed on the IEEE 14 and 30-Bus test systems to validate surrogate based learning based models. Moreover, input data was modified with noise to simulate measurement errors. Numerical results showed that all three models can find state variables reasonably well even with measurement noise.more » « less
-
Abstract. Time-dependent simulations of ice sheets require two equations to be solved:the mass transport equation, derived from the conservation of mass, and thestress balance equation, derived from the conservation of momentum. The masstransport equation controls the advection of ice from the interior of the icesheet towards its periphery, thereby changing its geometry. Because it isbased on an advection equation, a stabilization scheme needs to beemployed when solved using the finite-element method. Several stabilizationschemes exist in the finite-element method framework, but their respectiveaccuracy and robustness have not yet been systematically assessed forglaciological applications. Here, we compare classical schemes used in thecontext of the finite-element method: (i) artificial diffusion, (ii)streamline upwinding, (iii) streamline upwind Petrov–Galerkin, (iv)discontinuous Galerkin, and (v) flux-corrected transport. We also look at thestress balance equation, which is responsible for computing the ice velocitythat “advects” the ice downstream. To improve the velocity computationaccuracy, the ice-sheet modeling community employs several sub-elementparameterizations of physical processes at the grounding line, the point wherethe grounded ice starts to float onto the ocean. Here, we introduce a newsub-element parameterization for the driving stress, the force that drives theice-sheet flow. We analyze the response of each stabilization scheme byrunning transient simulations forced by ice-shelf basal melt. The simulationsare based on an idealized ice-sheet geometry for which there is no influenceof bedrock topography. We also perform transient simulations of the AmundsenSea Embayment, West Antarctica, where real bedrock and surface elevations areemployed. In both idealized and real ice-sheet experiments, stabilizationschemes based on artificial diffusion lead systematically to a bias towardsmore mass loss in comparison to the other schemes and therefore should beavoided or employed with a sufficiently high mesh resolution in the vicinityof the grounding line. We also run diagnostic simulations to assess theaccuracy of the driving stress parameterization, which, in combination with anadequate parameterization for basal stress, provides improved numericalconvergence in ice speed computations and more accurate results.more » « less
