检索结果-内蒙古大学图书馆

End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Zhang, Linfeng Han, Jiequn Wang, Han Saidi, Wissam A. Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University United States Institute of Applied Physics and Computational Mathematics China CAEP Software Center for High Performance Numerical Simulation China Department of Mechanical Engineering and Materials Science University of Pittsburgh United States Department of Chemistry and Department of Physics Princeton University United States Princeton Institute for the Science and Technology of Materials Princeton University United States Department of Mathematics Princeton University United States Beijing Institute of Big Data Research China

Machine learning models are changing the paradigm of molecular modeling, which is a fundamental tool for material science, chemistry, and computational biology. Of particular interest is the inter-atomic potential energy surface (PES). Here we develop Deep Potential - Smooth Edition (DeepPot-SE), an end-to-end machine learning-based PES model, which is able to efficiently represent the PES of a wide variety of systems with the accuracy of ab initio quantum mechanics models. By construction, DeepPot-SE is extensive and continuously differentiable, scales linearly with system size, and preserves all the natural symmetries of the system. Further, we show that DeepPot-SE describes finite and extended systems including organic molecules, metals, semiconductors, and insulators with high fidelity. Copyright © 2018, The Authors. All rights reserved.

关键词： Potential energy

Characterizing the SLOPE Trade-off: A Variational Perspective and the Donoho-Tanner Limit

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Bu, Zhiqi Klusowski, Jason M. Rush, Cynthia Su, Weijie J. Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States Department of Operations Research and Financial Engineering Princeton University United States Department of Statistics Columbia University United States Department of Statistics and Data Science University of Pennsylvania United States

Sorted l1 regularization has been incorporated into many methods for solving high-dimensional statistical estimation problems, including the SLOPE estimator in linear regression. In this paper, we study how this relatively new regularization technique improves variable selection by characterizing the optimal SLOPE trade-off between the false discovery proportion (FDP) and true positive proportion (TPP) or, equivalently, between measures of type I error and power. Assuming a regime of linear sparsity and working under Gaussian random designs, we obtain an upper bound on the optimal trade-off for SLOPE, showing its capability of breaking the Donoho-Tanner power limit. To put it into perspective, this limit is the highest possible power that the Lasso, which is perhaps the most popular l1-based method, can achieve even with arbitrarily strong effect sizes. Next, we derive a tight lower bound that delineates the fundamental limit of sorted l1 regularization in optimally trading the FDP off for the TPP. Finally, we show that on any problem instance, SLOPE with a certain regularization sequence outperforms the Lasso, in the sense of having a smaller FDP, larger TPP and smaller l2 estimation risk simultaneously. Our proofs are based on a novel technique that reduces a calculus of variations problem to a class of infinite-dimensional convex optimization problems and a very recent result from approximate message passing theory. Copyright © 2021, The Authors. All rights reserved.

关键词： Message passing

Understanding degeneracy of two-point correlation functions via debye random media

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Skolnick, Murray Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

It is well-known that the degeneracy of two-phase microstructures with the same volume fraction and two-point correlation function S2(r) is generally infinite. To elucidate the degeneracy problem explicitly, we examine Debye random media, which are entirely defined by a purely exponentially decaying two-point correlation function S2(r). In this work, we consider three different classes of Debye random media. First, we generate the "most probable" class using the Yeong-Torquato construction algorithm [Yeong and Torquato, Phys. Rev. E, 57, 495 (1998)]. A second class of Debye random media is obtained by demonstrating that the corresponding two-point correlation functions are effectively realized in the first three space dimensions by certain models of overlapping, polydisperse spheres. A third class is obtained by using the Yeong-Torquato algorithm to construct Debye random media that are constrained to have an unusual prescribed pore-size probability density function. We structurally discriminate these three classes of Debye random media from one another by ascertaining their other statistical descriptors, including the pore-size, surface correlation, chordlength probability density, and lineal-path functions. We also compare and contrast the percolation thresholds as well as the diffusion and fluid transport properties of these degenerate Debye random media. We find that these three classes of Debye random media are generally distinguished by the aforementioned descriptors and their microstructures are also visually distinct from one another. Our work further confirms the well-known fact that scattering information is insufficient to determine the effective physical properties of two-phase media. Additionally, our findings demonstrate the importance of the other two-point descriptors considered here in the design of materials with a spectrum of physical properties. © 2021, CC BY-SA.

关键词： Random processes

Nearly hyperuniform network models of amorphous silicon

学校读者我要写书评

暂无评论

Physical Review B 2013年第24期87卷 245204-245204页

作者： Miroslav Hejna Paul J. Steinhardt Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

We introduce the concept of nearly hyperuniform network (NHN) structures as alternatives to the conventional continuous random network (CRN) models for amorphous tetrahedrally coordinated solids, such as amorphous silicon (a-Si). A hyperuniform solid has a structure factor S(k) that approaches zero as the wavenumber k→0. We define a NHN as an amorphous network whose structure factor S(k→0) is smaller than the liquid value at the melting temperature. Using a novel implementation of the Stillinger-Weber potential for the interatomic interactions, we show that the energy landscape for a spectrum of NHNs includes a sequence of local minima with an increasing degree of hyperuniformity [smaller S(k→0)] that is significantly below the frozen-liquid value and that correlates with other measurable features in S(k) at intermediate and large k and with the width of the electronic band gap.

关键词： SPECTRUM analysis AMORPHOUS silicon WAVENUMBER INTERATOMIC angles ELECTRONIC band structure

Sensitivity Analysis of Wind Energy Resources with Bayesian non-Gaussian and nonstationary Functional ANOVA

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Zhang, Jiachen Crippa, Paola Genton, Marc G. Castruccio, Stefano Department of Applied and Computational Mathematics and Statistics University of Notre Dame United States Department of Civid and Environmental Engineering and Geoscience University of Notre Dame United States Statistics Program King Abdullah University of Science and Technology Saudi Arabia

The transition from non-renewable to renewable energies represents a global societal challenge, and developing a sustainable energy portfolio is an especially daunting task for developing countries where little to no information is available regarding the abundance of renewable resources such as wind. Weather model simulations are key to obtain such information when observational data are scarce and sparse over a country as large and geographically diverse as Saudi Arabia. However, output from such models is uncertain, as it depends on inputs such as the parametrization of the physical processes and the spatial resolution of the simulated domain. In such situations, a sensitivity analysis must be performed and the input may have a spatially heterogeneous influence of wind. In this work, we propose a latent Gaussian functional analysis of variance (ANOVA) model that relies on a nonstationary Gaussian Markov random field approximation of a continuous latent process. The proposed approach is able to capture the local sensitivity of Gaussian and non-Gaussian wind characteristics such as speed and threshold exceedances over a large simulation domain, and a continuous underlying process also allows us to assess the effect of different spatial resolutions. Our results indicate that (1) the non-local planetary boundary layer scheme and high spatial resolution are both instrumental in capturing wind speed and energy (especially over complex mountainous terrain), and (2) the impact of planetary boundary layer scheme and resolution on Saudi Arabia’s planned wind farms is small (at most 1.4%). Thus, our results lend support for the construction of these wind farms in the next decade. © 2021, CC BY-NC-ND.

关键词： Sensitivity analysis

Multifunctional Hyperuniform Cellular Networks: Optimality, Anisotropy and Disorder

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Torquato, S. Chen, D. Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States

Disordered hyperuniform heterogeneous materials are new, exotic amorphous states of matter that behave like crystals in the manner in which they suppress volume-fraction fluctuations at large length scales, and yet are statistically isotropic with no Bragg peaks. It has recently been shown that disordered hyperuniform dielectric two-dimensional cellular network solids possess complete photonic band gaps comparable in size to photonic crystals, while at the same time maintaining statistical isotropy, enabling waveguide geometries not possible with photonic crystals. Motivated by these developments, we explore other functionalities of various two-dimensional ordered and disordered hyperuniform cellular networks, including their effective thermal or electrical conductivities and elastic moduli. We establish the multifunctionality of a class of such low-density networks by demonstrating that they maximize or virtually maximize the effective conductivities and elastic moduli. This is accomplished using the machinery of homogenization theory, including optimal bounds and cross-property bounds, and statistical mechanics. We rigorously prove that anisotropic networks consisting of sets of intersecting parallel channels in the low-density limit, ordered or disordered, possess optimal effective conductivity tensors. For a variety of different disordered networks, we show that when short-range and long-range order increases, there is an increase in both the effective conductivity and elastic moduli of the network. Moreover, we demonstrate that the effective conductivity and elastic moduli of various disordered networks derived from disordered "stealthy" hyperuniform point patterns possess virtually optimal values. We note that the optimal networks for conductivity are also optimal for the fluid permeability associated with slow viscous flow through the channels as well as the mean survival time associated with diffusion-controlled reactions in the channels. In summary, we have

关键词： Elastic moduli

Assessing the reliability of wind power operations under a changing climate with a non-Gaussian bias correction

学校读者我要写书评

暂无评论

arXiv 2020年

Facing increasing societal and economic pressure, many countries have established strategies to develop renewable energy portfolios, whose penetration in the market can alleviate the dependence on fossil fuels. In the case of wind, there is a fundamental question related to the resilience, and hence profitability, of future wind farms to a changing climate, given that current wind turbines have lifespans of up to thirty years. In this work we develop a new non-Gaussian method to adjust assimilated observational data to simulations and to estimate future wind, predicated on a trans-Gaussian transformation and a cluster-wise minimization of the Kullback-Leibler divergence. Future winds abundance will be determined for Saudi Arabia, a country with a recently established plan to develop a portfolio of up to 16 GW of wind energy. Further, we estimate the change in profits over future decades using additional high-resolution simulations, an improved method for vertical wind extrapolation and power curves from a collection of popular wind turbines. We find an overall increase in daily profit of $272,000 for the wind energy market for the optimal locations for wind farming in the country. Copyright © 2020, The Authors. All rights reserved.

关键词： Wind power

Generation and structural characterization of Debye random media

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Ma, Zheng Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

In their seminal paper on scattering by an inhomogeneous solid, Debye and coworkers proposed a simple exponentially decaying function for the two-point correlation function of an idealized class of two-phase random media. Such Debye random media, which have been shown to be realizable, are singularly distinct from all other models of two-phase media in that they are entirely defined by their one- and two-point correlation functions. To our knowledge, there has been no determination of other microstructural descriptors of Debye random media. In this paper, we generate Debye random media in two dimensions using an accelerated Yeong-Torquato construction algorithm. We then ascertain microstructural descriptors of the constructed media, including their surface correlation functions, pore-size distributions, lineal-path function, and chord-length probability density function. Accurate semi-analytic and empirical formulas for these descriptors are devised. We compare our results for Debye random media to those of other popular models (overlapping disks and equilibrium hard disks), and find that the former model possesses a wider spectrum of hole sizes, including a substantial fraction of large holes. Our algorithm can be applied to generate other models defined by their two-point correlation functions, and their other microstructural descriptors can be determined and analyzed by the procedures laid out here. Copyright © 2020, The Authors. All rights reserved.

关键词： Random processes

Dynamic Measure of Hyperuniformity and Nonhyperuniformity in Heterogeneous Media via the Diffusion Spreadability

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Wang, Haina Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Center for Theoretical Science Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Time-dependent interphase diffusion processes in multiphase heterogeneous media arise ubiquitously in physics, chemistry and biology. Examples of heterogeneous media include composites, geological media, gels, foams and cell aggregates. The recently developed concept of spreadability, S(t), provides a direct link between time-dependent diffusive transport and the microstructure of two-phase media across length scales [Torquato, S., Phys. Rev. E., 104 054102 (2021)]. To investigate the capability of S(t) to probe microstructures of real heterogeneous media, we explicitly compute S(t) for well-known two-dimensional and three-dimensional idealized model structures that span across nonhyperuniform and hyperuniform classes. Among the former class, we study fully penetrable spheres and equilibrium hard spheres, and in the latter class, we examine sphere packings derived from "perfect glasses", uniformly randomized lattices (URL), disordered stealthy hyperuniform point processes and Bravais lattices. Hyperuniform media are characterized by an anomalous suppression of volume fraction fluctuations at large length scales compared to that of any nonhyperuniform medium. We further confirm that the small-, intermediate- and long-time behaviors of S(t) sensitively capture the small-, intermediate- and large-scale characteristics of the models. In instances in which the spectral density (Equation presented)V (k) has a power-law form B|k|α in the limit |k| → 0, the long-time spreadability provides a simple means to extract the value of the coefficients α and B that is robust against noise in (Equation presented)V (k) at small wavenumbers. For typical nonhyperuniform media, the intermediate-time spreadability is slower for models with larger values of the coefficient B = (Equation presented)V (0). Interestingly, the excess spreadability S(∞) - S(t) for URL packings has nearly exponential decay at small to intermediate t, but transforms to a power-law decay at large t, and the time f

关键词： Diffusion