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Deep potentials for materials science

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材料展望（英文）

材料展望（英文） 2022年第2期 89-115页

作者： Tongqi Wen Linfeng Zhang Han Wang Weinan E David J Srolovitz Department of Mechanical Engineering The University of Hong KongHong KongHong Kong Special Administrative Region of China DP Technology BeijingPeople's Republic of China AI for Science Institute BeijingPeople's Republic of China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijingPeople's Republic of China HEDPS CAPTCollege of EngineeringPeking UniversityBeijingPeople's Republic of China AI for Science Institute BeijingPeople's Republic of China School of Mathematical Sciences Peking UniversityBeijingPeople's Republic of China Department of Mathematics and Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJUnited States of America Department of Mechanical Engineering The University of Hong KongHong KongHong Kong Special Administrative Region of China International Digital Economy Academy(IDEA) ShenzhenPeople's Republic of China

To fill the gap between accurate(and expensive)ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials,a new class of descriptions of atomic interactions has emerged and been widely applied;*** learning potentials(MLPs).One recently developed type of MLP is the deep potential(DP)*** this review,we provide an introduction to DP methods in computational materials *** theory underlying the DP method is presented along with a step-by-step introduction to their development and *** also review materials applications of DPs in a wide range of materials *** DP Library provides a platform for the development of DPs and a database of extant *** discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials.

关键词： deep potential atomistic simulation machine learning potential neural network

Linear optimal control of transient growth in turbulent channel flows

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Acta Mechanica Sinica 2019年第4期35卷 729-739页

作者： Yang Song Chunxiao Xu Weixi Huang Institute of Applied Physics and Computational Mathematics Beijing 100094 China AML Department of Engineering MechanicsTsinghua University Beijing 100084 China

The suppression of linear transient growth in turbulent channel flows via linear optimal controls is investigated. The control algorithms are the LQR control based on full information of flow fields and the LQG control based on the information measured at walls. The influence of these controls on the development of small-scale and large-scale perturbations are considered respectively. It is found that the energy amplification of large-scale perturbations is suppressed significantly by both LQR and LQG control, while small-scale perturbations can be only affect by LQR control. Effects of the weighting parameters and control price on the control performance of both controls are analysed. It turns out that the different weighting parameters in cost function do not qualitatively change the evalution of control performance. As control price raises, the effectiveness of both controls decreases distinctly. For small-scale perturbations, the upper limit of the effective range of control price is lower than that for large-scale perturbations. As Reynolds number increases, it indicates that both LQR and LQG control get more effective on suppressing the energy amplification of large-scale perturbations.

关键词： Linear optimal control Turbulent channel flow Optimal transient growth

Theoretical evidence of H-He demixing under Jupiter and Saturn conditions

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arXiv 2023年

作者： Chang, Xiaoju Chen, Bo Zeng, Qiyu Wang, Han Chen, Kaiguo Tong, Qunchao Yu, Xiaoxiang Kang, Dongdong Zhang, Shen Guo, Fangyu Hou, Yong Zhao, Zengxiu Yao, Yansun Ma, Yanming Dai, Jiayu College of Science National University of Defense Technology Changsha410073 China Hunan Key Laboratory of Extreme Matter and Applications National University of Defense Technology Changsha410073 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China Department of Physics and Engineering Physics University of Saskatchewan SaskatoonSKS7N 5E2 Canada State Key Lab of Superhard Materials International Center for Computational Method and Software College of Physics Jilin University Changchun130012 China International Center of Future Science Jilin University Changchun130012 China

The immiscibility of hydrogen-helium mixture under the temperature and pressure conditions of planetary interiors is crucial for understanding the structures of gas giant planets (e.g., Jupiter and Saturn). While the experimental probe at such extreme conditions is challenging, theoretical simulation is heavily relied in an effort to unravel the mixing behavior of hydrogen and helium. Here we develop a method via a machine learning accelerated molecular dynamics simulation to quantify the physical separation of hydrogen and helium under the conditions of planetary interiors. The immiscibility line achieved with the developed method yields substantially higher demixing temperatures at pressure above 1.5 Mbar than earlier theoretical data, but matches better to the experimental estimate. Our results suggest a possibility that H-He demixing takes place in a large fraction of the interior radii of Jupiter and Saturn, i.e., 27.5% in Jupiter and 48.3% in Saturn. This indication of an H-He immiscible layer hints at the formation of helium rain and offers a potential explanation for the decrease of helium in the atmospheres of Jupiter and Saturn. © 2023, CC BY.

关键词： Planets

Extracting the Speed of Light from Matrix Product States

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arXiv 2023年

作者： Eberharter, Alexander A. Vanderstraeten, Laurens Verstraete, Frank Läuchli, Andreas M. Institut für Theoretische Physik Universität Innsbruck InnsbruckA-6020 Austria Department of Physics and Astronomy University of Ghent Belgium Center for Nonlinear Phenomena and Complex Systems Université Libre de Bruxelles Brussels Belgium Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge United Kingdom Laboratory for Theoretical and Computational Physics Paul Scherrer Institute Villigen5232 Switzerland Lausanne1015 Switzerland

We provide evidence that the spectrum of the local effective Hamiltonian and the transfer operator in infinitesystem matrix product state simulations are identical up to a global rescaling factor, i.e. the speed of light of the system, when the underlying system is described by a 1+1 dimensional CFT. We provide arguments for this correspondence based on a path integral point of view. This observation turns out to yield very precise estimates for the speed of light in practice, confirming exact results to high precision where available, but also allowing us to finally determine the speed of light of the non-integrable, critical SU(2) Heisenberg chains with halfinteger spin S > 1/2 with unprecedented accuracy. We also show that the same technology applied to doped Hubbard ladders provides highly accurate velocities for a range of dopings. Combined with measurements of compressibilities we present new results for the Luttinger liquid parameter in the Luther-Emery regime of doped Hubbard ladders, outperforming earlier approaches based on the fitting of real-space correlation functions. © 2023, CC BY.

关键词： Hamiltonians

The Modified Weak Galerkin Finite Element Method for Solving Brinkman Equations

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Journal of Mathematical Research with Applications 2019年第6期39卷 657-676页

作者： Li-na SUN Yue FENG Yuanyuan LIU Ran ZHANG Department of Mathematics Jilin University Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics

A modified weak Galerkin（MWG） finite element method is introduced for the Brinkman equations in this paper. We approximate the model by the variational formulation based on two discrete weak gradient operators. In the MWG finite element method, discontinuous piecewise polynomials of degree k and k-1 are used to approximate the velocity u and the pressure p, respectively. The main idea of the MWG finite element method is to replace the boundary functions by the average of the interior functions. Therefore, the MWG finite element method has fewer degrees of freedom than the WG finite element method without loss of accuracy. The MWG finite element method satisfies the stability conditions for any polynomial with degree no more than k-1. The MWG finite element method is highly flexible by allowing the use of discontinuous functions on arbitrary polygons or polyhedra with certain shape *** order error estimates are established for the velocity and pressure approximations in H1and L2norms. Some numerical examples are presented to demonstrate the accuracy, convergence and stability of the method.

关键词： the Brinkman equations the modified weak Galerkin finite element method discrete weak gradient

A deep potential model with long-range electrostatic interactions

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arXiv 2021年

作者： Zhang, Linfeng Wang, Han Muniz, Maria Carolina Panagiotopoulos, Athanassios Z. Car, Roberto Weinan, E. DP Technology Beijing China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China HEDPS CAPT College of Engineering Peking University Beijing100871 China Department of Chemical and Biological Engineering Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States School of Mathematical Sciences Peking University Beijing100871 China AI for Science Institute Beijing China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make possible molecular simulations with the accuracy of quantum mechanical density functional theory, at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that derive from the Coulombic tail of the forces. To overcome this limitation we extend the DP model by approximating the long-range electrostatic interaction between ions (nuclei+core electrons) and valence electrons with that of distributions of spherical Gaussian charges located at ionic and electronic sites. The latter are rigorously defined in terms of the centers of the maximally localized Wannier distributions, whose dependence on the local atomic environment is modeled accurately by a deep neural network. In the deep potential long-range (DPLR) model, the electrostatic energy of the Gaussian charge system is added to short-range interactions that are represented as in the standard DP model. The resulting potential energy surface is smooth and possesses analytical forces and virial. Missing effects in the standard DP scheme are recovered, improving on accuracy and predictive power. By including long-range electrostatics, DPLR correctly extrapolates to large systems the potential energy surface learned from quantum mechanical calculations on smaller systems. We illustrate the approach with three examples, the potential energy profile of the water dimer, the free energy of interaction of a water molecule with a liquid water slab, and the phonon dispersion curves of the NaCl crystal. © 2021, CC BY.

关键词： Electrostatics

CO oxidation by Pt2/Fe3O4: metastable dimer and support configurations facilitate lattice oxygen extraction

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arXiv 2022年

作者： Meier, Matthias Hulva, Jan Jakub, Zdenek Kraushofer, Florian Bobic, Mislav Bliem, Roland Setvin, Martin Schmid, Michael Diebold, Ulrike Franchini, Cesare Parkinson, Gareth S. Institute of Applied Physics TU Wien Vienna Austria Computational Materials Physics University of Vienna Vienna Austria Department of Surface and Plasma Science Faculty of Mathematics and Physics Charles University Prague Czech Republic Alma Mater Studiorum Universita di Bologna Bologna Italy

Heterogeneous catalysts based on sub-nanometer metal clusters often exhibit strongly size-dependent properties, and the addition or removal of a single atom can make all the difference. Identifying the most active species and deciphering the reaction mechanism is extremely difficult, however, because it is often not clear how the catalyst evolves in operando. Here, we utilize a combination of atomically resolved scanning probe microscopies, spectroscopic techniques, and density functional theory (DFT)-based calculations to study CO oxidation by a model Pt/Fe3O4(001) single-atom catalyst. We demonstrate that (PtCO)2dimers, formed dynamically through the agglomeration of mobile Pt-carbonyl species, catalyse a reaction involving the oxide support to form CO2. Pt2dimers produce one CO2molecule before falling apart into two adatoms, releasing the second CO. Interestingly, Olatticeextraction only becomes facile when both the Pt-dimer and the Fe3O4support can access metastable configurations, suggesting that substantial, concerted rearrangements of both cluster and support must be considered for reactions occurring at elevated temperature. © 2022, CC BY.

关键词： Platinum compounds

Fast-slow neural networks for learning singularly perturbed dynamical systems

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Journal of computational physics 2025年 537卷

作者： Serino, Daniel A. Alvarez Loya, Allen Burby, J.W. Kevrekidis, Ioannis G. Tang, Qi Los Alamos National Laboratory Los AlamosNM United States Department of Physics University of Texas at Austin AustinTX United States Department of Chemical and Biomolecular Engineering and Department of Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD United States School of Computational Science and Engineering Georgia Institute of Technology AtlantaGA United States

Singularly perturbed dynamical systems play a crucial role in climate dynamics and plasma physics. A powerful and well-known tool to address these systems is the Fenichel normal form, which significantly simplifies fast dynamics near slow manifolds through a transformation. However, this normal form is difficult to realize in conventional numerical algorithms. In this work, we explore an alternative way of realizing it through structure-preserving machine learning. Specifically, a fast-slow neural network (FSNN) is proposed for learning data-driven models of singularly perturbed dynamical systems with dissipative fast timescale dynamics. Our method enforces the existence of a trainable, attracting invariant slow manifold as a hard constraint. Closed-form representation of the slow manifold enables efficient integration on the slow time scale and significantly improves prediction accuracy beyond the training data. We demonstrate the FSNN on examples including the Grad moment system, two-scale Lorenz96 equations, and Abraham-Lorentz dynamics modeling radiation reaction of electrons. © 2025 Elsevier Inc.

关键词： Plant shutdowns

Generating large disordered stealthy hyperuniform systems with ultra-high accuracy to determine their physical properties

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arXiv 2023年

作者： Morse, Peter K. Kim, Jaeuk Steinhardt, Paul J. Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute of Materials Princeton University PrincetonNJ08544 United States Princeton Center for Theoretical Science Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Hyperuniform many-particle systems are characterized by a structure factor S(k) that is precisely zero as |k| → 0;and stealthy hyperuniform systems have S(k) = 0 for the finite range 0 30 for systems sizes more than an order of magnitude larger. We further show that this ultra-high accuracy is required to draw conclusions about their corresponding characteristics, such as the nature of the associated energy landscape and the presence or absence of Anderson localization, which might be masked, even when deviations are relatively small. © 2023, CC BY.

关键词： Physical properties