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Deep Potentials for Materials Science

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arXiv 2022年

作者： Wen, Tongqi Zhang, Linfeng Wang, Han Weinan, E. Srolovitz, David J. Department of Mechanical Engineering The University of Hong Kong Hong Kong DP Technology Beijing China AI for Science Institute Beijing China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing China HEDPS CAPT College of Engineering Peking University Beijing China School of Mathematical Sciences Peking University Beijing China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton United States Shenzhen 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;i.e., machine learning potentials (MLPs). One recently developed type of MLP is the Deep Potential (DP) method. In this review, we provide an introduction to DP methods in computational materials science. The theory underlying the DP method is presented along with a step-by-step introduction to their development and use. We also review materials applications of DPs in a wide range of materials systems. The DP Library provides a platform for the development of DPs and a database of extant DPs. We discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials. Copyright © 2022, The Authors. All rights reserved.

关键词： Calculations

Phase Diagram of a Deep Potential Water Model

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Physical Review Letters 2021年第23期126卷 236001-236001页

作者： Linfeng Zhang Han Wang Roberto Car Weinan E Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA and Beijing Institute of Big Data Research Beijing 100871 People’s Republic of China

Using the Deep Potential methodology, we construct a model that reproduces accurately the potential energy surface of the SCAN approximation of density functional theory for water, from low temperature and pressure to about 2400 K and 50 GPa, excluding the vapor stability region. The computational efficiency of the model makes it possible to predict its phase diagram using molecular dynamics. Satisfactory overall agreement with experimental results is obtained. The fluid phases, molecular and ionic, and all the stable ice polymorphs, ordered and disordered, are predicted correctly, with the exception of ice III and XV that are stable in experiments, but metastable in the model. The evolution of the atomic dynamics upon heating, as ice VII transforms first into ice VII′′ and then into an ionic fluid, reveals that molecular dissociation and breaking of the ice rules coexist with strong covalent fluctuations, explaining why only partial ionization was inferred in experiments.

关键词： Classical statistical mechanics First order phase transitions Interatomic & molecular potentials Phase diagrams Potential energy surfaces Water First-principles calculations Machine learning Molecular dynamics

Velocity-gauge Real-time Time-dependent Density Functional Tight-binding for Large-scale Condensed Matter Systems

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arXiv 2023年

作者： Xu, Qiang Del Ben, Mauro Okyay, Mahmut Sait Choi, Min Ibrahim, Khaled Z. Wong, Bryan M. Materials Science & Engineering Program Department of Chemistry Department of Physics & Astronomy University of California-Riverside RiversideCA92521 United States Applied Mathematics & Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

We present a new velocity-gauge real-time, time-dependent density functional tight-binding (VG-rtTDDFTB) implementation in the open-source DFTB+ software package (https://***) for probing electronic excitations in large, condensed matter systems. Our VG-rtTDDFTB approach enables real-time electron dynamics simulations of large, periodic, condensed matter systems containing thousands of atoms with a favorable computational scaling as a function of system size. We provide computational details and benchmark calculations to demonstrate its accuracy and computational parallelizability on a variety of large material systems. As a representative example, we calculate laser-induced electron dynamics in a 512-atom amorphous silicon supercell to highlight the large periodic systems that can be examined with our implementation. Taken together, our VG-rtTDDFTB approach enables new electron dynamics simulations of complex systems that require large periodic supercells, such as crystal defects, complex surfaces, nanowires, and amorphous materials. Copyright © 2023, The Authors. All rights reserved.

关键词： Gages

Effective Transport and Mechanical Properties of Two-Phase Materials Across the Order-Disorder Spectrum

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SSRN

SSRN 2025年

作者： Skolnick, Murray 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 Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Two-phase heterogeneous materials arise in a plethora of natural and synthetic situations, such as alloys, composites, geological media, complex fluids, and biological media, exhibit a wide-variety of microstructures, and thus display a broad-spectrum of effective physical properties. Elucidating how microstructural details (e.g., specific surface, phase volume fractions, geometries, and topologies) influence two-phase materials’ effective transport and mechanical properties enhances our fundamental understanding of microstructure-property relationships, and is of great practical use in the design of structural and functional materials. Here, we compute the three-point microstructural parameters ζ2 and η2 for phase 2 to evaluate bounds and accurate approximation formulas on the effective thermal/electrical conductivities σe as well as the bulk Ke and shear Ge moduli of a wide class of disordered 2D and 3D material microstructures;including various dispersions of hard and penetrable particles, certain amorphous dispersions, and networks. These parameters are determined using a Monte Carlo integration scheme that incorporates certain algorithmic enhancements that improve upon the accuracy and performance of previous methods. Our results reveal that ζ2 and η2 are sensitive to the phase-connectedness properties of microstructures. Using numerical simulations and rigorous approximations that incorporate ζ2 and η2, we show that certain disordered microstructures nearly realize the Hashin-Shtrikman lower and upper bounds on σe, Ke, and Ge across volume-fractions. We also describe how our algorithm can be used in inverse methodologies to realize ordered and disordered materials with desirable effective physical properties by targeting specific values of ζ2 and η2, and hence aid in materials by design. © 2025, The Authors. All rights reserved.

关键词： Inverse problems

Existence of Nonequilibrium Glasses in the Degenerate Stealthy Hyperuniform Ground-State Manifold

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arXiv 2025年

作者： Torquato, Salvatore Kim, Jaeuk Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Stealthy interactions are an emerging class of nontrivial, bounded long-ranged oscillatory pair potentials with classical ground states that can be disordered, hyperuniform, and infinitely degenerate. Their hybrid crystal-liquid nature endows them with novel physical properties with advantages over their crystalline counterparts. Here, we show the existence of nonequilibrium hard-sphere glasses within this unusual ground-state manifold as the stealthiness parameter χ tends to zero that are remarkably configurationally extremely close to hyperuniform 3D maximally random jammed (MRJ) sphere packings. The latter are prototypical glasses since they are maximally disordered, perfectly rigid, and perfectly nonergodic. Our optimization procedure, which leverages the maximum cardinality of the infinite ground-state set, not only guarantees that our packings are hyperuniform with the same structure-factor scaling exponent as the MRJ state, but they share other salient structural attributes, including a packing fraction of 0.638, a mean contact number per particle of 6, gap exponent of 0.44(1), and pair correlation functions g2(r) and structures factors S(k) that are virtually identical to one another for all r and k, respectively. Moreover, we demonstrate that stealthy hyperuniform packings can be created within the disordered regime (0 © 2025, CC0.

关键词： Liquid crystals

Multilevel Monte Carlo for a class of Partially Observed Processes in Neuroscience

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arXiv 2023年

作者： Maama, Mohamed Jasra, Ajay Kamatani, Kengo Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia School of Data Science The Chinese University of Hong Kong CN Shenzhen China Institute of Statistical Mathematics Tokyo190-0014 Japan

In this paper we consider Bayesian parameter inference associated to a class of partially observed stochastic differential equations (SDE) driven by jump processes. Such type of models can be routinely found in applications, of which we focus upon the case of neuroscience. The data are assumed to be observed regularly in time and driven by the SDE model with unknown parameters. In practice the SDE may not have an analytically tractable solution and this leads naturally to a time-discretization. We adapt the multilevel Markov chain Monte Carlo method of [15], which works with a hierarchy of time discretizations and show empirically and theoretically that this is preferable to using one single time discretization. The improvement is in terms of the computational cost needed to obtain a pre-specified numerical error. Our approach is illustrated on models applied to examples of Bayesian inference problems using both simulated and real observed data from neuroscience. Copyright © 2023, The Authors. All rights reserved.

关键词： Stochastic systems

An L2 Analysis of Reinforcement Learning in High Dimensions with Kernel and Neural Network Approximation

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arXiv 2021年

作者： Long, Jihao Han, Jiequn Weinan, E. Program of Applied and Computational Mathematics Princeton University United States Department of Mathematics Princeton University United States Center for Computational Mathematics Flatiron Institute School of Mathematical Sciences Peking University

Reinforcement learning (RL) algorithms based on high-dimensional function approximation have achieved tremendous empirical success in large-scale problems with an enormous number of states. However, most analysis of such algorithms gives rise to error bounds that involve either the number of states or the number of features. This paper considers the situation where the function approximation is made either using the kernel method or the two-layer neural network model, in the context of a fitted Q-iteration algorithm with explicit regularization. We establish an Õ(H3|A|1/4 n- 1/4) bound for the optimal policy with Hn samples, where H is the length of each episode and |A| is the size of action space. Our analysis hinges on analyzing the L2 error of the approximated Q-function using n data points. Even though this result still requires a finite-sized action space, the error bound is independent of the dimensionality of the state space. Copyright © 2021, The Authors. All rights reserved.

关键词： Error analysis

Transient rod-climbing in an Oldroyd-B fluid

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arXiv 2025年

作者： Ruangkriengsin, Tachin Brandão, Rodolfo Wu, Katie Hwang, Jonghyun Boyko, Evgeniy Stone, Howard A. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States School of Mathematics University of Bristol Fry Building Woodland Road BristolBS8 1UG United Kingdom Department of Mechanical and Aerospace Engineering Princeton University PrincetonNJ08544 United States Faculty of Mechanical Engineering Technion – Israel Institute of Technology Haifa3200003 Israel

The Weissenberg effect, or rod-climbing phenomenon, occurs in non-Newtonian fluids where the fluid interface ascends along a rotating rod. Despite its prominence, theoretical insights into this phenomenon remain limited. In earlier work, Joseph & Fosdick (Arch. Rat. Mech. Anal., vol. 49, 1973, pp. 321–380) employed domain perturbation methods for second-order fluids to determine the equilibrium interface height by expanding solutions based on the rotation speed. In this work, we investigate the time-dependent interface height through asymptotic analysis with dimensionless variables and equations using the Oldroyd-B model. We begin by neglecting surface tension and inertia to focus on the interaction between gravity and viscoelasticity. In the small-deformation scenario, the governing equations indicate the presence of a boundary layer in time, where the interface rises rapidly over a short time scale before gradually approaching a steady state. By employing a stretched time variable, we derive the transient velocity field and corresponding interface profile on this short time scale and recover the steady-state profile on a longer time scale. Subsequently, we reintroduce small but finite inertial effects to investigate their interplay with viscoelasticity and propose a criterion for determining the conditions under which rod-climbing occurs. © 2025, CC BY.

关键词： Non Newtonian liquids

Structural characterization of many-particle systems on approach to hyperuniform states

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Physical Review E 2021年第5期103卷 052126-052126页

作者： Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

The study of hyperuniform states of matter is an emerging multidisciplinary field, impinging on topics in the physical sciences, mathematics, and biology. The focus of this work is the exploration of quantitative descriptors that herald when a many-particle system in d-dimensional Euclidean space Rd approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative criteria to ascertain the extent of hyperuniform and nonhyperuniform distance-scaling regimes as well as the crossover point between them in terms of the “volume” coefficient A and “surface-area” coefficient B associated with the local number variance σ2(R) for a spherical window of radius R. The larger the ratio B/A, the larger the hyperuniform scaling regime, which becomes of infinite extent in the limit B/A→∞. To complement the known direct-space representation of the coefficient B in terms of the total correlation function h(r), we derive its corresponding Fourier representation in terms of the structure factor S(k), which is especially useful when scattering information is available experimentally or theoretically. We also demonstrate that the free-volume theory of the pressure of equilibrium packings of identical hard spheres that approach a strictly jammed state either along the stable crystal or metastable disordered branch dictates that such end states be exactly hyperuniform. Using the ratio B/A, as well as other diagnostic measures of hyperuniformity, including the hyperuniformity index H and the direct-correlation function length scale ξc, we study three different exactly solvable models as a function of the relevant control parameter, either density or temperature, with end states that are perfectly hyperuniform. Specifically, we analyze equilibrium systems of hard rods and “sticky” hard-sphere systems in arbitrary space dimension d as a function of density. We also examine low-temperature excited states of many-particle systems interacting with “stealt

关键词： Fluctuations & noise