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Deep Potential: A general representation of a many-body potential energy surface

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arXiv 2017年

作者： Han, Jiequn Zhang, Linfeng Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Mathematics Princeton University PrincetonNJ08544 United States Center for Data Science Beijing International Center for Mathematical Research Peking University Beijing Institute of Big Data Research Beijing100871 China

We present a simple, yet general, end-to-end deep neural network representation of the potential energy surface for atomic and molecular systems. This methodology, which we call Deep Potential, is "first-principle" based, in the sense that no ad hoc approximations or empirical fitting functions are required. The neural network structure naturally respects the underlying symmetries of the systems. When tested on a wide variety of examples, Deep Potential is able to reproduce the original model, either empirical or quantum mechanics based, within chemical accuracy. The computational cost of this new model is not substantially larger than that of empirical force fields. In addition, the method has promising scalability properties. This brings us one step closer to being able to carry out molecular simulations with accuracy comparable to that of quantum mechanics models and computational cost comparable to that of empirical potentials. Copyright © 2017, The Authors. All rights reserved.

关键词： Deep neural networks

Inverse design of disordered stealthy hyperuniform spin chains

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Physical Review B 2016年第6期93卷 064201-064201页

作者： Eli Chertkov Robert A. DiStasio, Jr. Ge Zhang Roberto Car Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Chemistry and Chemical Biology Cornell University Ithaca New York 14853 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Positioned between crystalline solids and liquids, disordered many-particle systems which are stealthy and hyperuniform represent new states of matter that are endowed with novel physical and thermodynamic properties. Such stealthy and hyperuniform states are unique in that they are transparent to radiation for a range of wave numbers around the origin. In this work, we employ recently developed inverse statistical-mechanical methods, which seek to obtain the optimal set of interactions that will spontaneously produce a targeted structure or configuration as a unique ground state, to investigate the spin-spin interaction potentials required to stabilize disordered stealthy hyperuniform one-dimensional (1D) Ising-type spin chains. By performing an exhaustive search over the spin configurations that can be enumerated on periodic 1D integer lattices containing N=2,3,...,36 sites, we were able to identify and structurally characterize all stealthy hyperuniform spin chains in this range of system sizes. Within this pool of stealthy hyperuniform spin configurations, we then utilized such inverse optimization techniques to demonstrate that stealthy hyperuniform spin chains can be realized as either unique or degenerate disordered ground states of radial long-ranged (relative to the spin-chain length) spin-spin interactions. Such exotic ground states appear to be distinctly different from spin glasses in both their inherent structural properties and the nature of the spin-spin interactions required to stabilize them. As such, the implications and significance of the existence of these disordered stealthy hyperuniform ground-state spin systems warrants further study, including whether their bulk physical properties and excited states, like their many-particle system counterparts, are singularly remarkable, and can be experimentally realized.

关键词： Optimization problems Ising model Spin chains

Domain morphology and mechanics of the H/T′ transition metal dichalcogenide monolayers

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Physical Review Materials 2018年第11期2卷 114002-114002页

作者： Joel Berry Songsong Zhou Jian Han David J. Srolovitz Mikko P. Haataja Department of Materials Science and Engineering University of Pennsylvania Philadelphia Pennsylvania 19104 USA Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544 USA Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Philadelphia Pennsylvania 19104 USA Department of Materials Science and Engineering City University of Hong Kong Hong Kong SAR People's Republic of China Princeton Institute for the Science and Technology of Materials (PRISM) Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

The properties of two-dimensional (2D) transition metal dichalcogenide (TMD) monolayers can be dynamically controlled via strain-induced displacive structural transformations between semiconducting (H) and metallic or semimetallic (T′) crystal structures. The shapes, symmetries, and kinetics of crystalline domains generated during these transformations and the mechanical response of transforming monolayers are of fundamental and applied interest in, e.g., phase change memory devices and the study of topologically protected edge states in quantum spin Hall insulating T′ crystals. We quantitatively characterize T′ domain morphologies during H→T′ transformations in both flat and bendable TMD monolayers using a combination of first principles and continuum calculations. Wulff constructions for MoTe2 and MoS2 show that T′ domains within much larger T′ domains are either rhombi of fixed proportions (if nonmisfitting) or rectangles whose aspect ratio AR increases with domain size L0 (if misfitting). Isolated T′ domains within much larger H domains undergo a morphological crossover from compact to elongated shapes at L0≈100–200 nm if the sheet is constrained to be flat or L0≳2μm if the sheet is free to bend. This crossover is driven by a competition between anisotropic interfacial energy and elastic misfit energy, and its position can be tuned via the monolayer-substrate interaction strength. It is shown that the aspect ratio AR obeys a scaling law AR∼L02/3. Stress-strain response characterized as a function of strain orientation reveals extreme anisotropy in the effective elastic modulus through H/T′ coexistence. Ferroelastic multidomain T′−WTe2 monolayers are found to exhibit two to three regimes of reversible mechanical response, and localized buckling in freely suspended T′ monolayers is shown to qualitatively alter T′ domain symmetries.

关键词： Bending Domain walls Mechanical deformation Microstructure Structural phase transition 2-dimensional systems Transition metal dichalcogenides Density functional theory Phase-field modeling

Neural canonical transformation with symplectic flows

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arXiv 2019年

作者： Li, Shuo-Hui Dong, Chen-Xiao Zhang, Linfeng Wang, Lei Institute of Physics Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States CAS Center for Excellence in Topological Quantum Computation University of Chinese Academy of Sciences Beijing100190 China Songshan Lake Materials Laboratory Dongguan Guangdong523808 China

Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. We construct flexible and powerful canonical transformations as generative models using symplectic neural networks. The model transforms physical variables towards a latent representation with an independent harmonic oscillator Hamiltonian. Correspondingly, the phase space density of the physical system flows towards a factorized Gaussian distribution in the latent space. Since the canonical transformation preserves the Hamiltonian evolution, the model captures nonlinear collective modes in the learned latent representation. We present an efficient implementation of symplectic neural coordinate transformations and two ways to train the model. The variational free energy calculation is based on the analytical form of physical Hamiltonian. While the phase space density estimation only requires samples in the coordinate space for separable Hamiltonians. We demonstrate appealing features of neural canonical transformation using toy problems including two-dimensional ring potential and harmonic chain. Finally, we apply the approach to real-world problems such as identifying slow collective modes in alanine dipeptide and conceptual compression of the MNIST dataset. Copyright © 2019, The Authors. All rights reserved.

关键词： Hamiltonians

Microstructural degeneracy associated with a two-point correlation function and its information content

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Physical Review E 2012年第5期85卷 051140-051140页

作者： C. J. Gommes Y. Jiao S. Torquato Department of Chemical Engineering University of Liège Liège 4000 Belgium Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

A two-point correlation function provides a crucial yet an incomplete characterization of a microstructure because distinctly different microstructures may have the same correlation function. In an earlier Letter [Gommes, Jiao, and Torquato, Phys. Rev. Lett. 108, 080601 (2012)], we addressed the microstructural degeneracy question: What is the number of microstructures compatible with a specified correlation function? We computed this degeneracy, i.e., configurational entropy, in the framework of reconstruction methods, which enabled us to map the problem to the determination of ground-state degeneracies. Here, we provide a more comprehensive presentation of the methodology and analyses, as well as additional results. Since the configuration space of a reconstruction problem is a hypercube on which a Hamming distance is defined, we can calculate analytically the energy profile of any reconstruction problem, corresponding to the average energy of all microstructures at a given Hamming distance from a ground state. The steepness of the energy profile is a measure of the roughness of the energy landscape associated with the reconstruction problem, which can be used as a proxy for the ground-state degeneracy. The relationship between this roughness metric and the ground-state degeneracy is calibrated using a Monte Carlo algorithm for determining the ground-state degeneracy of a variety of microstructures, including realizations of hard disks and Poisson point processes at various densities as well as those with known degeneracies (e.g., single disks of various sizes and a particular crystalline microstructure). We show that our results can be expressed in terms of the information content of the two-point correlation functions. From this perspective, the a priori condition for a reconstruction to be accurate is that the information content, expressed in bits, should be comparable to the number of pixels in the unknown microstructure. We provide a formula to calculate the

关键词： MICROSTRUCTURE CORRELATION (Statistics) INFORMATION theory ENTROPY (Information theory) GROUND state (Quantum mechanics) MONTE Carlo method POISSON processes

Manifestations of metastable criticality in the long-range structure of model water glasses

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arXiv 2021年

作者： Gartner, Thomas E. Torquato, Salvatore Car, Roberto Debenedetti, Pablo G. Department of Chemistry Princeton University PrincetonNJ United States Department of Physics Princeton University PrincetonNJ United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ United States Department of Chemical and Biological Engineering Princeton University PrincetonNJ United States

Much attention has been devoted to water’s metastable phase behavior, including polyamorphism (multiple amorphous solid phases), and the hypothesized liquid-liquid transition and associated critical point. However, the possible relationship between these phenomena remains incompletely understood. Using molecular dynamics simulations of the realistic TIP4P/2005 model, we found a striking signature of the liquid-liquid critical point in the structure of water glasses, manifested as a pronounced increase in long-range density fluctuations at pressures proximate to the critical pressure. By contrast, these signatures were absent in glasses of two model systems that lack a critical point. We also characterized the departure from equilibrium upon vitrification via the non-equilibrium index;water-like systems exhibited a strong pressure dependence in this metric, whereas simple liquids did not. These results reflect a surprising relationship between the metastable equilibrium phenomenon of liquid-liquid criticality and the non-equilibrium structure of glassy water, with implications for our understanding of water phase behavior and glass physics. Our calculations suggest a possible experimental route to probing the existence of the liquid-liquid transition in water and other fluids. © 2021, CC BY.

关键词： Criticality (nuclear fission)

Causal unit of rotors in a cardiac system

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arXiv 2017年

作者： Ashikaga, Hiroshi Prieto-Castrillo, Francisco Kawakatsu, Mari Dehghani, Nima Cardiac Arrhythmia Service Johns Hopkins University School of Medicine 600 N Wolfe Street Carnegie 568 BaltimoreMD21287 United States Media Lab Massachusetts Institute of Technology CambridgeMA United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Physics Massachusetts Institute of Technology CambridgeMA United States

The heart exhibits complex systems behaviors during atrial fibrillation (AF), where the macroscopic collective behavior of the heart causes the microscopic behavior. However, the relationship between the downward causation and scale is nonlinear. We describe rotors in multiple spatiotemporal scales by generating a renormalization group from a numerical model of cardiac excitation, and evaluate the causal architecture of the system by quantifying causal emergence. Causal emergence is an information-theoretic metric that quantifies emergence or reduction between microscopic and macroscopic behaviors of a system by evaluating effective information at each spatiotemporal scale. We find that there is a spatiotemporal scale at which effective information peaks in the cardiac system with rotors. There is a positive correlation between the number of rotors and causal emergence up to the scale of peak causation. In conclusion, one can coarse-grain the cardiac system with rotors to identify a macroscopic scale at which the causal power reaches the maximum. This scale of peak causation should correspond to that of the AF driver, where networks of cardiomyocytes serve as the causal units. Those causal units, if identified, can be reasonable therapeutic targets of clinical intervention to cure AF. Copyright © 2017, The Authors. All rights reserved.

关键词： Heart

Antithetic Multilevel Methods for Elliptic and Hypo-Elliptic Diffusions with Applications

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arXiv 2024年

作者： Iguchi, Yuga Jasra, Ajay Maama, Mohamed Beskos, Alexandros Department of Statistical Science University College London LondonWC1E 6BT United Kingdom School of Data Science The Chinese University of Hong Kong Shenzhen China 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

In this paper we present a new antithetic multilevel Monte Carlo (MLMC) method for the estimation of expectations with respect to laws of diffusion processes that can be elliptic or hypo-elliptic. In particular, we consider the case where one has to resort to time discretization of the diffusion and numerical simulation of such schemes. Motivated by recent developments, we introduce a new MLMC estimator of expectations, which does not require simulation of intractable Lévy areas but has a weak error of order 2 and achieves the optimal computational complexity. We then show how this approach can be used in the context of the filtering problem associated to partially observed diffusions with discrete time observations. We illustrate with numerical simulations that our new approaches provide efficiency gains for several problems relative to some existing methods. © 2024, CC BY.

关键词： Diffusion

Disordered Heterogeneous Universe: Galaxy Distribution and Clustering across Length Scales

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Physical Review X 2023年第1期13卷 011038-011038页

作者： Oliver H. E. Philcox Salvatore Torquato Department of Astrophysical Sciences Princeton University Princeton New Jersey 08540 USA School of Natural Sciences Institute for Advanced Study 1 Einstein Drive Princeton New Jersey 08540 USA Center for Theoretical Physics Department of Physics Columbia University New York New York 10027 USA Simons Foundation New York New York 10010 USA Department of Chemistry Department of Physics Princeton Materials Institute and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA

The studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the disordered distribution of particles and/or building blocks at microscales to predict physical properties of the medium at macroscales, whether it be a liquid, colloidal suspension, composite material, galaxy cluster, or entire Universe. The theory of disordered heterogeneous media provides an array of theoretical and computational techniques to characterize a wide class of complex material microstructures. In this work, we apply them to describe the disordered distributions of galaxies obtained from recent suites of dark matter simulations. We focus on the determination of lower-order correlation functions, void and particle nearest-neighbor functions, certain cluster statistics, pair-connectedness functions, percolation properties, and a scalar order metric to quantify the degree of order. Compared to analogous homogeneous Poisson and typical disordered systems, the cosmological simulations exhibit enhanced large-scale clustering and longer tails in the void and particle nearest-neighbor functions, due to the presence of quasi-long-range correlations imprinted by early Universe physics, with a minimum particle separation far below the mean nearest-neighbor distance. On large scales, the system appears hyperuniform, as a result of primordial density fluctuations, while on the smallest scales, the system becomes almost antihyperuniform, as evidenced by its number variance. Additionally, via a finite-scaling analysis, we compute the percolation threshold of the galaxy catalogs, finding this to be significantly lower than for Poisson realizations (at reduced density ηc=0.25 in our fiducial analysis compared to ηc=0.34), with strong dependence on the mean density; this is consistent with the observation that the galaxy distribution contains voids of up to 50% larger radius. However, the two sets of simulations appear to share the same fractal dimension on scales much l

关键词： Large scale structure of the Universe