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MONGE-AMPÈRE FLOW FOR GENERATIVE MODELING

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arXiv 2018年

作者： Zhang, Linfeng Weinan, E. Wang, Lei Program in Applied and Computational Mathematics Princeton University United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University United States Center for Data Science Peking University Beijing Institute of Big Data Research Beijing100871 China Institute of Physics Chinese Academy of Sciences Beijing100190 China

We present a deep generative model, named Monge-Ampère flow, which builds on continuous-time gradient flow arising from the Monge-Ampère equation in optimal transport theory. The generative map from the latent space to the data space follows a dynamical system, where a learnable potential function guides a compressible fluid to flow towards the target density distribution. Training of the model amounts to solving an optimal control problem. The Monge-Ampère flow has tractable likelihoods and supports efficient sampling and inference. One can easily impose symmetry constraints in the generative model by designing suitable scalar potential functions. We apply the approach to unsupervised density estimation of the MNIST dataset and variational calculation of the two-dimensional Ising model at the critical point. This approach brings insights and techniques from Monge-Ampère equation, optimal transport, and fluid dynamics into reversible flow-based generative models. Copyright © 2018, The Authors. All rights reserved.

关键词： Statistical mechanics

Hard convex lens-shaped particles: Characterization of dense disordered packings

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arXiv 2019年

作者： Cinacchi, Giorgio Torquato, Salvatore Instituto de Ciencias de Materiales "Nicolás Cabrera" Universidad Autónoma de Madrid Ciudad Universitaria de Cantoblanco MadridE-28049 Spain Department of Chemistry Department of Physics Institute for the Science and Technology of Materials Program for Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Among the family of hard convex lens-shaped particles (lenses), the one with aspect ratio equal to 2/3 is ‘optimal’ in the sense that the maximally random jammed (MRJ) packings of such lenses achieve the highest packing fraction φMRJ ' 0.73. This value is only a few percent lower than φDKP = 0.76210 . . . , the packing fraction of the corresponding densest-known crystalline (degenerate) packings. By exploiting the appreciably reduced propensity that a system of such optimal lenses has to positionally and orientationally order, disordered packings of them are progressively generated by a Monte Carlo method-based procedure from the dilute equilibrium isotropic fluid phase to the dense nonequilibrium MRJ state. This allows one to closely monitor how the (micro)structure of these packings changes in the process of formation of the MRJ state. The gradual changes undergone by the many structural descriptors calculated can coherently and consistently be traced back to the gradual increase in contacts between the hard particles until the isostatic mean value of 10 contact neighbors per lens is reached at the effectively hyperuniform MRJ state. Compared to the MRJ state of hard spheres, the MRJ state of such optimal lenses is denser (less porous), more disordered, and rattler-free. This set of characteristics makes them good glass formers. It is possible that this conclusion may also hold for other hard convex uniaxial particles with a correspondingly similar aspect ratio, be they oblate or prolate, and that, by using suitable biaxial variants of them, that set of characteristics might further improve. Copyright © 2019, The Authors. All rights reserved.

关键词： Aspect ratio

New tessellation-based procedure to design perfectly hyperuniform disordered dispersions for materials discovery

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arXiv 2019年

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

Disordered hyperuniform dispersions are exotic amorphous two-phase materials characterized by an anomalous suppression of long-wavelength volume-fraction fluctuations, which endows them with novel physical properties. While such unusual materials have received considerable attention, a stumbling block has been an inability to create large samples that are truly hyperuniform due to current computational and experimental limitations. To overcome such barriers, we introduce a new and simple construction procedure that guarantees perfect hyperuniformity for very large sample sizes. This methodology involves tessellating space into cells and then inserting a particle into each cell such that the local-cell particle packing fractions are identical to the global packing fraction. We analytically prove that such dispersions are perfectly hyperuniform in the infinite-sample-size limit. Our methodology enables a remarkable mapping that converts a very large nonhyperuniform disordered dispersion into a perfectly hyperuniform one, which we numerically demonstrate in two and three dimensions. A similar analysis also establishes the hyperuniformity of the famous Hashin-Shtrikman multiscale dispersions, which possess optimal transport and elastic properties. Our hyperuniform designs can be readily fabricated using modern photolithographic and 3D printing technologies. The exploration of the enormous class of hyperuniform dispersions that can be designed and tuned by our tessellation-based methodology paves the way for accelerating the discovery of novel hyperuniform materials. Copyright © 2019, The Authors. All rights reserved.

关键词： 3D printers

Multifunctional Composites for Elastic and Electromagnetic Wave Propagation

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arXiv 2019年

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

Composites are ideally suited to achieve desirable multifunctional effective properties, since the best properties of different materials can be judiciously combined with designed microstructures. Here we establish the first cross-property relations for two-phase composite media that link effective elastic and electromagnetic wave characteristics to one another, including effective wave speeds and attenuation coefficients. This is achieved by deriving accurate formulas for the effective elastodynamic properties that depend on the microstructure via the spectral density and utilizing previous analogous results for effective electromagnetic properties. Our formulas enable us to explore the wave characteristics of a broad class of disordered microstructures, including exotic disordered "hyperuniform" varieties, that can have advantages over crystalline ones, such as nearly optimal, direction-independent properties and robustness against defects. We specifically show that disordered "stealthy" hyperuniform/nonhyperuniform microstructures exhibit novel elastic wave characteristics that have the potential for future applications, e.g., low-pass or narrow-band-pass (using negative Poisson ratio materials) filters that transmit or absorb elastic waves "isotropically" for a range of wavenumbers. We also demonstrate that two-phase media with engineered disorder and phase properties can exhibit "anomalous dispersion" with resonance-like attenuation. Our cross-property relations for effective wave characteristics can be applied to design multifunctional composites via inverse techniques, including exterior components of spacecraft or building materials that require both excellent stiffness and electromagnetic absorption, and heat-sinks for CPUs that have to efficiently emit thermal radiation and suppress mechanical vibrations, and nondestructive evaluation of the elastic moduli of materials from the effective dielectric response. DR Copyright © 2019, The Authors. All rights res

关键词： Microstructure

Methodology to construct large realizations of perfectly hyperuniform disordered packings

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arXiv 2019年

Disordered hyperuniform packings (or dispersions) are unusual amorphous two-phase materials that are endowed with exotic physical properties. Such hyperuniform systems are characterized by an anomalous suppression of volume-fraction fluctuations at infinitely long-wavelengths, compared to ordinary disordered materials. While there has been growing interest in such singular states of amorphous matter, a major obstacle has been an inability to produce large samples that are perfectly hyperuniform due to practical limitations of conventional numerical and experimental methods. To overcome these limitations, we introduce a general theoretical methodology to construct perfectly hyperuniform packings in d-dimensional Euclidean space Rd. Specifically, beginning with an initial general tessellation of space by disjoint cells that meets a "bounded-cell" condition, hard particles are placed inside each cell such that the local-cell particle packing fractions are identical to the global packing fraction. We prove that the constructed packings with a polydispersity in size in Rd are perfectly hyperuniform in the infinite-sample-size limit and the hyperuniformity of such packings is independent of particle shapes, positions, and numbers per cell. We use this theoretical formulation to devise an efficient and tunable algorithm to generate extremely large realizations of such packings. We employ two distinct initial tessellations: Voronoi as well as sphere tessellations. Beginning with Voronoi tessellations, we show that our algorithm can remarkably convert extremely large nonhyperuniform packings into hyperuniform ones in R2 and R3. Implementing our theoretical methodology on sphere tessellations, we establish the hyperuniformity of the classical Hashin-Shtrikman multiscale coated-spheres structures, which are known to be two-phase media microstructures that possess optimal effective transport and elastic properties. A consequence of our work is a rigorous demonstration that pack

关键词： Cells

Active learning of uniformly accurate inter-atomic potentials for materials simulation

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arXiv 2018年

作者： Zhang, Linfeng Lin, De-Ye Wang, Han Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China CAEP Software Center for High Performance Numerical Simulation Huayuan Road 6 Beijing100088 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China 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 Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Beijing Institute of Big Data Research Beijing100871 China

An active learning procedure called Deep Potential Generator (DP-GEN) is proposed for the construction of accurate and transferable machine learning-based models of the potential energy surface (PES) for the molecular modeling of materials. This procedure consists of three main components: exploration, generation of accurate reference data, and training. Application to the sample systems of Al, Mg and Al-Mg alloys demonstrates that DP-GEN can produce uniformly accurate PES models with a minimal number of reference data. Copyright © 2018, The Authors. All rights reserved.

关键词： Potential energy

Regularized matrix data clustering and its application to image analysis

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arXiv 2018年

作者： Gao, Xu Shen, Weining Ombao, Hernando Department of Statistics University of California IrvineCA United States Program on Applied Mathematics & Computational Science King Abdullah University of Science and Technology Saudi Arabia

In this paper, we propose a regularized mixture probabilistic model to cluster matrix data and apply it to brain signals. The approach is able to capture the sparsity (low rank, small/zero values) of the original signals by introducing regularization terms into the likelihood function. Through a modified EM algorithm, our method achieves the optimal solution with low computational cost. Theoretical results are also provided to establish the consistency of the proposed estimators. Simulations show the advantages of the proposed method over other existing methods. We also apply the approach to two real datasets from different experiments. Promising results imply that the proposed method successfully characterizes signals with different patterns while yielding insightful scientific interpretation. Copyright © 2018, The Authors. All rights reserved.

关键词： Matrix algebra

DeePCG: Constructing coarse-grained models via deep neural networks

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arXiv 2018年

作者： Weinan, E. Zhang, Linfeng Han, Jiequn Wang, Han Car, Roberto Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China Caep Software Center for High Performance Numerical Simulation Huayuan Road 6 Beijing100088 China Program in Applied and Computational Mathematics Princeton Institute for Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Beijing Institute of Big Data Research Beijing100871 China

We introduce a general framework for constructing coarse-grained potential models without ad hoc approximations such as limiting the potential to two- A nd/or three-body contributions. The scheme, called Deep Coarse-Grained Potential (abbreviated DeePCG), exploits a carefully crafted neural network to construct a many-body coarse-grained potential. The network is trained with full atomistic data in a way that preserves the natural symmetries of the system. The resulting model is very accurate and can be used to sample the configurations of the coarse-grained variables in a much faster way than with the original atomistic model. As an application we consider liquid water and use the oxygen coordinates as the coarse-grained variables, starting from a full atomistic simulation of this system at the ab initio molecular dynamics level. We find that the two-body, three-body, and higher-order oxygen correlation functions produced by the coarse-grained and full atomistic models agree very well with each other, illustrating the effectiveness of the DeePCG model on a rather challenging task. Copyright © 2018, The Authors. All rights reserved.

关键词： Deep neural networks

Interface-driven unusual anomalous Hall effect in MnxGa/Pt bilayers

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Physical Review B 2019年第18期100卷 184410-184410页

作者： K. K. Meng L. J. Zhu Z. H. Jin E. K. Liu X. P. Zhao I. A. Malik Z. G. Fu Y. Wu J. Miao X. G. Xu J. X. Zhang J. H. Zhao Y. Jiang Beijing Advanced Innovation Center for Materials Genome Engineering School of Materials Science and Engineering University of Science and Technology Beijing Beijing China Cornell University Ithaca New York 14853 USA Department of Applied Physics Graduate School of Engineering Tohoku University 6-6-05 Aoba-yama 980-8579 Sendai Japan Institute of Physics Chinese Academy of Sciences Beijing China State Key Laboratory of Superlattices and Microstructures Institute of Semiconductors Chinese Academy of Sciences Beijing China Department of Physics Beijing Normal University Beijing China Institute of Applied Physics and Computational Mathematics Beijing China

The effects of spin-orbit coupling and symmetry breaking at the interface between a ferromagnet and heavy metal are particularly important for spin-based information storage and computation. Recent discoveries suggest they can create novel chiral spin structures (e.g., skyrmions), which have often been identified through the appearance of the bump/dip features of Hall signals, the so-called topological Hall effect (THE). In this work, however, we present an unusual anomalous Hall effect (UAHE) in MnxGa/Pt bilayers and demonstrate that the features extremely similar to THE can be generated without involving any chiral spin structures. Low-temperature magnetic force microscopy has been used to explore the magnetic field-dependent behavior of spin structures, and the UAHE as a function of magnetic field does not peak near the maximal density of magnetic bubbles. Our results unambiguously evidence that the UAHE in MnxGa/Pt bilayers shows no correlation with chiral spin structures but is driven by the modified interfacial properties, indicating a wealth of underlying and interesting physics.

关键词： Anomalous Hall effect Spin-orbit coupling Topological Hall effect