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Methodology to construct large realizations of perfectly hyperuniform disordered packings

Physical Review E 2019年第5期99卷 052141-052141页

作者： Jaeuk Kim Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 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

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 of general shape 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 are perfectly hyperuniform in the infinite-sample-size limit, regardless 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 packings that have identical tessella

关键词： Fluctuations & noise

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End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems 18

End-to-end symmetry preserving inter-atomic potential energy...

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Proceedings of the 32nd International Conference on Neural Information Processing Systems

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

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Isotope effects in liquid water via deep potential molecular dynamics

arXiv

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arXiv 2019年

作者： Ko, Hsin-Yu Zhang, Linfeng Santra, Biswajit Wang, Han Weinan, E. DiStasio, Robert A. Cara, Roberto Department of Chemistry Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Physics Temple University PhiladelphiaPA19122 United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China Department of Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry and Chemical Biology Cornell University IthacaNY14853 United States Department of Physics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States

A comprehensive microscopic understanding of ambient liquid water is a major challenge for ab initio simulations as it simultaneously requires an accurate quantum mechanical description of the underlying potential energy surface (PES) as well as extensive sampling of configuration space. Due to the presence of light atoms (e.g., H or D), nuclear quantum fluctuations lead to observable changes in the structural properties of liquid water (e.g., isotope effects), and therefore provide yet another challenge for ab initio approaches. In this work, we demonstrate that the combination of dispersion-inclusive hybrid density functional theory (DFT), the Feynman discretized path-integral (PI) approach, and machine learning (ML) constitutes a versatile ab initio based framework that enables extensive sampling of both thermal and nuclear quantum fluctuations on a quite accurate underlying PES. In particular, we employ the recently developed deep potential molecular dynamics (DPMD) model - a neural-network representation of the ab initio PES - in conjunction with a PI approach based on the generalized Langevin equation (PIGLET) to investigate how isotope effects influence the structural properties of ambient liquid H2O and D2O. Through a detailed analysis of the interference differential cross sections as well as several radial and angular distribution functions, we demonstrate that this approach can furnish a semi-quantitative prediction of these subtle isotope effects. Copyright © 2019, The Authors. All rights reserved.

关键词： Deep neural networks

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Universal approximation of symmetric and anti-symmetric functions

arXiv

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arXiv 2019年

作者： Han, Jiequn Li, Yingzhou Lin, Lin Lu, Jianfeng Zhang, Jiefu Zhang, Linfeng Department of Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Duke University DurhamNC27708 United States Department of Mathematics University of California BerkeleyCA94720 United States Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Department of Mathematics Department of Physics Department of Chemistry Duke University DurhamNC27708 United States Department of Mathematics University of California BerkeleyCA94720 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We consider universal approximations of symmetric and anti-symmetric functions, which are important for applications in quantum physics, as well as other scientific and engineering computations. We give constructive approximations with explicit bounds on the number of parameters with respect to the dimension and the target accuracy ǫ. While the approximation still suffers from curse of dimensionality, to the best of our knowledge, these are first results in the literature with explicit error bounds. Moreover, we also discuss neural network architecture that can be suitable for approximating symmetric and anti-symmetric functions. Copyright © 2019, The Authors. All rights reserved.

关键词： Network architecture

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End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems 32

End-to-end symmetry preserving inter-atomic potential energy...

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32nd Conference on Neural Information Processing Systems, NeurIPS 2018

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 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

关键词： Potential energy

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Impacts of permeability heterogeneities on foam flow in porous media: Uncertainty quantification and sensitivity analysis

Gas Science and Engineering

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Gas Science and Engineering 2025年 142卷

作者： Berilo de Oliveira Santos Rodrigo Weber dos Santos Iury Igreja Grigori Chapiro Bernardo Martins Rocha Laboratory of Applied Mathematics (LAMAP) Federal University of Juiz de Fora Campus Universitário Rua José Lourenço Kelmer s/n - São Pedro Juiz de Fora 36036-900 Minas Gerais Brazil Graduate Program in Computational Modeling Federal University of Juiz de Fora Campus Universitário Rua José Lourenço Kelmer s/n - São Pedro Juiz de Fora 36036-900 Minas Gerais Brazil Department of Computer Science Federal University of Juiz de Fora Campus Universitário Rua José Lourenço Kelmer s/n - São Pedro Juiz de Fora 36036-900 Minas Gerais Brazil Department of Mathematics Federal University of Juiz de Fora Campus Universitário Rua José Lourenço Kelmer s/n - São Pedro Juiz de Fora 36036-900 Minas Gerais Brazil

Foam injection in porous media has been extensively studied for its ability to improve sweep efficiency by mitigating nonlinear phenomena such as gravitational segregation and viscous fingering. However, modeling foam flow remains a significant challenge, mainly due to the complex interactions between foam and heterogeneous geological formations, which are often difficult to characterize. In particular, the spatial distribution of absolute permeability is difficult to obtain, due to scarce data and strong heterogeneity. These challenges introduce uncertainties into predictive models. In particular, the relationship between foam flow and uncertainties related to absolute permeability fields remains underexplored in the literature. This work performs uncertainty propagation studies to investigate the influence of permeability heterogeneity on foam flow in porous media. This is achieved by coupling the Karhunen-Loève expansion (KLE), which generates Gaussian random permeability fields, with Polynomial Chaos Expansion (PCE), a method for propagating uncertainties in a computationally efficient manner. This approach allows for the evaluation of permeability variations impact on key quantities of interest (QoIs) related to flow performance. The results, derived from uncertainty quantification (UQ) and sensitivity analysis (SA), reveal that foam behavior is highly sensitive to the spatial correlation structures of permeability, with important implications for optimizing foam flow processes. The integration of KLE and PCE provides the first systematic framework for uncertainty propagation in foam flow analysis, unveiling previously unexplored correlations and behaviors. These findings highlight the importance of incorporating permeability uncertainties into modeling to improve the reliability and efficiency of both subsurface flow applications, including resource recovery and carbon sequestration efforts. The proposed methodology can be particularly beneficial in practical

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Manifold learning-based methods for analyzing single-cell RNA-sequencing data

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Current Opinion in Systems Biology 2018年 7卷 36-46页

作者： Moon, Kevin R. Stanley, Jay S. Burkhardt, Daniel van Dijk, David Wolf, Guy Krishnaswamy, Smita Department of Genetics Yale University New Haven CT United States Applied Mathematics Program Yale University New Haven CT United States Computational Biology and Bioinformatics Program Yale University New Haven CT United States Department of Computer Science Yale University New Haven CT United States

Recent advances in single-cell RNA sequencing technologies enable deep insights into cellular development, gene regulation, and phenotypic diversity by measuring gene expression for thousands of cells in a single experiment. While these technologies hold great potential for improving our understanding of cellular states and progression, they also pose new challenges and require advanced mathematical and algorithmic tools to extract underlying biological signals. In this review, we cover one of the most promising avenues of research into unlocking the potential of scRNA-seq data: the field of manifold learning, and the related manifold assumption in data analysis. Manifold learning provides a powerful structure for algorithmic approaches to process the data, extract its dynamics, and infer patterns in it. In particular, we cover manifold learning-based methods for denoising the data, revealing gene interactions, extracting pseudotime progressions with model fitting, visualizing the cellular state space via dimensionality reduction, and clustering the data. © 2017 Published by Elsevier Ltd.

关键词： Data mining Gene regulatory networks Imputation Manifold learning Pseudotime trends Single cell RNA sequencing

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Geometry based data generation 32

Geometry based data generation

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32nd Conference on Neural Information Processing Systems, NeurIPS 2018

作者： Lindenbaum, Ofir Wolf, Guy Stanley, Jay S. Krishnaswamy, Smita Applied Mathematics Program Yale University New HavenCT06511 United States Computational Biology and Bioinformatics Program Yale University New HavenCT06510 United States Departments of Genetics and Computer Science Yale University New HavenCT06510 United States

We propose a new type of generative model for high-dimensional data that learns a manifold geometry of the data, rather than density, and can generate points evenly along this manifold. This is in contrast to existing generative models that represent data density, and are strongly affected by noise and other artifacts of data collection. We demonstrate how this approach corrects sampling biases and artifacts, thus improves several downstream data analysis tasks, such as clustering and classification. Finally, we demonstrate that this approach is especially useful in biology where, despite the advent of single-cell technologies, rare subpopulations and gene-interaction relationships are affected by biased sampling. We show that SUGAR can generate hypothetical populations, and it is able to reveal intrinsic patterns and mutual-information relationships between genes on a single-cell RNA sequencing dataset of hematopoiesis. © 2018 Curran Associates Inc..All rights reserved.

关键词： Genes

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Inverting the markovian projection, with an application to local stochastic volatility models

arXiv

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arXiv 2019年

作者： Lacker, Daniel Shkolnikov, Mykhaylo Zhang, Jiacheng Ieor Department Columbia University New YorkNY10027 United States Orfe Department Bendheim Center for Finance Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 Orfe Department Princeton University PrincetonNJ08544 United States

We study two-dimensional stochastic differential equations (SDEs) of McKean- Vlasov type in which the conditional distribution of the second component of the solution given the first enters the equation for the first component of the solution. Such SDEs arise when one tries to invert the Markovian projection developed in [Gyö86], typically to produce an It o process with the fixed-time marginal distributions of a given one-dimensional diffusion but richer dynamical features. We prove the strong existence of stationary solutions for these SDEs, as well as their strong uniqueness in an important special case. Variants of the SDEs discussed in this paper enjoy frequent application in the calibration of local stochastic volatility models in finance, despite the very limited theoretical understanding. Copyright © 2019, The Authors. All rights reserved.

关键词： Stochastic systems

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Characterization of maximally random jammed sphere packings. III. Transport and electromagnetic properties via correlation functions

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Physical Review E 2018年第1期97卷 012118-012118页

作者： Michael A. Klatt 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

In the first two papers of this series, we characterized the structure of maximally random jammed (MRJ) sphere packings across length scales by computing a variety of different correlation functions, spectral functions, hole probabilities, and local density fluctuations. From the remarkable structural features of the MRJ packings, especially its disordered hyperuniformity, exceptional physical properties can be expected. Here we employ these structural descriptors to estimate effective transport and electromagnetic properties via rigorous bounds, exact expansions, and accurate analytical approximation formulas. These property formulas include interfacial bounds as well as universal scaling laws for the mean survival time and the fluid permeability. We also estimate the principal relaxation time associated with Brownian motion among perfectly absorbing traps. For the propagation of electromagnetic waves in the long-wavelength limit, we show that a dispersion of dielectric MRJ spheres within a matrix of another dielectric material forms, to a very good approximation, a dissipationless disordered and isotropic two-phase medium for any phase dielectric contrast ratio. We compare the effective properties of the MRJ sphere packings to those of overlapping spheres, equilibrium hard-sphere packings, and lattices of hard spheres. Moreover, we generalize results to micro- and macroscopically anisotropic packings of spheroids with tensorial effective properties. The analytic bounds predict the qualitative trend in the physical properties associated with these structures, which provides guidance to more time-consuming simulations and experiments. They especially provide impetus for experiments to design materials with unique bulk properties resulting from hyperuniformity, including structural-color and color-sensing applications.

关键词： Classical statistical mechanics

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