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European signal processing conference

作者： Sina Jafarpour Guengor Polatkan Eugene Brevdo Shannon Hughes Andrei Brasoveanu Ingrid Daubechies Departments of Electrical Engineering Computer Science and Mathematics and the Program in Applied and Computational Mathematics Princeton NJ 08544

ISBN: (纸本)9781617388767

Wavelet transforms and machine learning tools can be used to assist art experts in the stylistic analysis of paintings. A dual-tree complex wavelet transform, Hidden Markov Tree modeling and Random Forest classifiers are used here for a stylistic analysis of Vincent van Gogh's paintings with results on two stylometry challenges that concern "dating, resp. extracting distinguishing features".

关键词： Support vector machines Abstracts Image resolution Radio frequency

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Inertial Hegselmann-Krause systems

Inertial Hegselmann-Krause systems

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American Control Conference (ACC)

作者： Bernard Chazelle Chu Wang Department of Computer Science Princeton University Program in Applied and Computational Mathematics Princeton University

ISBN: (纸本)9781467386838

We derive an energy bound for inertial Hegselmann-Krause (HK) systems, which we define as a variant of the classic HK model in which the agents can change their weights arbitrarily at each step. We use the bound to prove the convergence of HK systems with closed-minded agents, which settles a conjecture of long standing. This paper also introduces anchored HK systems and show their equivalence to the symmetric heterogeneous model.

关键词： Convergence Communication networks Kinetic theory Protocols Nickel Mobile communication Turning

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Machine-learning-based non-Newtonian fluid model with molecular fidelity

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Physical Review E 2020年第4期102卷 043309-043309页

作者： Huan Lei Lei Wu Weinan E Department of Computational Mathematics Science & Engineering and Department of Statistics & Probability Michigan State University East Lansing Michigan 48824 USA Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

We introduce a machine-learning-based framework for constructing continuum a non-Newtonian fluid dynamics model directly from a microscale description. Dumbbell polymer solutions are used as examples to demonstrate the essential ideas. To faithfully retain molecular fidelity, we establish a micro-macro correspondence via a set of encoders for the microscale polymer configurations and their macroscale counterparts, a set of nonlinear conformation tensors. The dynamics of these conformation tensors can be derived from the microscale model, and the relevant terms can be parametrized using machine learning. The final model, named the deep non-Newtonian model (DeePN2), takes the form of conventional non-Newtonian fluid dynamics models, with a generalized form of the objective tensor derivative that retains the microscale interpretations. Both the formulation of the dynamic equation and the neural network representation rigorously preserve the rotational invariance, which ensures the admissibility of the constructed model. Numerical results demonstrate the accuracy of DeePN2 where models based on empirical closures show limitations.

关键词： Learning Neuronal networks Complex fluids Non-Newtonian fluids Rheology Viscoelasticity Multiscale modeling

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Deep potentials for materials science

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Materials Futures 2022年第2期1卷 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 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 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

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Ordered and disordered stealthy hyperuniform point patterns across spatial dimensions

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Physical Review Research 2024年第3期6卷 033260页

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

In previous work [Phys. Rev. X 5, 021020 (2015)] it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier space in the sense that the structure factor is exactly zero in a spherical region around the origin in analogy with the pair-correlation function of real-space hard spheres. While this earlier work focused on spatial dimensions d=1–4, here we extend the analysis to higher dimensions in order to make connections to high-dimensional sphere packings and the mean-field theory of glasses. We exploit this correspondence to confirm that the densest Fourier-space hard-sphere system is that of a Bravais lattice in contrast to real-space hard spheres, whose densest configuration is conjectured to be disordered. In passing, we give a concise form for the position of the first Bragg peak. We also extend the virial series previously suggested for disordered stealthy hyperuniform systems to higher dimensions in order to predict spatial decorrelation as a function of dimension. This prediction is then borne out by numerical simulations of disordered stealthy hyperuniform ground states in dimensions d=2–8, which have only recently been made possible due to a highly parallelized algorithm.

关键词： Classical statistical mechanics Disordered systems

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A Flow Artist for High-Dimensional Cellular Data 33

A Flow Artist for High-Dimensional Cellular Data

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33rd IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2023

作者： MacDonald, Kincaid Bhaskar, Dhananjay Thampakkul, Guy Nguyen, Nhi Zhang, Joia Perlmutter, Michael Adelstein, Ian Krishnaswamy, Smita Yale University Department of Mathematics United States Pomona College Department of Mathematics United States University of Washington Department of Statistics United States Boise State University Department of Mathematics United States Yale University Department of Computer Science United States Yale University Applied Mathematics Program United States Yale University Computational Biology and Bioinformatics Program United States

ISBN: (纸本)9798350324112

We consider the problem of embedding point cloud data sampled from an underlying manifold with an associated flow or velocity. Such data arises in many contexts where static snapshots of dynamic entities are measured, including in high-throughput biology such as single-cell transcriptomics. Existing embedding techniques either do not utilize velocity information or embed the coordinates and velocities independently, i.e., they either impose velocities on top of an existing point embedding or embed points within a prescribed vector field. Here we present FlowArtist, a neural network that embeds points while jointly learning a vector field around the points. The combination allows FlowArtist to better separate and visualize velocity-informed structures. Our results, on toy datasets and single-cell RNA velocity data, illustrate the value of utilizing coordinate and velocity information in tandem for embedding and visualizing high-dimensional data. © 2023 IEEE.

关键词： RNA

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Convolutional neural networks with low-rank regularization 4

Convolutional neural networks with low-rank regularization

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4th International Conference on Learning Representations, ICLR 2016

作者： Tai, Cheng Xiao, Tong Zhang, Yi Wang, Xiaogang Weinan, E. Program in Applied and Computational Mathematics Princeton University United States Department of Electronic Engineering Chinese University of Hong Kong Hong Kong Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor United States

Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have been used for speeding up CNNs. In this paper, we further develop the tensor decomposition technique. We propose a new algorithm for computing the low-rank tensor decomposition for removing the redundancy in the convolution kernels. The algorithm finds the exact global optimizer of the decomposition and is more effective than iterative methods. Based on the decomposition, we further propose a new method for training low-rank constrained CNNs from scratch. Interestingly, while achieving a significant speedup, sometimes the low-rank constrained CNNs delivers significantly better performance than their non-constrained counterparts. On the CIFAR-10 dataset, the proposed low-rank NIN model achieves 91.31% accuracy (without data augmentation), which also improves upon state-of-the-art result. We evaluated the proposed method on CIFAR-10 and ILSVRC12 datasets for a variety of modern CNNs, including AlexNet, NIN, VGG and GoogleNet with success. For example, the forward time of VGG-16 is reduced by half while the performance is still comparable. Empirical success suggests that low-rank tensor decompositions can be a very useful tool for speeding up large CNNs. © ICLR 2016: San Juan, Puerto Rico. All Rights Reserved.

关键词： Iterative methods

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LATTICE-VALUED BOTTLENECK DUALITY

arXiv

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arXiv 2024年

作者： Ghrist, Robert Gould, Julian Lopez, Miguel Department of Mathematics Department of Electrical & Systems Engineering and Program in Applied Mathematics & Computational Science University of Pennsylvania United States

This note reformulates certain classical combinatorial duality theorems in the context of order lattices. For source-target networks, we generalize bottleneck path-cut and flow-cut duality results to edges with capacities in a distributive lattice. For posets, we generalize a bottleneck version of Dilworth’s theorem, again weighted in a distributive lattice. These results are applicable to a wide array of non-numerical network flow problems, as shown. All results, proofs, and applications were created in collaboration with AI language models. An appendix documents their role and *** Codes 06D05, 90C35, 06A07 © 2024, CC BY.

关键词： Combinatorial optimization

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Hyperuniformity order metric of Barlow packings

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Physical Review E 2019年第2期99卷 022111-022111页

作者： T. M. Middlemas F. H. Stillinger S. 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 New Jersey 08544 USA

The concept of hyperuniformity has been a useful tool in the study of density fluctuations at large length scales in systems ranging across the natural and mathematical sciences. One can rank a large class of hyperuniform systems by their ability to suppress long-range density fluctuations through the use of a hyperuniformity order metric Λ¯. We apply this order metric to the Barlow packings, which are the infinitely degenerate densest packings of identical rigid spheres that are distinguished by their stacking geometries and include the commonly known fcc lattice and hcp crystal. The “stealthy stacking” theorem implies that these packings are all stealthy hyperuniform, a strong type of hyperuniformity, which involves the suppression of scattering up to a wave vector K. We describe the geometry of three classes of Barlow packings, two disordered classes and small-period packings. In addition, we compute a lower bound on K for all Barlow packings. We compute Λ¯ for the aforementioned three classes of Barlow packings and find that, to a very good approximation, it is linear in the fraction of fcc-like clusters, taking values between those of least-ordered hcp and most-ordered fcc. This implies that the value of Λ¯ of all Barlow packings is primarily controlled by the local cluster geometry. These results highlight the special nature of anisotropic stacking disorder, which provides impetus for future research on the development of anisotropic order metrics and hyperuniformity properties.

关键词： Classical statistical mechanics

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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

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. © 2018 Curran Associates Inc..All rights reserved.

关键词： Potential energy

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