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12th International Conference on Learning Representations, ICLR 2024

作者： Huang, Xinmeng Li, Ping Li, Xiaoyun LinkedIn BellevueWA98004 United States The Graduate Group of Applied Mathematics and Computational Science The University of Pennsylvania United States

Communication compression has been an important topic in Federated Learning (FL) for alleviating the communication overhead. However, communication compression brings forth new challenges in FL due to the interplay of compression-incurred information distortion and inherent characteristics of FL such as partial participation and data heterogeneity. Despite the recent development, the existing approaches either cannot accommodate arbitrary data heterogeneity or partial participation, or require stringent conditions on compression. In this paper, we revisit the seminal stochastic controlled averaging method by proposing an equivalent but more efficient/simplified formulation with halved uplink communication costs, building upon which we propose two compressed FL algorithms, SCALLION and SCAFCOM, to support unbiased and biased compression, respectively. Both the proposed methods outperform the existing compressed FL methods in terms of communication and computation complexities. Moreover, SCALLION and SCAFCOM attain fast convergence rates under arbitrary data heterogeneity without any additional assumptions on compression errors. Experiments show that SCALLION and SCAFCOM outperform recent compressed FL methods under the same communication budget. © 2024 12th International Conference on Learning Representations, ICLR 2024. All rights reserved.

关键词： Stochastic systems

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On Local Wellposedness of the Schrodinger-Boussinesq System

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Journal of Partial Differential Equations 2022年第4期35卷 360-381页

作者： SHAO Jjie GUO Boling Department of Mathematics Nanjing University of Science and TechnologyNanjing210094China Institute of Applied Physics and Computational Mathematics Beijing 100088China The Graduate School of China Academy of Engineering Physics Beijing 100088China

In this paper we prove that the Schrodinger-Boussinesq system with solution(u,v,(-∂xx)-^(2/1)vt)is locally wellposed in H^(s)×H^(s)×Hs^(-1),s≥-1/*** local wellposedness is obtained by the transformation from the problem into a nonlinear Schrodinger type equation system and the contraction mapping theorem in a suitably modified Bourgain type space inspired by the work of Kishimoto,*** result improves the known local wellposedness in H^(s)×H^(s)×H^(s-1),s>-1/4 given by Farah.

关键词： Schrodinger-Boussinesq system Cauchy problem local wellposedness low regularity.

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ANALYSIS ON A NUMERICAL SCHEME WITH SECOND-ORDER TIME ACCURACY FOR NONLINEAR DIFFUSION EQUATIONS

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Journal of computational mathematics 2021年第5期39卷 777-800页

作者： Xia Cui Guangwei Yuan Fei Zhao Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsP.O.Box 8009-26Beijing 100088China College of Science North China University of TechnologyBeijing 1OO144China Graduate School of China Academy of Engineering Physics Beijing 100088China

A nonlinear fully implicit finite difference scheme with second-order time evolution for nonlinear diffusion problem is *** scheme is constructed with two-layer coupled discretization(TLCD)at each time *** does not stir numerical oscillation,while permits large time step length,and produces more accurate numerical solutions than the other two well-known second-order time evolution nonlinear schemes,the Crank-Nicolson(CN)scheme and the backward difference formula second-order(BDF2)*** developing a new reasoning technique,we overcome the difficulties caused by the coupled nonlinear discrete diffusion operators at different time layers,and prove rigorously the TLCD scheme is uniquely solvable,unconditionally stable,and has second-order convergence in both s-pace and *** tests verify the theoretical results,and illustrate its superiority over the CN and BDF2 schemes.

关键词： Nonlinear diffusion problem Nonlinear two-layer coupled discrete scheme Second-order time accuracy Property analysis Unique existence Convergence

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GAUGE METHOD FOR VISCOUS INCOMPRESSIBLE FLOWS

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Communications in Mathematical sciences 2003年第2期1卷 317-332页

作者： Weinan, E. Liu, Jian-Guo Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton 08544 NJ United States Institute for Physical Science and Technology and Department of Mathematics University of Maryland College Park 20742 MD United States

We present a new formulation of the incompressible Navier-Stokes equation in terms of an auxiliary field that differs from the velocity by a gauge transformation. The gauge freedom allows us to assign simple and specific boundary conditions for both the auxiliary field and the gauge field, thus eliminating the issue of pressure boundary condition in the usual primitive variable formulation. The resulting dynamic and kinematic equations can then be solved by standard methods for heat and Poisson equations. A normal mode analysis suggests that in contrast to the classical projection method, the gauge method does not suffer from the problem of numerical boundary layers. Thus the subtleties in the spatial discretization for the projection method are removed. Consequently, the projection step in the gauge method can be accomplished by standard Poisson solves. We demonstrate the efficiency and accuracy of the gauge method by several numerical examples, including the flow past cylinder © 2003 International Press

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Utilization of nanohydroxyapatite-kaolin composites as a slow-release materials of urea

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Materials Chemistry and Physics 2025年 342卷

作者： Noviyanti, Atiek Rostika Fajrina, Yulia Eddy, Diana Rakhmawaty Irkham Hartati, Yeni Wahyuni Rupaedah, Bedah Suryana Permana, Muhamad Diki Karnjanakom, Surachai Guan, Guoqing Kurnia, Irwan Department of Chemistry Faculty of Mathematics and Natural Sciences Universitas Padjadjaran Jl. Raya Bandung-Sumedang Km 21 Jatinangor West Java Sumedang45363 Indonesia Research Center for Applied Microbiology National Research and Innovation Agency Jl. Raya Jakarta-Bogor Km. 46 Cibinong West Java Bogor16911 Indonesia Department of Biology Faculty of Mathematics and Natural Sciences Universitas Padjadjaran Jl. Raya Bandung-Sumedang Km 21 Jatinangor West Java Sumedang45363 Indonesia Special Educational Program for Green Energy Conversion Science and Technology Integrated Graduate School of Medicine Engineering and Agricultural Sciences University of Yamanashi Kofu400-8511 Japan Center for Crystal Science and Technology University of Yamanashi Kofu400-8511 Japan Department of Chemistry Faculty of Science Rangsit University 52/347 Phahonyothin Road Pathum Thani 12000 Thailand Institute of Regional Innovation Hirosaki University 3-Bunkyocho Hirosaki036-8561 Japan

Urea is widely used as a nitrogen-source fertilizer in agriculture, but its leaching due to rainwater leads to eutrophication and environmental pollution. To address this, urea was incorporated into nanohydroxyapatite (nHA)–kaolin (KA) composites (HKs) that were synthesized via a two-step hydrothermal method as a slow-release materials (SRMs). Among the composites, HK1 (nHA:KA 75:25) is the most promising slow-release material with a urea release rate of 57.0 μgurea min−1 (20.3 % for 240 min), which is 4.6 times slower than urea release rate of nHA-urea for 262.9 μgurea min−1 (93.5 %, 240 min). This enhanced slow-release behavior is attributed to synergistic interactions between nHA and KA, as reflected on their zeta potentials. These findings suggest that HKs are promising slow-release materials for improving fertilizer efficiency and mitigating environmental impact in agricultural applications. © 2025 Elsevier B.V.

关键词： Urea fertilizers

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Exact Periodic Solitary Solutions to the Shallow Water Wave Equation

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Chinese Physics Letters 2009年第5期26卷 151-153页

作者：李栋龙赵俊霄 Department of Information and Computation Science Guangxi University of Technology Liuzhou 545006 Institute of Applied Physics and Computational Mathematics Beijing 100088 School of Mathematical Sciences Graduate University of Chinese Academy of Sciences Beijing 100049

Exact solutions to the shallow wave equation are studied based on the idea of the extended homoclinic test and bilinear method. Some explicit solutions, such as the one soliton solution, the doubly-periodic wave solution and the periodic solitary wave solutions, are obtained. In addition, the properties of the solutions are investigated.

关键词： gamma-ray bursts gamma-rays relativity

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An Iterative Thresholding Method for the Minimum Compliance Problem

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Communications in computational Physics 2023年第4期33卷 1189-1216页

作者： Luyu Cen Wei Hu Dong Wang Xiaoping Wang Department of Mathematics Hong Kong University of Science and TechnologyClear Water BayKowloonHong KongChina The Program in Applied and Computational Mathematics Princeton UniversityPrincetonNew JerseyUSA School of Science and Engineering The Chinese University of Hong KongShenzhenGuangdong 518172China Shenzhen International Center for Industrial and Applied Mathematics Shenzhen Research Institute of Big DataGuangdong 518172China

In this paper,we propose a simple energy decaying iterative thresholding algorithm to solve the two-phase minimum compliance *** material domain is implicitly represented by its characteristic function,and the problem is formulated into a minimization problem by the principle of minimum complementary *** prove that the energy is decreasing in each *** effective continuation schemes are proposed to avoid trapping into the local *** results on 2D isotropic linear material demonstrate the effectiveness of the proposed methods.

关键词： Minimum compliance convolution thresholding linear elasticity

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DeePKS + ABACUS as a Bridge between Expensive Quantum Mechanical Models and Machine Learning Potentials

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Journal of Physical Chemistry A 2022年第49期126卷 9154-9164页

作者： Li, Wenfei Ou, Qi Chen, Yixiao Cao, Yu Liu, Renxi Zhang, Chunyi Zheng, Daye Cai, Chun Wu, Xifan Wang, Han Chen, Mohan Zhang, Linfeng AI for Science Institute Beijing100080 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States HEDPS CAPT College of Engineering School of Physics Peking University Beijing100871 China Department of Physics Temple University PhiladelphiaPA19122 United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China DP Technology Beijing100080 China

Recently, the development of machine learning (ML) potentials has made it possible to perform large-scale and long-time molecular simulations with the accuracy of quantum mechanical (QM) models. However, for different levels of QM methods, such as density functional theory (DFT) at the meta-GGA level and/or with exact exchange, quantum Monte Carlo, etc., generating a sufficient amount of data for training an ML potential has remained computationally challenging due to their high cost. In this work, we demonstrate that this issue can be largely alleviated with Deep Kohn-Sham (DeePKS), an ML-based DFT model. DeePKS employs a computationally efficient neural network-based functional model to construct a correction term added upon a cheap DFT model. Upon training, DeePKS offers closely matched energies and forces compared with high-level QM method, but the number of training data required is orders of magnitude less than that required for training a reliable ML potential. As such, DeePKS can serve as a bridge between expensive QM models and ML potentials: one can generate a decent amount of high-accuracy QM data to train a DeePKS model and then use the DeePKS model to label a much larger amount of configurations to train an ML potential. This scheme for periodic systems is implemented in a DFT package ABACUS, which is open source and ready for use in various applications. © 2022 The Journal of Physical Chemistry A. All right reserved.

关键词： Density functional theory

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SURREAL-GAN:SEMI-SUPERVISED REPRESENTATION LEARNING VIA GAN FOR UNCOVERING HETEROGENEOUS DISEASE-RELATED IMAGING PATTERNS 10

SURREAL-GAN:SEMI-SUPERVISED REPRESENTATION LEARNING VIA GAN ...

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10th International Conference on Learning Representations, ICLR 2022

作者： Yang, Zhijian Wen, Junhao Davatzikos, Christos Center for Biomedical Image Computing and Analytics University of Pennsylvania United States Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States

A plethora of machine learning methods have been applied to imaging data, enabling the construction of clinically relevant imaging signatures of neurological and neuropsychiatric diseases. Oftentimes, such methods do not explicitly model the heterogeneity of disease effects, or approach it via nonlinear models that are not interpretable. Moreover, unsupervised methods may parse heterogeneity that is driven by nuisance confounding factors that affect global brain structure or function, rather than heterogeneity relevant to a pathology of interest. On the other hand, semi-supervised clustering methods seek to derive a pathology-related dichotomous subtypes, ignoring the truth that disease heterogeneity spatially and temporally extends along a continuum. To address the aforementioned limitations, herein, we propose a novel method, termed Surreal-GAN (Semi-SUpeRvised ReprEsentAtion Learning via GAN). Using cross-sectional imaging data, Surreal-GAN dissects underlying disease-related heterogeneity under the principle of semi-supervised clustering [cluster mappings from the normal control (CN) to patient (PT) domain], proposes a continuously dimensional representation, and infers the disease severity of patients at individual level along each dimension. The model first learns a transformation function from the CN domain to the PT domain with latent variables controlling transformation directions. An inverse mapping function together with regularization on function continuity, pattern orthogonality and monotonicity was also imposed to make sure that the transformation function captures necessarily meaningful imaging patterns with clinical significance. We first validated the model through semi-synthetic experiments, and then demonstrated its potential in capturing biologically plausible imaging patterns in Alzheimer's disease (AD). © 2022 ICLR 2022 - 10th International Conference on Learning Representationss. All rights reserved.

关键词： Pathology

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Simulation of Hydrogen Emission Spectrum in Debye Plasmas

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Chinese Physics Letters 2011年第5期28卷 84-87页

作者： DING Qi-Yong ZHANG Song-Bin WANG Jian-Guo The Key Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsP.O.Box 8009Beijing 100088 Graduate School of China Academy of Engineering Physics P.O.Box 2101Beijing 100088 Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics University of Science and Technology of ChinaHefei 230026

We investigate the screening effects on the spectrum of spontaneous radiation and radiative recombination to the 1s,2s and 2p states of hydrogen with total atom density N=1.7×10^(19)cm^(-3)and electron temperatures 1eV,2eV and 5eV under the local thermodynamic equilibrium(LTE)*** needed atomic energy levels,the radiative transition probabilities and radiative recombination cross sections are calculated by solving the Schr(o)dinger equation numerically incorporating the Debye-Hückel model in *** plasma emission spectrum is simulated for the first time by using the screened atomic *** red shift and the cutoff of Rydberg spectra are observed and it is also found that the 2 eV electron temperature case has the strongest screening effects and the emission spectra to the 2s and 2p states are more likely affected by screening effects than that of the ls state.

关键词： Debye radiative spectrum

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