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Efficient multigrid reduction-in-time for method-of-lines discretizations of linear advection

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arXiv 2022年

作者： De Sterck, H. Falgout, R.D. Krzysik, O.A. Schroder, J.B. Department of Applied Mathematics University of Waterloo WaterlooON Canada Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA United States Department of Mathematics and Statistics University of New Mexico AlbuquerqueNM United States

Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that many of these methods perform quite poorly for advection-dominated problems. Here we analyze the particular iterative parallel-in-time algorithm of multigrid reduction-in-time (MGRIT) for discretizations of constant-wave-speed linear advection problems. We focus on common method-of-lines discretizations that employ upwind finite differences in space and Runge-Kutta methods in time. Using a convergence framework we developed in previous work, we prove for a subclass of these discretizations that, if using the standard approach of rediscretizing the fine-grid problem on the coarse grid, robust MGRIT convergence with respect to CFL number and coarsening factor is not possible. This poor convergence and non-robustness is caused, at least in part, by an inadequate coarse-grid correction for smooth Fourier modes in space-time known as characteristic components. We propose an alternative coarse-grid operator that provides a better correction of these modes. This coarse-grid operator is related to previous work and uses a semi-Lagrangian discretization combined with an implicitly treated truncation error correction. Theory and numerical experiments show the proposed coarse-grid operator yields fast MGRIT convergence for many of the method-of-lines discretizations considered, including for both implicit and explicit discretizations of high order. Parallel results demonstrate substantial speed-up over sequential time-stepping. Copyright © 2022, The Authors. All rights reserved.

关键词： Advection

Reservoir computing with Error Correction: Long-term Behaviors of Stochastic Dynamical Systems

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arXiv 2023年

作者： Fang, Cheng Lu, Yubin Gao, Ting Duan, Jinqiao School of Mathematics and Statistics Center for Mathematical Sciences Huazhong University of Science and Technology Hubei Wuhan430074 China Department of Applied Mathematics College of Computing Illinois Institute of Technology ChicagoIL60616 United States Department of Mathematics Department of Physics Great Bay University Guangdong Dongguan523000 China

The prediction of stochastic dynamical systems and the capture of dynamical behaviors are profound problems. In this article, we propose a data-driven framework combining Reservoir computing and Normalizing Flow to study this issue, which mimics error modeling to improve traditional Reservoir computing performance and integrates the virtues of both approaches. With few assumptions about the underlying stochastic dynamical systems, this model-free method successfully predicts the long-term evolution of stochastic dynamical systems and replicates dynamical behaviors. We verify the effectiveness of the proposed framework in several experiments, including the stochastic Van der Pal oscillator, El Niño-Southern Oscillation simplified model, and stochastic Lorenz system. These experiments consist of Markov/non-Markov and stationary/non-stationary stochastic processes which are defined by linear/nonlinear stochastic differential equations or stochastic delay differential equations. Additionally, we explore the noise-induced tipping phenomenon, relaxation oscillation, stochastic mixed-mode oscillation, and replication of the strange attractor. Copyright © 2023, The Authors. All rights reserved.

关键词： Error correction

High-Fidelity Description of Platelet Deformation Using a Neural Operator

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arXiv 2024年

作者： Laudato, Marco Manzari, Luca Shukla, Khemraj FLOW Research Center Department of Engineering Mechanics KTH Royal Institute of Technology StockholmSE-10044 Sweden PDC Center for High Performance Computing KTH Royal Institute of Technology StockholmSE-11428 Sweden Division of Applied Mathematics Brown University ProvidenceRI02906 United States

The goal of this work is to investigate the capability of a neural operator (DeepONet) to accurately capture the complex deformation of a platelet’s membrane under shear flow. The surrogate model approximated by the neural operator predicts the deformed membrane configuration based on its initial configuration and the shear stress exerted by the blood flow. The training dataset is derived from particle dynamics simulations implemented in LAMMPS. The neural operator captures the dynamics of the membrane particles with a mode error distribution of approximately 0.5%. The proposed implementation serves as a scalable approach to integrate sub-platelet dynamics into multi-scale computational models of thrombosis. © 2024, CC BY.

关键词： Shear flow

tLaSDI: Thermodynamics-informed latent space dynamics identification

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arXiv 2024年

作者： Park, Jun Sur Richard Cheung, Siu Wun Choi, Youngsoo Shin, Yeonjong Seoul02455 Korea Republic of Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 United States Department of Mathematics North Carolina State University RaleighNC27695 United States Pohang37673 Korea Republic of

We propose a data-driven latent space dynamics identification method (tLaSDI) that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The dynamics of the latent variables are constructed by a neural network-based model that preserves certain structures to respect the thermodynamic laws through the GENERIC formalism. An abstract error estimate of the approximation is established, which provides a new loss formulation involving the Jacobian computation of autoencoder. Both the autoencoder and the latent dynamics are trained to minimize the new loss. Numerical examples are presented to demonstrate the performance of tLaSDI, which exhibits robust generalization ability, even in extrapolation. In addition, an intriguing correlation is empirically observed between the entropy production rates in the latent space and the behaviors of the full-state solution. © 2024, CC BY.

关键词： Dynamical systems

Modeling Multi-Scale Consistent Information for Network Alignment

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SSRN

SSRN 2024年

作者： Jiao, Pengfei Chen, Zhihao Liu, Yuanqi Tang, Huijun Wang, Yinghui Zhang, Jilin Wu, Huaming School of Cyberspace Hangzhou Dianzi University Hangzhou310018 China School of Computer Hangzhou Dianzi University Hangzhou310018 China College of Intelligence and Computing Tianjin University Tianjin300350 China Center for Applied Mathematics Tianjin University Tianjin300072 China

The network alignment task aims to identify the correspondence of the same nodes across the network, which plays an important role in many fields. Network alignment methods can be mainly divided into structured-based methods and embedding-based methods. Most of them are based on consistency assumptions at the node-level, i.e., the alignment of neighboring node pairs tends to be consistent with each other. However, they ignore information from other scales, such as non-neighboring node pairs. This may easily lead to over smoothing. In this paper, we first study the phenomenon of multi-scale consistency of anchor nodes in network alignment, and then find that the multi-scale consistency can be characterized by the similarity of multi-order subgraphs (i.e., multi-order consistency) and the node-level consistency. We propose a novel embedding-based multi-scale consistent network alignment method, namely MSC. We adopt the principle of multi-scale consistency and perform network alignment from node-level and subgraph-level scales. We consider that subgraphs consisting of anchor nodes and their highly correlated surrounding nodes should be similar across different networks. Thus, we utilize importance sampling to extract subgraphs. In addition, different from the previous two-step methods, our model performs the network alignment task in a unified general framework, avoiding the destruction of the unique features of each network to a certain extent. We perform extensive experiments on three real-world datasets to verify the effectiveness of the MSC model. © 2024, The Authors. All rights reserved.

关键词： Embeddings

SUNDIALS Time Integrators for Exascale Applications with Many Independent ODE Systems

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arXiv 2024年

作者： Balos, Cody J. Day, Marc Esclapez, Lucas Felden, Anne M. Gardner, David J. Hassanaly, Malik Reynolds, Daniel R. Rood, Jon Sexton, Jean M. Wimer, Nicholas T. Woodward, Carol S. Center for Applied Scientific Computing Lawrence Livermore National Laboratory United States Department of Mathematics Southern Methodist University United States National Renewable Energy Laboratory United States Lawrence Berkeley National Laboratory United States TU Delft Netherlands

Many complex systems can be accurately modeled as a set of coupled time-dependent partial differential equations (PDEs). However, solving such equations can be prohibitively expensive, easily taxing the world's largest supercomputers. One pragmatic strategy for attacking such problems is to split the PDEs into components that can more easily be solved in isolation. This operator splitting approach is used ubiquitously across scientific domains, and in many cases leads to a set of ordinary differential equations (ODEs) that need to be solved as part of a larger "outer-loop" time-stepping approach. The SUNDIALS library provides a plethora of robust time integration algorithms for solving ODEs, and the U.S. Department of Energy Exascale computing Project (ECP) has supported its extension to applications on exascale-capable computing hardware. In this paper, we highlight some SUNDIALS capabilities and its deployment in combustion and cosmology application codes (Pele and Nyx, respectively) where operator splitting gives rise to numerous, small ODE systems that must be solved concurrently. Copyright © 2024, The Authors. All rights reserved.

关键词： Initial value problems

Steady flow of couple stress fluid through a rectangular channel under transverse magnetic field with suction

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Partial Differential Equations in applied mathematics 2024年 12卷

作者： Muduganti, Pavan Kumar Reddy Podila, Aparna Nalimela, Pothanna Garvandha, Mahesh Josyula, Venkata Ramana Murthy Department of Mathematics VNR Vignana Jyothi Institute of Engineering and Technology Telangana Hyderabad 500090 India Mathematics and Computing Skills Curriculum and Assessment Unit Preparatory Studies Center University of Technology and Applied Sciences- Shinas Sultanate of Oman Oman Oman Department of Mathematics National Institute of Technology Telangana Warangal 506004 India

In this work, we have analysed the impact of a transverse magnetic field on the steady flow of an incompressible conducting couple stress fluid within a rectangular channel of uniform cross-section, incorporating suction or injection at the lateral walls. In order to get the velocity ‘w’ along the axis of the rectangular tube, we ignore the induced electric and magnetic fields. To find w, we apply the standard hyper stick and no slip boundary conditions. The velocity w and temperature θ were calculated using Fourier series. The velocity distribution compared for various magnetic parameter values by taking suction velocity zero and the results are in good agreement (99.99 %) with the existing results. The volumetric flow rate and skin friction are obtained and the effects of physical parameters like magnetic parameter, Reynolds number and couple stress parameter on this are studied through graphs. © 2024 The Authors

关键词： Couple stress fluid Magnetic field Rectangular channel Skin friction

Multipath Components Modeling and Measuring in Device-Free Underground Parking Localization

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Multipath Components Modeling and Measuring in Device-Free U...

IEEE International Conference on Communications in China (ICCC)

作者： Sihai Yang Xing Xiao Xing Wang Zhuoting Chen Menggang Sheng Zhiqiang Yao School of Automation and Electronic Information Xiangtan University Xiangtan China Hunan Province Key Laboratory of Credible Intelligent Navigation and Positioning Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan Xiangtan University Xiangtan China School of Mathematics and Computational Science Xiangtan University Xiangtan China

ISBN: (数字)9798350378412

ISBN: (纸本)9798350378429

The Device-Free Localization (DFL) system hold significant application value in NLOS (Non-Line-of-Sight) environments where GPS signals are unavailable. It is a challenge to accurately distinguish whether the changes in spatial signals are caused by the presence of users or the changes of environment, particularly in Non-Line-of-Sight (NLOS) environments without GPS signals. To address this issue, we proposes a DFL method utilizing Multipath Components (MPCs), which involves a detailed analysis of how the presence of users affects the MPCs. Specifically, a calculation method for signal propagation paths using virtual anchors has been developed to accurately construct a user-based diffraction model. An algorithm for extracting MPCs from actual signal measurements was also proposed. The maximum average absolute error between the simulated and measured MPC amplitudes with UWB was 0.9461 dB, validating the possibility of substituting simulation models for actual measurements. Moreover, by utilizing a deep learning network with MPCs as input features, the DFL method achieves a positioning accuracy of 0.44 m in an underground parking with only two sensors. This represents an improvement of $\mathbf{0. 3 5 m}$ over traditional RSS-based fingerprinting localization methods.

关键词： Location awareness Deep learning Accuracy Diffraction Measurement uncertainty Sensor phenomena and characterization Fingerprint recognition

How (not) to Build Quantum PKE in Minicrypt

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arXiv 2024年

作者： Li, Longcheng Li, Qian Li, Xingjian Liu, Qipeng State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences China Shenzhen International Center For Industrial And Applied Mathematics Shenzhen Research Institute of Big Data China Tsinghua University China University of California San Diego United States

The seminal work by Impagliazzo and Rudich (STOC’89) demonstrated the impossibility of constructing classical public key encryption (PKE) from one-way functions (OWF) in a black-box manner. Quantum information has the potential to bypass classical limitations, enabling the realization of seemingly impossible tasks such as quantum money, copy protection for software, and commitment without one-way functions. However, the question remains: can quantum PKE (QPKE) be constructed from quantumly secure OWF? A recent line of work has shown that it is indeed possible to build QPKE from OWF, but with one caveat. These constructions necessitate public keys being quantum and unclonable, diminishing the practicality of such "public" encryption schemes — public keys cannot be authenticated and reused. In this work, we re-examine the possibility of perfect complete QPKE in the quantum random oracle model (QROM), where OWF exists. Our first main result: QPKE with classical public keys, secret keys and ciphertext, does not exist in the QROM, if the key generation only makes classical queries. Therefore, a necessary condition for constructing such QPKE from OWF is to have the key generation classically "un-simulatable". Previous results (Austrin et al. CRYPTO’22) on the impossibility of QPKE from OWF rely on a seemingly strong conjecture. Our work makes a significant step towards a complete and unconditional quantization of Impagliazzo and Rudich’s results. Our second main result extends to QPKE with quantum public keys. The second main result: QPKE with quantum public keys, classical secret keys and ciphertext, does not exist in the QROM, if the key generation only makes classical queries and the quantum public key is either pure or "efficiently clonable". The result is tight due to these existing QPKEs with quantum public keys, classical secret keys, quantum/classical ciphertext and classical-query key generation require the public key to be mixed instead of pure;or require quantu

关键词： Reusability