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data-driven computational Methods for Quasi-Stationary Distribution and Sensitivity Analysis

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS 2023年第3期35卷 2069-2097页

作者： Li, Yao Yuan, Yaping Univ Massachusetts Dept Math & Stat Amherst MA 01002 USA

This paper studies computational methods for quasi-stationary distributions (QSDs). We first proposed a data-driven solver that solves Fokker-Planck equations for QSDs. Similar to the case of Fokker-Planck equations for invariant probability measures, we set up an optimization problem that minimizes the distance from a low-accuracy reference solution, under the constraint of satisfying the linear relation given by the discretized Fokker-Planck operator. Then we use coupling method to study the sensitivity of a QSD against either the change of boundary condition or the diffusion coefficient. The 1-Wasserstein distance between a QSD and the corresponding invariant probability measure can be quantitatively estimated. Some numerical results about both computation of QSDs and their sensitivity analysis are provided.

关键词： Quasi-stationary distribution Monte Carlo simulation data-driven computation Coupling method

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HomPINNs: Homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2022年 121卷 62-73页

作者： Huang, Yao Hao, Wenrui Lin, Guang Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Shaanxi Peoples R China Penn State Univ Dept Math University Pk PA 16802 USA Purdue Univ Sch Mech Engn Dept Math W Lafayette IN 47907 USA Natl Univ Singapore Dept Elect & Comp Engn Singapore 117583 Singapore

Physics-informed neural networks (PINNs) based machine learning is an emerging framework for solving nonlinear differential equations. However, due to the implicit regularity of neural network structure, PINNs can only find the flattest solution in most cases by minimizing the loss functions. In this paper, we combine PINNs with the homotopy continuation method, a classical numerical method to compute isolated roots of polynomial systems, and propose a new deep learning framework, named homotopy physics-informed neural networks (HomPINNs), for solving multiple solutions of nonlinear elliptic differential equations. The implementation of an HomPINN is a homotopy process that is composed of the training of a fully connected neural network, named the starting neural network, and training processes of several PINNs with different tracking parameters. The starting neural network is to approximate a starting function constructed by the trivial solutions, while other PINNs are to minimize the loss functions defined by boundary condition and homotopy functions, varying with different tracking parameters. These training processes are regraded as different steps of a homotopy process, and a PINN is initialized by the well-trained neural network of the previous step, while the first starting neural network is initialized using the default initialization method. Several numerical examples are presented to show the efficiency of our proposed HomPINNs, including reaction-diffusion equations with a heart-shaped domain.

关键词： Machine learning Physics-informed neural networks Nonlinear elliptic differential equation Multiple solutions Homotopy method data-driven computation

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Magnetic Field Simulation With data-driven Material Modeling

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IEEE TRANSACTIONS ON MAGNETICS 2020年第8期56卷 1-6页

作者： De Gersem, Herbert Galetzka, Armin Ion, Ion Gabriel Loukrezis, Dimitrios Roemer, Ulrich Tech Univ Darmstadt Inst Teilchenbeschleunigung & Elektromagnet Felde D-64289 Darmstadt Germany Tech Univ Darmstadt Grad Sch Computat Engn D-64289 Darmstadt Germany KU Leuven Kulak Wave Propagat & Signal Proc Res Grp B-8500 Kortrijk Belgium TU Braunschweig Inst Dynam & Schwingungen D-38106 Braunschweig Germany

This article develops a data-driven magnetostatic finite-element (FE) solver that directly exploits the measured material data instead of a material curve constructed from it. The distances between the field solution and the measurement points are minimized while enforcing Maxwell's equations. The minimization problem is solved by employing the Lagrange multiplier approach. The procedure wraps the FE method within an outer data-driven iteration. The method is capable of considering anisotropic materials and is adapted to deal with models featuring a combination of exact material knowledge and measured material data. Thereto, three approaches with an increasing level of intrusivity according to the FE formulation are proposed. The numerical results for a quadrupole-magnet model show that data-driven field simulation is feasible and affordable and overcomes the need of modeling the material law.

关键词： data science data-driven computation electromagnetic field simulation finite element (FE) analysis magnetic materials scientific computing

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computation Model of data Intensive Computing with MapReduce 14

Computation Model of Data Intensive Computing with MapReduce

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14th IEEE International Conference on Application of Information and Communication Technologies (AICT)

作者： Adamov, Abzetdin Z. ADA Univ Ctr Data Analyt Res CeDAR Baku Azerbaijan

ISBN: (纸本)9781728173863

It becomes obvious that traditional platforms and processing paradigms can't store and process huge amounts of data. The only solution is to use specially designed ad-hoc platform/architecture based on parallelization that distributes data across large cluster of physical machines. data Intensive Computing is a subclass of general parallel computing concept which is based on division of large amounts of data into independent parts and processing them in parallel. In the paper the alternative parallelization architectures are reviewed. MapReduce Programming model associated with distributed massive parallel processing of large amount of data is examined. The main objective of this study is to investigate conceptual fundament behind very popular data-drive computation model MapReduce.

关键词： Parallel Computing MapReduce data-driven computation HDFS Flynn's Taxonomy

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μTC -: An intermediate language for programming chip multiprocessors

μTC -: An intermediate language for programming chip multip...

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11th Asia-Pacific Conference on Advances in Computer Systems Architecture

作者： Jesshope, Chris Univ Amsterdam Inst Informat NL-1098 SJ Amsterdam Netherlands

ISBN: (纸本)3540400567

mu TC is a language that has been designed for programming chip multiprocessors. Indeed, to be more specific, it has been developed to program chip multiprocessors based on arrays of microthreaded microprocessors as these processors directly implement the concepts introduced in the language. However, it is more general than that and is being used in other projects as an interface defining dynamic concurrency. Ideally, a program written in mu TC is a dynamic, concurrent control structure over small sequences of code, which in the limit could be a few instructions each. mu TC is being used as an intermediate language to capture concurrency from data-parallel languages such as single-assignment C, parallelising compilers for sequential languages such as C and concurrent composition languages, such as Suet. mu TC's advantage over other approaches is that it allows an abstract representation of maximal concurrency in a schedule-independent form. Both Snet and mu TC are being used in a European project called AETHER, in order to support all aspects of self-adaptive computation.

关键词： self-adaptive computing concurrent languages data-driven computation programming chip multiprocessors

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CONVERSION FROM data-driven TO SYNCHRONOUS EXECUTION IN LOOP PROGRAMS

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ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS 1987年第4期9卷 599-617页

作者： CUNY, JE SNYDER, L UNIV WASHINGTON DEPT COMP SCISEATTLEWA 98195

Conversion algorithms are presented that would enable programmers to write programs in a high-level, data flow language and then run those programs on a synchronous machine. A model of interprocess communication systems is developed in which both data-driven and synchronous execution modes are represented. Balancing equations are used to characterize a subclass of parallel programs, called loop programs, for which conversions are possible. We show that all loop programs having the finite buffer property can be converted into synchronous mode. Finally two algorithms for the conversion of loop programs are presented and discussed.

关键词： data-driven computation parallel languages parallel program optimization

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A data-driven MODEL FOR A SUBSET OF LOGIC PROGRAMMING

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ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS 1987年第4期9卷 618-645页

作者： BIC, L LEE, C Univ. of California Irvine Univ. of California Irvine

There is a direct correspondence between semantic networks and a subset of logic programs, restricted only to binary predicates. The advantage of the latter is that it can describe not only the nodes and arcs comprising a semantic net, but also the data-retrieval operations applied to such nets. The main objective of this paper is to present a data-driven model of computation that permits this subset of logic programs to be executed on a highly parallel computer architecture. We demonstrate how logic programs may be converted into collections of data-flow graphs in which resolution is viewed as a process of finding matches between certain graph templates and portions of the data-flow graphs. This graph fitting process is carried out by messages propagating asynchronously through the data-flow graph; thus computation is entirely data driven, without the need for any centralized control and centralized memory. This permits a potentially large number of independent processing elements to cooperate in solving a given query.

关键词： data-driven computation parallel logic programming

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data-driven prediction of air bending

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Procedia Manufacturing 2019年 29卷 177-184页

作者： Vitalii Vorkov Alberto Tomás García Gonçalo Costa Rodrigues Joost R. Duflou Department of Mechanical Engineering KU Leuven Celestijnenlaan 300 3001 Leuven Beglium Member of Flanders Make

Experimental data can provide a rich source of information and opportunities for the improvement of production processes. This paper provides a conceptual description of a data-driven model and discusses its possible implementation strategies. Two data-driven methods are applied to air bending, a conventional sheet metal forming process. Self-improving data-driven prediction based on an available experimental database is implemented for two calculation approaches: the gray box and the black box. A significant improvement in terms of springback prediction has been achieved with only a limited set of training data: with 100 training samples the relative error decreases from 6.75%, as given by a state-of-the-art analytical model, to 1.6%. Additionally, a material model-free approach is studied. In this model, no predefined material model is used and all necessary material related parameters are calculated based on experimental data. With only 10 training samples and using Kriging interpolation, this approach resulted in a relative error of 5%. Such results demonstrate that data-driven calculation methods allow for significant improvements in prediction accuracy with limited number of test samples. In the case of air bending, this allows the use of a data-driven response purely based on experimental data instead of on a material law that is typically expensive to obtain.

关键词： Industry 4.0 data-driven computation machine-learning air bending springback

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Modeling switch-level simulation using data flow 85

Modeling switch-level simulation using data flow

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Proceedings of the 22nd ACM/IEEE Design Automation Conference

作者： V. Ashok R. Costello P. Sadayappan Department of Computer and Information Science The Ohio State University Columbus OH

ISBN: (纸本)9780818606359

The complexity of simulating large circuits is a bottleneck in the design process. Considerable attention is being focused on using multiprocessing architectures to speed up simulation. In order to utilize these architectures one first needs to capture the parallelism inherent in the simulation process. This paper explores data flow graphs as a means of expressing the parallelism in switch-level simulation. These data flow graphs, when executed on general purpose or special purpose data flow machines should result in considerable speed up.

关键词： data-driven computation

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