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Renewable Scenario Generation Using Controllable Generative Adversarial Networks with Transparent Latent Space

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CSEE Journal of Power and Energy Systems 2021年第1期7卷 66-77页

作者： Ji Qiao Tianjiao pu Xinying Wang the China Electric Power Research Institute Haidian DistrictBeijing 100192China

With the growing penetration of renewable energysources in power systems, it becomes increasingly important tocharacterize their inherent variability and uncertainty. Scenariogeneration is a key approach to provide a series of possible powerscenarios in the future for the system planner and operator tomake decisions. In this paper, a data-driven method is presentedfor renewable scenario generation using stable and controllablegenerative adversarial networks with transparent latent space(ctrl-GANs). The machine learning based algorithm can capturethe nonlinear and dynamic renewable patterns without the needfor modeling assumptions and complicated sampling *** orthogonal regularization and spectral normalization areadopted to improve the training stabilization of the GAN *** control the generation process, a relationship is built betweenfeatures of the generated scenarios and latent vectors on themanifold. Moreover, several new metrics for GANs are used toevaluate the quality of the scenarios. The proposed approachis applied to generate realistic time series data of wind andphotovoltaic power. The results demonstrate that our methodhas a better performance on numerical stabilization and is ableto control the generation process with latent space.

关键词： Renewable scenario generation deep learning generative adversarial networks neural network transparent latent spacer

A NEW HIGH PERFORMANCE SPARSE STATIC SOLVER IN FINITE ELEMENT ANALYSIS WITH LOOP-UNROLLING

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Acta Mechanica Solida Sinica 2005年第3期18卷 248-255页

作者： Chen pu Sun Shuli LTSC Department of Mechanics and Engineering Science Peking University Beijing 100871 China

In the previous papers, a high performance sparse static solver with two-level unrolling based on a cell-sparse storage scheme was reported. Although the solver reaches quite a high efficiency for a big percentage of finite element analysis benchmark tests, the MFLOPS （million floating operations per second） of LDL^T factorization of benchmark tests vary on a Dell Pentium IV 850 MHz machine from 100 to 456 depending on the average size of the super-equations, i.e., on the average depth of unrolling. In this paper, a new sparse static solver with two-level unrolling that employs the concept of master-equations and searches for an appropriate depths of unrolling is proposed. The new solver provides higher MFLOPS for LDL^T factorization of benchmark tests, and therefore speeds up the solution process.

关键词： high performance computing sparse matrix finite element analysis

Multistability and Critical Fluctuation in a Split Bose—Einstein COndensate

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Communications in Theoretical Physics 2002年第6X期38卷 675-678页

作者： WUYing SUNChang-pu NationalKeyLaboratoryforLaserTechnique HuazhongUniversityofScienceandTechnologyWuhan430074China InstituteofTheoreticalPhysics theChineseAcademyofSciencesBeijing100080China

By using a two-mode description, we show that there exist the multistability, phase transition and associatedcritical fluctuations in the macroscopic tunnelling process between the halves of a double-well trap containing a Bose-Einstein condensate. The phase transition that two of the triple stable states and an unstable state merge into one stablestate or a reverse process takes place whenever the ratio of the mean field energy per particle to the tunnelling energygoes across a critical value of order one. The critical fluctuation phenomenon corresponds to squeezed states for thephase difference between the two wells accompanying with large fluctuations of atom numbers.

关键词：玻色-爱因斯坦凝聚态临界涨落稳定性

Gorenstein-Projective Modules over T_(m,n)(A)

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Chinese Annals of Mathematics,Series B 2011年第2期32卷 201-208页

作者： Xiuhua LUO pu ZHANG Department of Mathematics Shanghai Jiaotong University Shanghai 200240 China Corresponding author. Department of Mathematics Shanghai Jiaotong University Shanghai 200240 China

A new class of Gorenstein algebras Tm,n(A) is introduced,their module categories are described,and all the Gorenstein-projective Tm,n(A)-modules are explicitly determined.

关键词： Gorenstein algebra Gorenstein-projective module

Middle and Late Devonian brachiopod assemblages,sea level change and paleogeography of Hunan,China

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Science China Earth Sciences 2010年第12期53卷 1849-1863页

作者： XuePing Ma pu Zong Peking Univ Key Lab Orogen Belts & Crustal Evolut MOE Dept Geol Beijing 100871 Peoples R China

Givetian through middle Famennian brachiopods of Hunan are used to define five biozones,comprising,in ascending order,the Stringocephalus Abundance Zone,the Ambocoeliid-Leiorhynchid Assemblage Zone,the Cyrtospiriferid Assemblage Zone,the Yunnanellina-Sinospirifer Assemblage Zone,and the Yunnanella-Hunanospirifer Assemblage *** correspond approximately to the *** Zone to *** Zone,*** Zone to *** Zone,*** Zone to *** Zone,*** Zone to Upper *** Zone,and Uppermost *** Zone to *** Zone,*** rifting activity in South China during the Devonian began in the middle of the Lower *** Zone(a level marked by the first appearance of ***),which is consistent with the Lower-Middle Givetian substage boundary suggested by the International Subcommission on Devonian Stratigraphy(SDS).This assumed that rifting activity in the Lower *** Zone was signified by the deposition of the Baqi Formation in Guangxi and was marked largely by the extensive deposition of the Qiziqiao Formation in central Hunan,which probably led to an opposite pattern of relative sea level change-rising in deeper water trough areas and lowering in carbonate platform *** previously recognized *** Zone sea level rise in platform margin areas of Guangxi can be identified not only in the trough areas but also in platform areas,which probably indicates an overall marine transgression at this time,rather than tectonically induced sea level ***,this level coincides with the Middle-Upper Givetian substage boundary suggested by the *** the sea level rise may have occurred in the deeper water trough areas of South China towards the end of the Givetian,platformal areas experienced uplifting at various degrees,especially in the central and northern regions of Hunan where Early Frasnian deposits were apparently absent in many ***,the end-Frasnian regre

关键词： Hunan Devonian Brachiopoda rifting sea level paleogeography

Ensemble-based Kalman Filters in Strongly Nonlinear Dynamics

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Advances in Atmospheric Sciences 2009年第3期26卷 373-380页

作者： Zhaoxia pu Joshua HACKER Department of Atmospheric Sciences University of Utah USA National Center for Atmospheric Research USA

This study examines the effectiveness of ensemble Kalman filters in data assimilation with the strongly nonlinear dynamics of the Lorenz-63 model, and in particular their use in predicting the regime transition that occurs when the model jumps from one basin of attraction to the other. Four configurations of the ensemble-based Kalman filtering data assimilation techniques, including the ensemble Kalman filter, en- semble adjustment Kalman filter, ensemble square root filter and ensemble transform Kalman filter, are evaluated with their ability in predicting the regime transition （also called phase transition） and also are compared in terms of their sensitivity to both observational and sampling errors. The sensitivity of each ensemble-based filter to the size of the ensemble is also examined.

关键词： ensemble Kalman filter nonlinear data assimilation Lorenz model

Low dimensional modules over quantum complete intersections in two variables

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Frontiers of Mathematics in China 2019年第2期14卷 449-474页

作者： Hanyang YOU pu ZHANG School of Mathematical Sciences Shanghai Jiao Tong University Shanghai 200241 China

We classify all the indecomposable modules of dimension ≤ 5 over the quantum exterior algebra k(x, y)/(x^2, y^2, xy + qyx) in two variables, and all the indecomposable modules of dimension ≤3 over the quantum complete intersection k(x,y)/(x^m,y^n,xy + qyx) in two variables, where m or n ≥3, by giving explicitly their diagram presentations.

关键词： Quantum ext erior algebra quantum comple te int ersection diagram presentation of a module

Objective Triangle Functors in Adjoint Pairs

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Algebra Colloquium 2017年第4期24卷 639-646页

作者： pu Zhang Lin Zhu School of Mathematics Shanghai Jiao Tong University Shanghai 200240 China

An additive functor F： A→B between additive categories is objective if any morphism f in A with F（f） = 0 factors through an object K with F（K） = 0. We consider when a triangle functor in an adjoint pair is objective. We show that a triangle functor is objective provided that its adjoint （whatever left adjoint or right adjoint） is full or dense. We Mso give an example to show that the adjoint of a faithful triangle functor is not necessarily objective. In particular, the adjoint of an objective triangle functor is not necessarily objective. This is in contrast to the well-known fact that the adjoint of a triangle functor is always a triangle functor. Also, for an arbitrary a^tjoint pair （F, G） between categories which are not necessarily additive, we give a sufficient and necessary condition such that F （resp., G） is full or faithful.

关键词： adjoint pair objective triangle functor unit and counit

Integrability and Exact Solutions of the(2+1)-dimensional KdV Equation with Bell Polynomials Approach

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Acta Mathematicae Applicatae Sinica 2022年第4期38卷 861-881页

作者： Jun-cai pu Yong CHEN School of Mathematical Sciences Shanghai Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal UniversityShanghai 200062China College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China

In this paper,the bilinear formalism,bilinear B?cklund transformations and Lax pair of the(2+1)-dimensional KdV equation are constructed by the Bell polynomials *** N-soliton solution is derived directly from the bilinear ***,based on the two-soliton solution,the lump solution is given out analytically by taking special parameters and using Taylor expansion *** the help of the multidimensional Riemann theta function,multiperiodic(quasiperiodic)wave solutions for the(2+1)-dimensional KdV equation are obtained by employing the Hirota bilinear ***,the asymptotic properties of the one-and two-periodic wave solution,which reveal the relations with the single and two-soliton solution,are presented in detail.

关键词： the bilinear formalism bilinear B?cklund transformations Lax pair lump solution periodic wave solution the asymptotic properties