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IEEE Transactions on Energy Markets, Policy and Regulation 2024年第1期2卷 40-51页

作者： Ferrando, Robert Pagnier, Laurent Mieth, Robert Liang, Zhirui Dvorkin, Yury Bienstock, Daniel Chertkov, Michael University of Arizona Program in Applied Mathematics and Department of Mathematics TucsonAZ85721 United States Department of Industrial and Systems Engineering at Rutgers University PiscatawayNJ08854 United States Johns Hopkins University Department of Electrical and Computer Engineering BaltimoreMD21218-2625 United States Elec. and Comp. Eng. and Ralph o'Connor Sustainable Energy Institute Department of Civil and Systems Engineering Johns Hopkins University BaltimoreMD21218-2625 United States Columbia University IEOR New YorkNY10027 United States

This article addresses the challenge of efficiently recovering exact solutions to the optimal power flow problem in real-time electricity markets. The proposed solution, named Physics-Informed Market-Aware Active Set learning OPF (PIMA-AS-OPF), leverages physical constraints and market properties to ensure physical and economic feasibility of market-clearing outcomes. Specifically, PIMA-AS-OPF employs the active set learning technique and expands its capabilities to account for curtailment in load or renewable power generation, which is a common challenge in real-world power systems. The core of PIMA-AS-OPF is a fully-connected neural network that takes the net load and the system topology as input. The outputs of this neural network include active constraints such as saturated generators and transmission lines, as well as non-zero load shedding and wind curtailments. These outputs allow for reducing the original market-clearing optimization to a system of linear equations, which can be solved efficiently and yield both the dispatch decisions and the locational marginal prices (LMPs). The dispatch decisions and LMPs are then tested for their feasibility with respect to the requirements for efficient market-clearing results. The accuracy and scalability of the proposed method is tested on a realistic 1814-bus NYISO system with current and future renewable energy penetration levels. © 2023 IEEE.

关键词： Costs

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On the Granular Representation of Fuzzy Quantifier-Based Fuzzy Rough Sets

arXiv

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arXiv 2023年

作者： Theerens, Adnan Cornelis, Chris Computational Web Intelligence Department of Applied Mathematics Computer Science and Statistics Ghent University Ghent Belgium

Rough set theory is a well-known mathematical framework that can deal with inconsistent data by providing lower and upper approximations of concepts. A prominent property of these approximations is their granular representation: that is, they can be written as unions of simple sets, called granules. The latter can be identified with "if..., then..." rules, which form the backbone of rough set rule induction. It has been shown previously that this property can be maintained for various fuzzy rough set models, including those based on ordered weighted average (OWA) operators. In this paper, we will focus on some instances of the general class of fuzzy quantifier-based fuzzy rough sets (FQFRS). In these models, the lower and upper approximations are evaluated using binary and unary fuzzy quantifiers, respectively. One of the main targets of this study is to examine the granular representation of different models of FQFRS. The main findings reveal that Choquet-based fuzzy rough sets can be represented granularly under the same conditions as OWA-based fuzzy rough sets, whereas Sugeno-based FRS can always be represented granularly. This observation highlights the potential of these models for resolving data inconsistencies and managing noise. © 2023, CC BY-NC-ND.

关键词： Machine learning

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Symmetry groups and invariant solutions of plane Poiseuille flow

arXiv

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arXiv 2024年

作者： Aghor, Pratik P. Gibson, John F. School of Earth and Atmospheric Sciences Georgia Institute of Technology United States Integrated Applied Mathematics Program Department of Mathematics & Statistics University of New Hampshire United States

Equilibrium, traveling-wave, and periodic-orbit solutions of the Navier-Stokes equations provide a promising avenue for investigating the structure, dynamics, and statistics of transitional flows. Many such invariant solutions have been computed for wall-bounded shear flows, including plane Couette, plane Poiseuille, and pipe flow. However, the organization of invariant solutions is not well understood. In this paper we focus on the role of symmetries in the organization and computation of invariant solutions of plane Poiseuille *** show that enforcing symmetries while computing invariant solutions increases the efficiency of the numerical methods, and that redundancies between search spaces can be eliminated by consideration of equivalence relations between symmetry subgroups. We determine all symmetry subgroups of plane Poiseuille flow in a doubly-periodic domain up to translations by half the periodic lengths and classify the subgroups into equivalence classes, each of which represents a physically distinct set of symmetries and an associated set of physically distinct invariant *** calculate fifteen new traveling waves of plane Poiseuille flow in seven distinct symmetry groups and discuss their relevance to the dynamics of transitional turbulence. We present a few examples of subgroups with fractional shifts other than half the periodic lengths and one traveling wave solution whose symmetry involves shifts by one-third of the periodic lengths. We conclude with a discussion and some open questions about the role of symmetry in the behavior of shear flows. © 2024, CC BY.

关键词： Navier Stokes equations

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Data-driven reduced-order modelling for blood flow simulations with geometry-informed snapshots

arXiv

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arXiv 2023年

作者： Ye, Dongwei Krzhizhanovskaya, Valeria Hoekstra, Alfons G. Mathematics of Imaging & AI Department of Applied Mathematics University of Twente Netherlands Computational Science Lab Informatics Institute Faculty of Science University of Amsterdam Netherlands

Parametric reduced-order modelling often serves as a surrogate method for hemodynamics simulations to improve the computational efficiency in many-query scenarios or to perform real-time simulations. However, the snapshots of the method require to be collected from the same discretisation, which is a straightforward process for physical parameters, but becomes challenging for geometrical problems, especially for those domains featuring unparameterised and unique shapes, e.g. patient-specific geometries. In this work, a data-driven surrogate model is proposed for the efficient prediction of blood flow simulations on similar but distinct domains. The proposed surrogate model leverages group surface registration to parameterise those shapes and formulates corresponding hemodynamics information into geometry-informed snapshots by the diffeomorphisms constructed between a reference domain and original domains. A non-intrusive reduced-order model for geometrical parameters is subsequently constructed using proper orthogonal decomposition, and a radial basis function interpolator is trained for predicting the reduced coefficients of the reduced-order model based on compressed geometrical parameters of the shape. Two examples of blood flowing through a stenosis and a bifurcation are presented and analysed. The proposed surrogate model demonstrates its accuracy and efficiency in hemodynamics prediction and shows its potential application toward real-time simulation or uncertainty quantification for complex patient-specific *** Codes 65Mxx, 68Txx, 76Zxx Copyright © 2023, The Authors. All rights reserved.

关键词： computational fluid dynamics

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Estimation of Digamma Distribution Parameters for Random Sample Size

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Moscow University computational mathematics and Cybernetics 2023年第1期47卷 23-32页

作者： Kudryavtsev, A. A. Shestakov, O. V. Department of Computational Mathematics and Cybernetics Moscow State University Moscow Russia Moscow Center for Fundamental and Applied Mathematics Moscow Russia Federal Research Center ‘‘Informatics and Control ’’ Russian Academy of Sciences Moscow Russia

In this paper asymptotic theorems are proved for estimates of the characteristic index, the scale parameter, and the shape and scale parameters for the remaining fixed parameters of the digamma distribution with a random sample size. Particular cases of limit distributions are given in the case when the sample size has a mixed Poisson distribution.

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REACTION-DIFFUSION EQUATIONS ON METRIC GRAPHS WITH EDGE NOISE

arXiv

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arXiv 2023年

作者： Sikolya, Eszter Department of Applied Analysis and Computational Mathematics Eötvös Loránd University Budapest Hungary

We investigate stochastic reaction-diffusion equations on finite metric graphs. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given. The vertex conditions are the standard continuity and generalized, non-local Neumann-Kirchhoff-type law in each vertex. The reaction term on each edge is assumed to be an odd degree polynomial, not necessarily of the same degree on each edge, with possibly stochastic coefficients and negative leading term. The model is a generalization of the problem in [14] where polynomials with much more restrictive assumptions are considered and no first order differential operator is involved. We utilize the semigroup approach from [15] to obtain existence and uniqueness of solutions with sample paths in the space of continuous functions on the *** Codes 60H15, 35R02, 35R60, 47D06 Copyright © 2023, The Authors. All rights reserved.

关键词： Gaussian noise (electronic)

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Online Ensemble of Models for Optimal Predictive Performance with Applications to Sector Rotation Strategy

arXiv

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arXiv 2023年

作者： Miao, Jiaju Polak, Pawel Department of Applied Mathematics and Statistics Stony Brook University United States Department of Applied Mathematics and Statistics Institute for Advanced Computational Science Stony Brook University Stony BrookNY United States

Asset-specific factors are commonly used to forecast financial returns and quantify asset-specific risk premia. Using various machine learning models, we demonstrate that the information contained in these factors leads to even larger economic gains in terms of forecasts of sector returns and the measurement of sector-specific risk premia. To capitalize on the strong predictive results of individual models for the performance of different sectors, we develop a novel online ensemble algorithm that learns to optimize predictive performance. The algorithm continuously adapts over time to determine the optimal combination of individual models by solely analyzing their most recent prediction performance. This makes it particularly suited for time series problems, rolling window backtesting procedures, and systems of potentially black-box models. We derive the optimal gain function, express the corresponding regret bounds in terms of the out-of-sample R-squared measure, and derive optimal learning rate for the algorithm. Empirically, the new ensemble outperforms both individual machine learning models and their simple averages in providing better measurements of sector risk premia. Moreover, it allows for performance attribution of different factors across various sectors, without conditioning on a specific model. Finally, by utilizing monthly predictions from our ensemble, we develop a sector rotation strategy that significantly outperforms the market. The strategy remains robust against various financial factors, periods of financial distress, and conservative transaction costs. Notably, the strategy’s efficacy persists over time, exhibiting consistent improvement throughout an extended backtesting period and yielding substantial profits during the economic turbulence of the COVID-19 pandemic. Copyright © 2023, The Authors. All rights reserved.

关键词： Machine learning

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ENHANCED GRADIENT RECOVERY-BASED A POSTERIORI ERROR ESTIMATOR AND ADAPTIVE FINITE ELEMENT METHOD FOR ELLIPTIC EQUATIONS

arXiv

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arXiv 2025年

作者： Liu, Ying Xiao, Jingjing Yi, Nianyu Cao, Huihui Department of Mathematics School of Science Xi’an University of Technology Xi’an710000 China School of Mathematics Shandong University Jinan250100 China School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Hunan National Center for Applied Mathematics Xiangtan411105 China

Recovery type a posteriori error estimators are popular, particularly in the engineering community, for their computationally inexpensive, easy to implement, and generally asymptotically exactness. Unlike the residual type error estimators, one can not establish upper and lower a posteriori error bounds for the classical recovery type error estimators without the saturation assumption. In this paper, we first present three examples to show the unsatisfactory performance in the practice of standard residual or recovery-type error estimators, then, an improved gradient recovery-based a posteriori error estimator is constructed. The proposed error estimator contains two parts, one is the difference between the direct and post-processed gradient approximations, and the other is the residual of the recovered gradient. The reliability and efficiency of the enhanced estimator are derived. Based on the improved recovery-based error estimator and the newest-vertex bisection refinement method with a tailored mark strategy, an adaptive finite element algorithm is designed. We then prove the convergence of the adaptive method by establishing the contraction of gradient error plus oscillation. Numerical experiments are provided to illustrate the asymptotic exactness of the new recovery-based a posteriori error estimator and the high efficiency of the corresponding adaptive algorithm. Copyright © 2025, The Authors. All rights reserved.

关键词： Finite element method

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RE-ANCHORING QUANTUM MONTE CARLO WITH TENSOR-TRAIN SKETCHING

arXiv

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arXiv 2024年

作者： Yu, Ziang Zhang, Shiwei Khoo, Yuehaw Committee on Computational and Applied Mathematics University of Chicago United States Center for Computational Quantum Physics Flatiron Institute United States Department of Statistics University of Chicago United States

We propose a novel algorithm for calculating the ground-state energy of quantum many-body systems by combining auxiliary-field quantum Monte Carlo (AFQMC) with tensor-train sketching. In AFQMC, having a good trial wavefunction to guide the random walk is crucial for avoiding sign problems. Typically, this trial wavefunction is fixed throughout the simulation. Our proposed method iterates between determining a new trial wavefunction in the form of a tensor train, derived from the current walkers, and using this updated trial wavefunction to anchor the next phase of AFQMC. Numerical results demonstrate that our algorithm is highly accurate for large spin systems, achieving a relative error of 10−5 in estimating ground-state energies. Additionally, the overlap between our estimated trial wavefunction and the ground-state wavefunction achieves a high-fidelity. We provide a convergence proof, highlighting how an effective trial wavefunction can reduce the variance in the AFQMC energy *** Codes 15A69, 62G07, 65C05 Copyright © 2024, The Authors. All rights reserved.

关键词： Tensors

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EFFICIENT QUANTUM GIBBS SAMPLERS WITH KUBO-MARTIN-SCHWINGER DETAILED BALANCE CONDITION

arXiv

引用

arXiv 2024年

作者： Ding, Zhiyan Li, Bowen Lin, Lin Department of Mathematics University of California BerkeleyCA94720 United States Department of Mathematics City University of Hong Kong Kowloon Tong Hong Kong Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

Lindblad dynamics and other open-system dynamics provide a promising path towards efficient Gibbs sampling on quantum computers. In these proposals, the Lindbladian is obtained via an algorithmic construction akin to designing an artificial thermostat in classical Monte Carlo or molecular dynamics methods, rather than treated as an approximation to weakly coupled system-bath unitary dynamics. Recently, Chen, Kastoryano, and Gilyén (arXiv:2311.09207) introduced the first efficiently implementable Lindbladian satisfying the Kubo-Martin-Schwinger (KMS) detailed balance condition, which ensures that the Gibbs state is a fixed point of the dynamics and is applicable to non-commuting Hamiltonians. This Gibbs sampler uses a continuously parameterized set of jump operators, and the energy resolution required for implementing each jump operator depends only logarithmically on the precision and the mixing time. In this work, we build upon the structural characterization of KMS detailed balanced Lindbladians by Fagnola and Umanità, and develop a family of efficient quantum Gibbs samplers using a finite set of jump operators (the number can be as few as one), akin to the classical Markov chain-based sampling algorithm. Compared to the existing works, our quantum Gibbs samplers have a comparable quantum simulation cost but with greater design flexibility and a much simpler implementation and error analysis. Moreover, it encompasses the construction of Chen, Kastoryano, and Gilyén as a special instance. © 2024, CC BY.

关键词： Hamiltonians

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