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SSRN 2023年

作者： Le, Thi Thai Koch, Thorsten Zuse Institute Berlin Applied Algorithmic Intelligence Methods Department Takustr. 7 Berlin14195 Germany TU Berlin Chair of Software and Algorithms for Discrete Optimization Str. des 17. Juni 135 Berlin10623 Germany

The present study investigates the stability of a tangential-velocity discontinuity in porous media during the withdrawing and injecting processes of natural gases from and into underground gas storages. The focus is on analyzing the impact of inertia forces on the interface stability using the Forchheimer equations. Other publications have relied primarily on Darcy's law to describe flow stability in porous media. However, Darcy's law only adequately describes flows in which viscous forces dominate over inertia forces. As the flow rate increases, the significance of inertia forces becomes more pronounced, and Darcy's law becomes insufficient for describing such flows. Our findings indicate that even a slight consideration of the inertia effect leads to permanent destabilization of the discontinuity interface, regardless of the fluid viscosity or the Mach number. In contrast, when the inertia effect is neglected, the interface is stabilized across the entire Mach number range if the fluid viscosity is strong enough. © 2023, The Authors. All rights reserved.

关键词： Porous materials

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PYSCIPOPT-ML: EMBEDDING TRAINED MACHINE LEARNING MODELS INTO MIXED-INTEGER PROGRAMS

arXiv

引用

arXiv 2023年

作者： Turner, Mark Chmiela, Antonia Koch, Thorsten Winkler, Michael Zuse Institute Berlin Department of Mathematical Optimization Takustr. 7 Berlin14195 Germany Chair of Software and Algorithms for Discrete Optimization Institute of Mathematics Technische Universität Berlin Straße des 17. Juni 135 Berlin10623 Germany Gurobi GmbH Ulmenstr. 37-39 Frankfurt am Main60325 Germany

A standard tool for modelling real-world optimisation problems is mixed-integer programming (MIP). However, for many of these problems, information about the relationships between variables is either incomplete or highly complex, making it difficult or even impossible to model the problem directly. To overcome these hurdles, machine learning (ML) predictors are often used to represent these relationships and are then embedded in the MIP as surrogate models. Due to the large amount of available ML frameworks and the complexity of many ML predictors, formulating such predictors into MIPs is a highly non-trivial task. In this paper, we introduce PySCIPOpt-ML, an open-source tool for the automatic formulation and embedding of trained ML predictors into MIPs. By directly interfacing with a broad range of commonly used ML frameworks and an open-source MIP solver, PySCIPOpt-ML provides a way to easily integrate ML constraints into optimisation problems. Alongside PySCIPOpt-ML, we introduce, SurrogateLIB, a library of MIP instances with embedded ML constraints, and present computational results over SurrogateLIB, providing intuition on the scale of ML predictors that can be practically embedded. © 2023, CC BY.

关键词： Machine learning

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The variational bayesian inference for network autoregression models

arXiv

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arXiv 2021年

作者： Lai, Wei-Ting Chen, Ray-Bing Chen, Ying Koch, Thorsten Department of Statistics National Cheng Kung University Tainan Taiwan Institute of Data Science National Cheng Kung University Tainan Taiwan Department of Mathematics National University of Singapore Singapore Risk Management Institute National University of Singapore Singapore Institute of Data Science National University of Singapore Singapore Chair of Software and Algorithms for Discrete Optimization Technische Universität Berlin Berlin Germany Department of Applied Algorithmic Intelligence Methods Zuse Institute Berlin Berlin Germany

We develop a variational Bayesian (VB) approach for estimating large-scale dynamic network models in the network autoregression framework. The VB approach allows for the automatic identification of the dynamic structure of such a model and obtains a direct approximation of the posterior density. Compared to Markov Chain Monte Carlo (MCMC) based sampling approaches, the VB approach achieves enhanced computational efficiency without sacrificing estimation accuracy. In the simulation study conducted here, the proposed VB approach detects various types of proper active structures for dynamic network models. Compared to the alternative approach, the proposed method achieves similar or better accuracy, and its computational time is halved. In a real data analysis scenario of day-ahead natural gas flow prediction in the German gas transmission network with 51 nodes between October 2013 and September 2015, the VB approach delivers promising forecasting accuracy along with clearly detected structures in terms of dynamic dependence. Copyright © 2021, The Authors. All rights reserved.

关键词： Computational efficiency

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