Documents published in Scipedia

• Analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

  M. Martin, S. Krumscheid, F. Nobile

  (2020). MATHICSE Technical Report Nr. 04.2018 March 2018

  
  

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• D6.3 Report on stochastic optimisation for simple problems

  Q. Ayoul-Guilmard, S. Ganesh, F. Nobile, R. Rossi, C. Soriano

  Open Access Repository of the ExaQUte project: Deliverables (2021). 11

  
  

  Abstract

  This report addresses the general matter of optimisation under uncertainties, following a previous report on stochastic sensitivities (deliverable 6.2). It describes several theoretical methods, as well their application into implementable algorithms. The specific case of the conditional value at risk chosen as risk measure, with its challenges, is prominently discussed. In particular, the issue of smoothness – or lack thereof – is addressed through several possible approaches. The whole report is written in the context of high-performance computing, with concern for parallelisation and cost-efficiency. 

  Abstract
  This report addresses the general matter of optimisation under uncertainties, following a previous report on stochastic sensitivities (deliverable 6.2). It describes several [...]

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• D5.3 Report on theoretical work to allow the use of MLMC with adaptive mesh refinement

  Q. Ayoul-Guilmard, S. Ganesh, M. Nuñez, R. Tosi, F. Nobile, R. Rossi, C. Soriano

  Open Access Repository of the ExaQUte project: Deliverables (2021). 10

  
  

  Abstract

  This documents describes several studies undertaken to assess the applicability of MultiLevel Monte Carlo (MLMC) methods to problems of interest; namely in turbulent fluid flow over civil engineering structures. Several numerical experiments are presented wherein the convergence of quantities of interest with mesh parameters are studied at different Reynolds’ numbers and geometries. It was found that MLMC methods could be used successfully for low Reynolds’ number flows when combined with appropriate Adaptive Mesh Refinement (AMR) strategies. However, the hypotheses for optimal MLMC performance were found to not be satisfied at higher turbulent Reynolds’ numbers despite the use of AMR strategies. Recommendations are made for future research directions based on these studies. A tentative outline for an MLMC algorithm with adapted meshes is made, as well as recommendations for alternatives to MLMC methods for cases where the underlying assumptions for optimal MLMC performance are not satisfied. 

  Abstract
  This documents describes several studies undertaken to assess the applicability of MultiLevel Monte Carlo (MLMC) methods to problems of interest; namely in turbulent fluid [...]

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• D6.4 Report on stochastic optimisation for unsteady problems

  Q. Ayoul-Guilmard, F. Nobile, S. Ganesh, M. Nuñez, A. Kodakkal, R. Rossi, C. Soriano

  Open Access Repository of the ExaQUte project: Deliverables (2021). 9

  
  

  Abstract

  This report brings together methodological research on stochastic optimisation and work on benchmark and target applications of the ExaQute project, with a focus on unsteady problems. A practical, general method for the optimisation of the conditional value at risk is proposed. Three different optimisation problems are described: an oscillator problem selected as a suitable trial and illustration case; the shape optimisation of an airfoil, chosen as a benchmark application in the project; the shape optimisation of a tall building, which is the challenging target application set for ExaQUte. For each problem, the current developments and results are presented, the application of the proposed method is discussed, and the work to be done until the end of the project is laid out. 

  Abstract
  This report brings together methodological research on stochastic optimisation and work on benchmark and target applications of the ExaQute project, with a focus on unsteady [...]

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• D5.4 Report on MLMC for time dependent problems

  Q. Ayoul-Guilmard, S. Ganesh, M. Nuñez, R. Tosi, F. Nobile, R. Rossi, C. Soriano

  Open Access Repository of the ExaQUte project: Deliverables (2021). 7

  
  

  Abstract

  In this report, we study the use of Multi-Level Monte Carlo (MLMC) methods for time dependent problems. It was found that the usability of MLMC methods depends strongly on whether or not the underlying time dependent problem is chaotic in nature. Numerical experiments are conducted on both simple problems, as well as fluid flow problems of practical interest to the ExaQUte project, to demonstrate this. For the non-chaotic cases, the hypotheses that enable the use of MLMC methods were found to be satisfied. For the chaotic cases, especially the case of high Reynolds’ number fluid flow, the hypotheses were not satisfied. However, it was found that correlations between the different levels were high enough to merit the use of multi-fidelity or control-variate approaches. It was also noted that MLMC methods could work for chaotic problems if the time window of analysis were chosen to be small enough. Future studies are proposed to examine this possibility.

  Abstract
  In this report, we study the use of Multi-Level Monte Carlo (MLMC) methods for time dependent problems. It was found that the usability of MLMC methods depends strongly on [...]

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• D6.2 Report on the calculation of stochastic sensitivities

  S. Ganesh, Q. Ayoul-Guilmard, F. Nobile, C. Soriano, R. Rossi

  Open Access Repository of the ExaQUte project: Deliverables (2021). 2

  
  

  Abstract
  In the following sections, the formulation of a possible stochastic optimisation problem relevant to the ExaQUte project is first presented.

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• D5.2 Release of ExaQUte MLMC Python engine

  R. Amela, Q. Ayoul-Guilmard, S. Ganesh, R. Tosi, R. Badia, F. Nobile, R. Rossi, C. Soriano

  Open Access Repository of the ExaQUte project: Deliverables (2021). 3

  
  

  Abstract

  In this deliverable, the ExaQUte xmc library is introduced. This report is meant to serve as a supplement to the publicly release of the library. In the following sections, the ExaQUte xmc library is described along with its current and future capabilities. The structure of the library, along with its  dynamic import mechanism, are described using samples of code. The algorithms behind the example files supplied with the public release are explained in detail as well.

  Abstract
  In this deliverable, the ExaQUte xmc library is introduced. This report is meant to serve as a supplement to the publicly release of the library. In the following sections, [...]

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• D8.1 Data Management Plan

  C. Soriano, R. Rossi, Q. Ayoul-Guilmard

  Open Access Repository of the ExaQUte project: Deliverables (2021). 8

  
  

  Abstract

  The ExaQUte project participates in the Pilot on Open Research Data launched by the European Commission (EC) along with the H2020 program. This pilot is part of the Open Access to Scientific Publications and Research Data program in H2020. The goal of the  program is to foster access to research data generated in H2020 projects. The use of a Data anagement Plan (DMP) is required for all projects participating in the Open Research Data Pilot, in which they will specify what data will be kept for the longer term. The underpinning idea is that Horizon 2020 beneficiaries have to make their research data findable, accessible, interoperable and re-usable (FAIR), to ensure it is soundly managed.

  Abstract
  The ExaQUte project participates in the Pilot on Open Research Data launched by the European Commission (EC) along with the H2020 program. This pilot is part of the Open Access [...]

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