arXiv subjects

Matthias De Lozzo

Publications and source records attributed to Matthias De Lozzo.

5 recordsLinked to original sources

arXiv2026

A methodology for creating multidisciplinary design optimization benchmark problems from optimization ones

Benchmark problems with known solutions play a central role in the assessment of optimization algorithms. While mono-disciplinary optimization benefits from a rich collection of such problems, multidisciplinary design optimization (MDO) lacks equivalent resources: existing MDO benchmarks are scarce, rarely scalable, and their solutions are generally not known theoretically. In this paper, we propose a systematic methodology to transform any mono-disciplinary optimization problem with a known solution into a family of parametric MDO problems sharing that same solution. The construction relies on two key ingredients: a set of coupling equations that introduce interdependencies between disciplines, and a link function that eliminates the coupling variables and recovers the original mono-disciplinary problem. Theoretical conditions guaranteeing the equivalence between the two problems are established. The methodology is agnostic to the number of disciplines and variable dimensions, making it naturally suited for scalability studies. As an illustration, we construct a family of scalable MDO Rosenbrock problems and use them to benchmark two MDO coupling algorithms, namely the Jacobi and Gauss-Seidel schemes, across varying problem sizes. The proposed framework opens a systematic route to generating MDO benchmarks of arbitrary scale and complexity from the extensive catalog of existing mono-disciplinary test problems.

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arXiv2026

Industrial Application of a Multi-Disciplinary Design Optimization with Uncertainties to a Pair of Telecommunication Satellites

In satellite design, it is common practice to add safety margins to the constraints to achieve conservative solutions that are robust to uncertainties. This robustness often comes at the expense of performance and it may be more appropriate to include uncertainties in the definition of the design problem. This work addresses such a challenge by applying techniques of multidisciplinary design optimization under uncertainty to an industrial use case. The latter is a pair of telecommunication satellites launched together in a stacked configuration. Each satellite is a strongly coupled multidisciplinary system while the two satellites are not coupled at all. This use case can be extended to an arbitrary number of satellites. By considering uncertainty quantification techniques such as sensitivity analysis and reliability-based design optimization, this study demonstrates that accounting for uncertainties in the design problem results in a 66% reduction in performance loss compared to the adding of a predefined safety margins, while guaranteeing the feasibility of constraints with high probability.

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arXiv2024

Multilevel Surrogate-based Control Variates

Monte Carlo (MC) sampling is a popular method for estimating the statistics (e.g. expectation and variance) of a random variable. Its slow convergence has led to the emergence of advanced techniques to reduce the variance of the MC estimator for the outputs of computationally expensive solvers. The control variates (CV) method corrects the MC estimator with a term derived from auxiliary random variables that are highly correlated with the original random variable. These auxiliary variables may come from surrogate models. Such a surrogate-based CV strategy is extended here to the multilevel Monte Carlo (MLMC) framework, which relies on a sequence of levels corresponding to numerical simulators with increasing accuracy and computational cost. MLMC combines output samples obtained across levels, into a telescopic sum of differences between MC estimators for successive fidelities. In this paper, we introduce three multilevel variance reduction strategies that rely on surrogate-based CV and MLMC. MLCV is presented as an extension of CV where the correction terms devised from surrogate models for simulators of different levels add up. MLMC-CV improves the MLMC estimator by using a CV based on a surrogate of the correction term at each level. Further variance reduction is achieved by using the surrogate-based CVs of all the levels in the MLMC-MLCV strategy. Alternative solutions that reduce the subset of surrogates used for the multilevel estimation are also introduced. The proposed methods are tested on a test case from the literature consisting of a spectral discretization of an uncertain 1D heat equation, where the statistic of interest is the expected value of the integrated temperature along the domain at a given time. The results are assessed in terms of the accuracy and computational cost of the multilevel estimators, depending on whether the construction of the surrogates, and the associated computational cost, precede the evaluation of the estimator. It was shown that when the lower fidelity outputs are strongly correlated with the high-fidelity outputs, a significant variance reduction is obtained when using surrogate models for the coarser levels only. It was also shown that taking advantage of pre-existing surrogate models proves to be an even more efficient strategy.

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arXiv2017

Comparison of Polynomial Chaos and Gaussian Process surrogates for uncertainty quantification and correlation estimation of spatially distributed open-channel steady flows

Data assimilation is widely used to improve flood forecasting capability, especially through parameter inference requiring statistical information on the uncertain input parameters (upstream discharge, friction coefficient) as well as on the variability of the water level and its sensitivity with respect to the inputs. For particle filter or ensemble Kalman filter, stochastically estimating probability density function and covariance matrices from a Monte Carlo random sampling requires a large ensemble of model evaluations, limiting their use in real-time application. To tackle this issue, fast surrogate models based on Polynomial Chaos and Gaussian Process can be used to represent the spatially distributed water level in place of solving the shallow water equations. This study investigates the use of these surrogates to estimate probability density functions and covariance matrices at a reduced computational cost and without the loss of accuracy, in the perspective of ensemble-based data assimilation. This study focuses on 1-D steady state flow simulated with MASCARET over the Garonne River (South-West France). Results show that both surrogates feature similar performance to the Monte-Carlo random sampling, but for a much smaller computational budget; a few MASCARET simulations (on the order of 10-100) are sufficient to accurately retrieve covariance matrices and probability density functions all along the river, even where the flow dynamic is more complex due to heterogeneous bathymetry. This paves the way for the design of surrogate strategies suitable for representing unsteady open-channel flows in data assimilation.

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arXiv2014

New improvements in the use of dependence measures for sensitivity analysis and screening

Physical phenomena are commonly modeled by numerical simulators. Such codes can take as input a high number of uncertain parameters and it is important to identify their influences via a global sensitivity analysis (GSA). However, these codes can be time consuming which prevents a GSA based on the classical Sobol' indices, requiring too many simulations. This is especially true as the number of inputs is important. To address this limitation, we consider recent advances in dependence measures, focusing on the distance correlation and the Hilbert-Schmidt independence criterion (HSIC). Our objective is to study these indices and use them for a screening purpose. Numerical tests reveal some differences between dependence measures and classical Sobol' indices, and preliminary answers to "What sensitivity indices to what situation?" are derived. Then, two approaches are proposed to use the dependence measures for a screening purpose. The first one directly uses these indices with independence tests; asymptotic tests and their spectral extensions exist and are detailed. For a higher accuracy in presence of small samples, we propose a non-asymptotic version based on bootstrap sampling. The second approach is based on a linear model associating two simulations, which explains their output difference as a weighed sum of their input differences. From this, a bootstrap method is proposed for the selection of the influential inputs. We also propose a heuristic approach for the calibration of the HSIC Lasso method. Numerical experiments are performed and show the potential of these approaches for screening when many inputs are not influential.

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