arXiv subjects

Pamphile T. Roy

Publications and source records attributed to Pamphile T. Roy.

5 recordsLinked to original sources

arXiv2024

Simple binning algorithm and SimDec visualization for comprehensive sensitivity analysis of complex computational models

Models of complex technological systems inherently contain interactions and dependencies among their input variables that affect their joint influence on the output. Such models are often computationally expensive and few sensitivity analysis methods can effectively process such complexities. Moreover, the sensitivity analysis field as a whole pays limited attention to the nature of interaction effects, whose understanding can prove to be critical for the design of safe and reliable systems. In this paper, we introduce and extensively test a simple binning approach for computing sensitivity indices and demonstrate how complementing it with the smart visualization method, simulation decomposition (SimDec), can permit important insights into the behavior of complex engineering models. The simple binning approach computes first-, second-order effects, and a combined sensitivity index, and is considerably more computationally efficient than the mainstream measure for Sobol indices introduced by Saltelli et al. The totality of the sensitivity analysis framework provides an efficient and intuitive way to analyze the behavior of complex systems containing interactions and dependencies.

stat.ME↗

arXiv2023

Discrepancy measures for sensitivity analysis

While sensitivity analysis improves the transparency and reliability of mathematical models, its uptake by modelers is still scarce. This is partially explained by its technical requirements, which may be hard to understand and implement by the non-specialist. Here we propose a sensitivity analysis approach based on the concept of discrepancy that is as easy to understand as the visual inspection of input-output scatterplots. Firstly, we show that some discrepancy measures are able to rank the most influential parameters of a model almost as accurately as the variance-based total sensitivity index. We then introduce an ersatz-discrepancy whose performance as a sensitivity measure matches that of the best-performing discrepancy algorithms, is simple to implement, easier to interpret and orders of magnitude faster.

stat.AP↗

arXiv2021

Newcomb-Benford's law as a fast ersatz of discrepancy measures

Thanks to the increasing availability in computing power, high-dimensional engineering problems seem to be at reach. But the curse of dimensionality will always prevent us to try out extensively all the hypotheses. There is a vast literature on efficient methods to construct a Design of Experiments (DoE) such as low discrepancy sequences and optimized designs. Classically, the performance of these methods is assessed using a discrepancy metric. Having a fast discrepancy measure is of prime importance if ones want to optimize a design. This work proposes a new methodology to assess the quality of a random sampling by using a flavor of Newcomb-Benford's law. The performance of the new metric is compared to classical discrepancy measures and showed to offer similar information at a fraction of the computational cost of traditional discrepancy measures.

stat.ME↗

arXiv2019

Reconstruction of Hydraulic Data by Machine Learning

Numerical simulation models associated with hydraulic engineering take a wide array of data into account to produce predictions: rainfall contribution to the drainage basin (characterized by soil nature, infiltration capacity and moisture), current water height in the river, topography, nature and geometry of the river bed, etc. This data is tainted with uncertainties related to an imperfect knowledge of the field, measurement errors on the physical parameters calibrating the equations of physics, an approximation of the latter, etc. These uncertainties can lead the model to overestimate or underestimate the flow and height of the river. Moreover, complex assimilation models often require numerous evaluations of physical solvers to evaluate these uncertainties, limiting their use for some real-time operational applications. In this study, we explore the possibility of building a predictor for river height at an observation point based on drainage basin time series data. An array of data-driven techniques is assessed for this task, including statistical models, machine learning techniques and deep neural network approaches. These are assessed on several metrics, offering an overview of the possibilities related to hydraulic time-series. An important finding is that for the same hydraulic quantity, the best predictors vary depending on whether the data is produced using a physical model or real observations.

cs.CE↗

arXiv2018

Sounding Spider: An Efficient Way for Representing Uncertainties in High Dimensions

This article proposes a visualization method for multidimensional data based on: (i) Animated functional Hypothetical Outcome Plots (f-HOPs); (ii) 3-dimensional Kiviat plot; and (iii) data sonification. In an Uncertainty Quantification (UQ) framework, such analysis coupled with standard statistical analysis tools such as Probability Density Functions (PDF) can be used to augment the understanding of how the uncertainties in the numerical code inputs translate into uncertainties in the quantity of interest (QoI). In contrast with static representation of most advanced techniques such as functional Highest Density Region (HDR) boxplot or functional boxplot, f-HOPs is a dynamic visualization that enables the practitioners to infer the dynamics of the physics and enables to see functional correlations that may exist. While this technique only allows to represent the QoI, we propose a 3-dimensional version of the Kiviat plot to encode all input parameters. This new visualization takes advantage of information from f-HOPs through data sonification. All in all, this allows to analyse large datasets within a high-dimensional parameter space and a functional QoI in the same canvas. The proposed method is assessed and showed its benefits on two related environmental datasets.

stat.ME↗