Global sensitivity analysis in the limited data setting with application to char combustion

In uncertainty quantification, variance-based global sensitivity analysis quantitatively determines the effect of each input random variable on the output by partitioning the total output variance into contributions from each input. However, computing conditional expectations can be prohibitively costly when working with expensive-to-evaluate models. Surrogate models can accelerate this, yet their accuracy depends on the quality and quantity of training data, which is expensive to generate (experimentally or computationally) for complex engineering systems. Thus, methods that work with limited data are desirable. We propose a diffeomorphic modulation under observable response preserving homotopy (D-MORPH) regression to train a polynomial dimensional decomposition surrogate of the output that minimizes the number of training data. The new method first computes a sparse Lasso solution and uses it to define the cost function. A subsequent D-MORPH regression minimizes the difference between the D-MORPH and Lasso solution. The resulting D-MORPH surrogate is more robust to input variations and more accurate with limited training data. We illustrate the accuracy and computational efficiency of the new surrogate for global sensitivity analysis using mathematical functions and an expensive-to-simulate model of char combustion. The new method is highly efficient, requiring only 15% of the training data compared to conventional regression.Comment: 26 pages, 11 figure

Analysis of uncertainty and variability in finite element computational models for biomedical engineering: characterization and propagation

Computational modeling has become a powerful tool in biomedical engineering thanks to its potential to simulate coupled systems. However, real parameters are usually not accurately known, and variability is inherent in living organisms. To cope with this, probabilistic tools, statistical analysis and stochastic approaches have been used. This article aims to review the analysis of uncertainty and variability in the context of finite element modeling in biomedical engineering. Characterization techniques and propagation methods are presented, as well as examples of their applications in biomedical finite element simulations. Uncertainty propagation methods, both non-intrusive and intrusive, are described. Finally, pros and cons of the different approaches and their use in the scientific community are presented. This leads us to identify future directions for research and methodological development of uncertainty modeling in biomedical engineering

L2-Boosting for sensitivity analysis with dependent inputs

International audienceThis paper is dedicated to the study of an estimator of the generalized Hoeffding decomposition. We build such an estimator using an empirical Gram-Schmidt approach and derive a consistency rate in a large dimensional setting. We then apply a greedy algorithm with these previous estimators to a sensitivity analysis. We also establish the consistency of this L2-boosting under sparsity assumptions of the signal to be analyzed. The paper concludes with numerical experiments, that demonstrate the low computational cost of our method, as well as its efficiency on the standard benchmark of sensitivity analysis

Clustering based Multiple Anchors High-Dimensional Model Representation

In this work, a cut high-dimensional model representation (cut-HDMR) expansion based on multiple anchors is constructed via the clustering method. Specifically, a set of random input realizations is drawn from the parameter space and grouped by the centroidal Voronoi tessellation (CVT) method. Then for each cluster, the centroid is set as the reference, thereby the corresponding zeroth-order term can be determined directly. While for non-zero order terms of each cut-HDMR, a set of discrete points is selected for each input component, and the Lagrange interpolation method is applied. For a new input, the cut-HDMR corresponding to the nearest centroid is used to compute its response. Numerical experiments with high-dimensional integral and elliptic stochastic partial differential equation as backgrounds show that the CVT based multiple anchors cut-HDMR can alleviate the negative impact of a single inappropriate anchor point, and has higher accuracy than the average of several expansions

Uncertainty and Sensitivity Analysis for policy decision making: An introductory guide

The European Commission is committed to transparent and evidence based policy making throughout the policy cycle. Simulation models are increasingly used in impact assessments to provide support to policy makers across a wide range of policy areas. To ensure model quality in support to policy, understanding and communicating uncertainty in model outputs is essential. In modelling, accounting for uncertainties and identifying its most important sources is an inherent issue. Uncertainty and sensitivity analysis should be systematically performed in modelling activities in support to policy making. This report aims at highlighting the added value that uncertainty and sensitivity analysis can bring to modelling activities to inform policy makers, and presents a specific software that has been developed within the Commission to help modellers and analysts.JRC.I.2-Foresight, Modelling, Behavioural Insights & Design for Polic

Generalized Sobol sensitivity indices for dependent variables: numerical methods

International audienceThe hierarchically orthogonal functional decomposition of any measurable function f of a random vector X=(X_1,...,X_p) consists in decomposing f(X) into a sum of increasing dimension functions depending only on a subvector of X. Even when X_1,..., X_p are assumed to be dependent, this decomposition is unique if components are hierarchically orthogonal. That is, two of the components are orthogonal whenever all the variables involved in one of the summands are a subset of the variables involved in the other. Setting Y=f(X), this decomposition leads to the definition of generalized sensitivity indices able to quantify the uncertainty of Y with respect to the dependent inputs X. In this paper, a numerical method is developed to identify the component functions of the decomposition using the hierarchical orthogonality property. Furthermore, the asymptotic properties of the components estimation is studied, as well as the numerical estimation of the generalized sensitivity indices of a toy model. Lastly, the method is applied to a model arising from a real-world problem

Developing a temperature-dependent simulation model for Sitobion avenae: Impacts of climate change for spring barley in Ireland

The last two decades have facilitated considerable progress in understanding the impacts of climate change on crop sensitivity and production, however very few of these studies have incorporated the activity of herbivorous insect pests into their assessments of potential yield losses. In Ireland, the grain aphid (Sitobion avenae) is the most commonly encountered aphid pest in cereal crops. This pest confers significant decreases in crop yields owing to its mechanical feeding damage, as well as its ability to vector plant viruses. Despite the damage potential, climate-induced changes to aphid populations have not been considered in the context of Irish agricultural production. The work presented here integrates biological data from various studies to inform the development of a simulation model to describe the population dynamics of S. avenae for multiple locations in Ireland in response to climate change. The simulation model (SAV4) describes the compartmentalised life cycle history of S. avenae in response to temperature, incorporating immigration, reproduction, survival, development and morph determination, facilitating the calculation of annual phenological and quantitative aphid metrics. The model was evaluated using observations describing aphid immigration, timing and size of populations in order to ensure that it was fit for purpose. Projected temperature data derived from three Global Climate Models (GCMs) and two green house gas projection pathways, were used to drive the aphid simulation model for eleven locations in Ireland. Reported findings include increases in both aphid abundance and voltinism, as well as advanced phenology across all sites for Ireland. The extent of modelled change was found to differ spatially, with current areas of spring barley cultivation experiencing some of the most significant alterations to S. avenae’s dynamics over time. These findings highlight potential increases in pest risk under climate change in Ireland, emphasising the need for monitoring programmes in conjunction with an Integrated Pest Management (IPM) approach in order to ensure crop resilience in the future. This work constitutes the first explicit incorporation of pest dynamics into climate change projections for the Republic of Ireland, as well as providing a novel pest model for use in pest risk analysis. More broadly, the findings presented here contribute to a growing body of work concerning the mediating effects of climate-induced pest activities in food security