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This master thesis addresses two challenges for the propagation of uncertainties related to the pyrolysis process in thermal protection materials, which are the high computational cost of numerical simulations and the correlation between input uncertainties. Due to this high computational cost, classical techniques such as Monte Carlo simulations are not applicable. In this respect, we propose exploring the so-called method of polynomial chaos, which consists in using a set of orthogonal polynomials to build a cheaper surrogate model from a limited number of runs of the reference model. First, some theoretical and computational aspects of the polynomial chaos are presented in details, then different test cases are considered in order to assess the relevance of the method in producing a surrogate model for complex pyrolysis and thermal ablation processes. In summary, the goal of this thesis is to successfully demonstrate the possibility of computing a cheap and accurate surrogate model for complex pyrolysis processes in moderately high dimensions when the uncertainties on the input parameters are correlated.

polynomial chaos --- pyrolysis --- athmospheric entry --- surrogate model --- propagation of uncertainty --- stochastic modeling --- embedded quadrature rule --- Ingénierie, informatique & technologie > Multidisciplinaire, généralités & autres

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Quantitative models are crucial to almost every area of ecosystem science. They provide a logical structure that guides and informs empirical observations of ecosystem processes. They play a particularly crucial role in synthesizing and integrating our understanding of the immense diversity of ecosystem structure and function. Increasingly, models are being called on to predict the effects of human actions on natural ecosystems. Despite the widespread use of models, there exists intense debate within the field over a wide range of practical and philosophical issues pertaining to quantitative modeling. This book--which grew out of a gathering of leading experts at the ninth Cary Conference--explores those issues. The book opens with an overview of the status and role of modeling in ecosystem science, including perspectives on the long-running debate over the appropriate level of complexity in models. This is followed by eight chapters that address the critical issue of evaluating ecosystem models, including methods of addressing uncertainty. Next come several case studies of the role of models in environmental policy and management. A section on the future of modeling in ecosystem science focuses on increasing the use of modeling in undergraduate education and the modeling skills of professionals within the field. The benefits and limitations of predictive (versus observational) models are also considered in detail. Written by stellar contributors, this book grants access to the state of the art and science of ecosystem modeling.

Ecology --- Mathematical models. --- 3D modeling. --- Accuracy and precision. --- Adaptive management. --- Addition. --- Agriculture. --- Algorithm. --- Bayesian inference. --- Bayesian. --- Biodiversity. --- Biogeochemical cycle. --- Biogeochemistry. --- Biology. --- Biomass (ecology). --- Calculation. --- Calibration. --- Carbon cycle. --- Case study. --- Chlorophyll. --- Climate change. --- Climate. --- Computer simulation. --- Conceptual model. --- Curriculum. --- Data set. --- Decision-making. --- Differential equation. --- Ecological Society of America. --- Ecological forecasting. --- Ecology. --- Ecosystem ecology. --- Ecosystem management. --- Ecosystem model. --- Ecosystem. --- Empirical relationship. --- Environmental issue. --- Estimation theory. --- Estimation. --- Eutrophication. --- Experiment. --- Fertilizer. --- Food web. --- Forecasting. --- General circulation model. --- Global warming. --- Implementation. --- Inference. --- Initial condition. --- Institute of Ecosystem Studies. --- Learning. --- Likelihood function. --- Mass balance. --- Mathematics. --- Measurement. --- Monte Carlo method. --- National Science Foundation. --- Nitrogen cycle. --- Nitrogen. --- Nutrient. --- Organism. --- Parameter. --- Parametrization. --- Phytoplankton. --- Predation. --- Predictability. --- Prediction. --- Predictive modelling. --- Predictive power. --- Primary production. --- Probability. --- Propagation of uncertainty. --- Proportion (architecture). --- Quantity. --- Regression analysis. --- Remote sensing. --- Requirement. --- Result. --- Risk assessment. --- Scientific method. --- Scientist. --- Sensitivity analysis. --- Simulation. --- Soil organic matter. --- Soil. --- Spatial scale. --- State variable. --- Statistic. --- Statistical hypothesis testing. --- Statistics. --- Suggestion. --- Time series. --- Trade-off. --- Trophic level. --- Uncertainty analysis. --- Uncertainty. --- Variable (mathematics). --- Vegetation. --- Water column. --- Water quality. --- Weather forecasting. --- Zooplankton.