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您的检索式：作者名="Didier Lucor"
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| 1 | Machine Learning With Data Assimilation and Uncertainty Quantification for Dynamical Systems:A Review显示文摘Data assimilation(DA)and uncertainty quantification(UQ)are extensively used in analysing and reducing error propagation in high-dimensional spatial-temporal dynamics.Typical applications span from computational fluid dynamics(CFD)to geoscience and climate systems.Recently,much effort has been given in combining DA,UQ and machine learning(ML)techniques.These research efforts seek to address some critical challenges in high-dimensional dynamical systems,including but not limited to dynamical system identification,reduced order surrogate modelling,error covariance specification and model error correction.A large number of developed techniques and methodologies exhibit a broad applicability across numerous domains,resulting in the necessity for a comprehensive guide.This paper provides the first overview of state-of-the-art researches in this interdisciplinary field,covering a wide range of applications.This review is aimed at ML scientists who attempt to apply DA and UQ techniques to improve the accuracy and the interpretability of their models,but also at DA and UQ experts who intend to integrate cutting-edge ML approaches to their systems.Therefore,this article has a special focus on how ML methods can overcome the existing limits of DA and UQ,and vice versa.Some exciting perspectives of this rapidly developing research field are also discussed.Index Terms-Data assimilation(DA),deep learning,machine learning(ML),reduced-order-modelling,uncertainty quantification(UQ). | Sibo Cheng César Quilodrán-Casas Said Ouala Alban Farchi Che Liu Pierre Tandeo Ronan Fablet Didier Lucor Bertrand Iooss Julien Brajard Dunhui Xiao Tijana Janjic Weiping Ding Yike Guo Alberto Carrassi Marc Bocquet Rossella Arcucci | 2023 | IEEE/CAA Journal of Automatica Sinica2023，10，6： | 1 |
| 2 | Adaptive Bayesian Inference for Discontinuous Inverse Problems,Application to Hyperbolic Conservation Laws显示文摘Various works from the literature aimed at accelerating Bayesian inference in inverse problems.Stochastic spectral methods have been recently proposed as surrogate approximations of the forward uncertainty propagation model over the support of the prior distribution.These representations are efficient because they allow affordable simulation of a large number of samples from the posterior distribution.Unfortunately,they do not perform well when the forward model exhibits strong nonlinear behavior with respect to its input.In this work,we first relate the fast(exponential)L2-convergence of the forward approximation to the fast(exponential)convergence(in terms of Kullback-Leibler divergence)of the approximate posterior.In particular,we prove that in case the prior distribution is uniform,the posterior is at least twice as fast as the convergence rate of the forward model in those norms.The Bayesian inference strategy is developed in the framework of a stochastic spectral projection method.The predicted convergence rates are then demonstrated for simple nonlinear inverse problems of varying smoothness.We then propose an efficient numerical approach for the Bayesian solution of inverse problems presenting strongly nonlinear or discontinuous system responses.This comes with the improvement of the forward model that is adaptively approximated by an iterative generalized Polynomial Chaos-based representation.The numerical approximations and predicted convergence rates of the former approach are compared to the new iterative numerical method for nonlinear time-dependent test cases of varying dimension and complexity,which are relevant regarding our hydrodynamics motivations and therefore regarding hyperbolic conservation laws and the apparition of discontinuities in finite time. | Alexandre Birolleau Gaël Poëtte Didier Lucor | 2014 | Communications in Computational Physics2014，16，6： | 0 |
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