A Posteriori Validation of Generalized Polynomial Chaos Expansions - Archive ouverte HAL
Article Dans Une Revue SIAM Journal on Applied Dynamical Systems Année : 2023

A Posteriori Validation of Generalized Polynomial Chaos Expansions

Résumé

Generalized polynomial chaos (gPC) expansions are a powerful tool for studying differential equations with random coefficients, allowing, in particular, one to efficiently approximate random invariant sets associated with such equations. In this work, we use ideas from validated numerics in order to obtain rigorous a posteriori error estimates together with existence results about gPC expansions of random invariant sets. This approach also provides a new framework for conducting validated continuation, i.e., for rigorously computing isolated branches of solutions in parameter-dependent systems, which generalizes in a straightforward way to multiparameter continuation. We illustrate the proposed methodology by rigorously computing random invariant periodic orbits in the Lorenz system, as well as branches and 2 dimensional manifolds of steady states of the Swift–Hohenberg equation.
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Dates et versions

hal-04296607 , version 1 (02-02-2024)

Identifiants

Citer

Maxime Breden. A Posteriori Validation of Generalized Polynomial Chaos Expansions. SIAM Journal on Applied Dynamical Systems, 2023, 22 (2), pp.765-801. ⟨10.1137/22M1493197⟩. ⟨hal-04296607⟩
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