Papers › The non-intrusive reduced basis two-grid method applied to sensitivity analysis
The non-intrusive reduced basis two-grid method applied to sensitivity analysis
Elise Grosjean, Bernd Simeon
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
This paper deals with the derivation of Non-Intrusive Reduced Basis (NIRB) techniques for sensitivity analysis, more specifically the direct and adjoint state methods. For highly complex parametric problems, these two approaches may become too costly. To reduce computational times, Proper Orthogonal Decomposition (POD) and Reduced Basis Methods (RBMs) have already been investigated. The majority of these algorithms are however intrusive in the sense that the High-Fidelity (HF) code must be modified. To address this issue, non-intrusive strategies are employed. The NIRB two-grid method uses the HF code solely as a ``black-box'', requiring no code modification. Like other RBMs, it is based on an offline-online decomposition. The offline stage is time-consuming, but it is only executed once, whereas the online stage is significantly less expensive than an HF evaluation. In this paper, we propose new NIRB two-grid algorithms for both the direct and adjoint state methods. On the direct method, we prove on a classical model problem, the heat equation, that HF evaluations of sensitivities reach an optimal convergence rate in L^∞(0,T;H¹(Ω)), and then establish that these rates are recovered by the proposed NIRB approximation. These results are supported by numerical simulations. We then numerically demonstrate that a Gaussian process regression can be used to approximate the projection coefficients of the NIRB two-grid method. This further reduces the computational costs of the online step while only computing a coarse solution of the initial problem. All numerical results are run with the model problem as well as a more complex problem, namely the Brusselator system.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections