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Conference Papers Year : 2022

Multi-Fidelity Transfer Learning for accurate data-based PDE approximation

Wenzhuo Liu
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Mouadh Yagoubi
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David Danan
Marc Schoenauer

Abstract

Data-driven approaches to accelerate computation time on PDE-based physical problems have recently received growing interest. Deep Learning algorithms are applied to learn from samples of accurate approximations of the PDEs solutions computed by numerical solvers. However, generating a large-scale dataset with accurate solutions using these classical solvers remains challenging due to their high computational cost. In this work, we propose a multi-fidelity transfer learning approach that combines a large amount of low-cost data from poor approximations with a small but accurately computed dataset. Experiments on two physical problems (airfoil flow and wheel contact) show that by transferring prior-knowledge learned from the inaccurate dataset, our approach can predict well PDEs solutions, even when only a few samples of highly accurate solutions are available.
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Dates and versions

hal-03878200 , version 1 (30-11-2022)
hal-03878200 , version 2 (08-12-2022)

Identifiers

  • HAL Id : hal-03878200 , version 2

Cite

Wenzhuo Liu, Mouadh Yagoubi, David Danan, Marc Schoenauer. Multi-Fidelity Transfer Learning for accurate data-based PDE approximation. NeurIPS 2022 - Workshop on Machine Learning and the Physical Sciences, Nov 2022, New Orleans, United States. ⟨hal-03878200v2⟩
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