| Autor: |
ZECHENG ZHANG, MOYA, CHRISTIAN, WING TAT LEUNG, GUANG LIN, SCHAEFFER, HAYDEN |
| Předmět: |
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| Zdroj: |
Multiscale Modeling & Simulation; 2024, Vol. 22 Issue 3, p956-972, 17p |
| Abstrakt: |
We present a new framework for computing fine-scale solutions of multiscale partial differential equations (PDEs) using operator learning tools. Obtaining fine-scale solutions of multiscale PDEs can be challenging, but there are many inexpensive computational methods for obtaining coarse-scale solutions. Additionally, in many real-world applications, fine-scale solutions can only be observed at a limited number of locations. In order to obtain approximations or predictions of fine-scale solutions over general regions of interest, we propose to learn the operator mapping from coarse-scale solutions to fine-scale solutions using observations of a limited number of (possible noisy) fine-scale solutions. The approach is to train multi-fidelity homogenization maps using mathematically motivated neural operators. The operator learning framework can efficiently obtain the solution of multiscale PDEs at any arbitrary point, making our proposed framework a mesh-free solver. We verify our results on multiple numerical examples showing that our approach is an efficient mesh-free solver for multiscale PDEs. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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