期刊
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
卷 29, 期 3, 页码 698-728出版社
GLOBAL SCIENCE PRESS
DOI: 10.4208/cicp.OA-2020-0142
关键词
Data-driven discovery; machine learning; deep neural network; sparse regression; noisy data
资金
- National Natural Science Foundation of China [51520105005, U1663208]
- National Science and Technology Major Project of China [2017ZX05009-005, 2017ZX05049-003]
In recent years, data-driven methods have been developed for learning dynamical systems and partial differential equations to discover unknown physics and corresponding equations. The proposed DL-PDE method combines deep learning through neural networks with data-driven discovery of PDE through sparse regressions.
In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is to discover unknown physics and corresponding equations. However, prior to achieving this goal, major challenges remain to be resolved, including learning PDE under noisy data and limited discrete data. To overcome these challenges, in this work, a deeplearning based data-driven method, called DL-PDE, is developed to discover the governing PDEs of underlying physical processes. The DL-PDE method combines deep learning via neural networks and data-driven discovery of PDE via sparse regressions. In the DL-PDE, a neural network is first trained, then a large amount of meta-data is generated, and the required derivatives are calculated by automatic differentiation. Finally, the form of PDE is discovered by sparse regression. The proposed method is tested with physical processes, governed by the diffusion equation, the convectiondiffusion equation, the Burgers equation, and the Korteweg-de Vries (KdV) equation, for proof-of-concept and applications in real-world engineering settings. The proposed method achieves satisfactory results when data are noisy and limited.
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