Discover governing differential equations from evolving systems
- URL: http://arxiv.org/abs/2301.07863v3
- Date: Sun, 16 Jul 2023 04:36:56 GMT
- Title: Discover governing differential equations from evolving systems
- Authors: Yuanyuan Li, Kai Wu, Jing Liu
- Abstract summary: We propose an online modeling method capable of handling samples one by one sequentially.
The proposed method performs well in discovering ordinary differential equations (ODEs) and partial differential equations (PDEs) from streaming data.
- Score: 17.883650663817836
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Discovering the governing equations of evolving systems from available
observations is essential and challenging. In this paper, we consider a new
scenario: discovering governing equations from streaming data. Current methods
struggle to discover governing differential equations with considering
measurements as a whole, leading to failure to handle this task. We propose an
online modeling method capable of handling samples one by one sequentially by
modeling streaming data instead of processing the entire dataset. The proposed
method performs well in discovering ordinary differential equations (ODEs) and
partial differential equations (PDEs) from streaming data. Evolving systems are
changing over time, which invariably changes with system status. Thus, finding
the exact change points is critical. The measurement generated from a changed
system is distributed dissimilarly to before; hence, the difference can be
identified by the proposed method. Our proposal is competitive in identifying
the change points and discovering governing differential equations in three
hybrid systems and two switching linear systems.
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