Online Weak-form Sparse Identification of Partial Differential Equations
- URL: http://arxiv.org/abs/2203.03979v1
- Date: Tue, 8 Mar 2022 10:11:09 GMT
- Title: Online Weak-form Sparse Identification of Partial Differential Equations
- Authors: Daniel A. Messenger, Emiliano Dall'Anese and David M. Bortz
- Abstract summary: This paper presents an online algorithm for identification of partial differential equations (PDEs) based on the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy)
The core of the method combines a weak-form discretization of candidate PDEs with an online proximal gradient descent approach to the sparse regression problem.
- Score: 0.5156484100374058
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: This paper presents an online algorithm for identification of partial
differential equations (PDEs) based on the weak-form sparse identification of
nonlinear dynamics algorithm (WSINDy). The algorithm is online in a sense that
if performs the identification task by processing solution snapshots that
arrive sequentially. The core of the method combines a weak-form discretization
of candidate PDEs with an online proximal gradient descent approach to the
sparse regression problem. In particular, we do not regularize the
$\ell_0$-pseudo-norm, instead finding that directly applying its proximal
operator (which corresponds to a hard thresholding) leads to efficient online
system identification from noisy data. We demonstrate the success of the method
on the Kuramoto-Sivashinsky equation, the nonlinear wave equation with
time-varying wavespeed, and the linear wave equation, in one, two, and three
spatial dimensions, respectively. In particular, our examples show that the
method is capable of identifying and tracking systems with coefficients that
vary abruptly in time, and offers a streaming alternative to problems in higher
dimensions.
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