Online Weak-form Sparse Identification of Partial Differential Equations
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 the 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 ℓ0-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.
| Medienart: |
E-Artikel |
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| Erscheinungsjahr: |
2022 |
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| Erschienen: |
2022 |
| Enthalten in: |
Zur Gesamtaufnahme - volume:190 |
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| Enthalten in: |
Proceedings of machine learning research - 190(2022) vom: 17. Aug., Seite 241-256 |
| Sprache: |
Englisch |
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| Beteiligte Personen: |
Messenger, Daniel A [VerfasserIn] |
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| Themen: |
Journal Article |
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| Anmerkungen: |
Date Revised 25.01.2024 published: Print Citation Status PubMed-not-MEDLINE |
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| Förderinstitution / Projekttitel: |
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NLM367547333 |
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| 500 | |a Date Revised 25.01.2024 | ||
| 500 | |a published: Print | ||
| 500 | |a Citation Status PubMed-not-MEDLINE | ||
| 520 | |a 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 the 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 ℓ0-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 | ||
| 650 | 4 | |a Journal Article | |
| 650 | 4 | |a Online optimization | |
| 650 | 4 | |a partial differential equations | |
| 650 | 4 | |a sparse regression | |
| 650 | 4 | |a system identification | |
| 650 | 4 | |a weak form | |
| 700 | 1 | |a Dall'anese, Emiliano |e verfasserin |4 aut | |
| 700 | 1 | |a Bortz, David M |e verfasserin |4 aut | |
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