Group Projected subspace pursuit for IDENTification of variable coefficient differential equations (GP-IDENT)

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

  • Yuchen He
  • Sung Ha Kang
  • Wenjing Liao
  • Hao Liu
  • Yingjie Liu

Related Research Unit(s)

Detail(s)

Original languageEnglish
Article number112526
Journal / PublicationJournal of Computational Physics
Volume494
Online published29 Sept 2023
Publication statusPublished - 1 Dec 2023

Abstract

We propose an effective and robust algorithm for identifying partial differential equations (PDEs) with space-time varying coefficients from the noisy observation of a single solution trajectory. Identifying unknown differential equations from noisy data is a difficult task, and it is even more challenging with space and time varying coefficients in the PDE. The proposed algorithm, GP-IDENT, has three ingredients: (i) we use B-spline bases to express the unknown space and time varying coefficients, (ii) we propose Group Projected Subspace Pursuit (GPSP) to find a sequence of candidate PDEs with various levels of complexity, and (iii) we propose a new criterion for model selection using the Reduction in Residual (RR) to choose an optimal one among a pool of candidates. The new GPSP considers group projected subspaces which is more robust than existing methods in distinguishing correlated group features. We test GP-IDENT on a variety of PDEs and PDE systems, and compare it with the state-of-the-art parametric PDE identification algorithms under different settings to illustrate its outstanding performance. Our experiments show that GP-IDENT is effective in identifying the correct terms from a large dictionary, and our model selection scheme is robust to noise. © 2023 Elsevier Inc.

Research Area(s)

  • Data-driven method, Model selection, PDE identification, Sparse regression

Citation Format(s)

Group Projected subspace pursuit for IDENTification of variable coefficient differential equations (GP-IDENT). / He, Yuchen; Kang, Sung Ha; Liao, Wenjing et al.
In: Journal of Computational Physics, Vol. 494, 112526, 01.12.2023.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review