Group Projected subspace pursuit for IDENTification of variable coefficient differential equations (GP-IDENT)
Group Projected subspace pursuit for IDENTification of variable coefficient differential equations (GP-IDENT)
复制标题
变系数微分方程辨识的群投影子空间追踪 (GP-IDENT)
DOI：
10.1016/j.jcp.2023.112526
复制
发表时间：
2023
影响因子：
4.1
通讯作者：
Liu, Yingjie
中科院分区：
文献类型：
--
作者：
He, Yuchen;Kang, Sung Ha;Liao, Wenjing;Liu, Hao;Liu, Yingjie
本文提出了一种有效的、鲁棒的算法，用于从单解轨迹的噪声观测中识别具有时空变化系数的偏微分方程。从噪声数据中识别未知微分方程是一项艰巨的任务，而在PDE中，随着系数的时空变化，识别未知微分方程就更加困难了。所提出的GP-IDENT算法有三个组成部分：(i)我们使用b样条基来表示未知的空间和时变系数，（ii）我们提出了群投影子空间追踪（GPSP）来寻找具有不同复杂度的候选pde序列，以及（iii）我们提出了一个新的模型选择准则，使用残差还原（RR）在候选库中选择最优的pde。该方法考虑了群投影子空间，在识别相关群特征方面比现有方法具有更强的鲁棒性。我们在各种PDE和PDE系统上测试了GP-IDENT，并将其与最先进的参数PDE识别算法在不同设置下进行了比较，以说明其出色的性能。我们的实验表明，GP-IDENT可以有效地从大词典中识别正确的术语，并且我们的模型选择方案对噪声具有鲁棒性。
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.