论文标题
Sindy弱：基于Galerkin的数据驱动模型选择
Weak SINDy: Galerkin-Based Data-Driven Model Selection
论文作者
论文摘要
我们从嘈杂的测量数据中提出了系统发现问题的薄弱配方和离散化。从数据中学习微分方程的方法拟合到新的一类算法中，这些算法用线性变换和降低方差替代了点式衍生近似值。我们的方法通过数量级来改善标准的信德算法。我们首先表明，在无噪声方向上，这个所谓的弱信也（WSINDY）框架能够将动态系数恢复至非常高的精度，而有效数字的数量等于数据模拟方案的公差。接下来，我们表明弱形式通过识别具有系数误差的正确非线性，以符合信号噪声比率的误差缩放，同时显着降低了算法中线性系统的大小，从而自然地说明了白噪声。在此过程中，我们结合了Sindy算法的易于实施，与整合的自然降噪相结合，以达到一种更强大且用户友好的稀疏恢复方法，可以正确识别小噪声和大噪声方案中的系统。
We present a weak formulation and discretization of the system discovery problem from noisy measurement data. This method of learning differential equations from data fits into a new class of algorithms that replace pointwise derivative approximations with linear transformations and a variance reduction technique. Our approach improves on the standard SINDy algorithm by orders of magnitude. We first show that in the noise-free regime, this so-called Weak SINDy (WSINDy) framework is capable of recovering the dynamic coefficients to very high accuracy, with the number of significant digits equal to the tolerance of the data simulation scheme. Next we show that the weak form naturally accounts for white noise by identifying the correct nonlinearities with coefficient error scaling favorably with the signal-to-noise ratio while significantly reducing the size of linear systems in the algorithm. In doing so, we combine the ease of implementation of the SINDy algorithm with the natural noise-reduction of integration to arrive at a more robust and user-friendly method of sparse recovery that correctly identifies systems in both small-noise and large-noise regimes.
