论文标题
基于衍生的Sindy（DSINDY）：解决从嘈杂数据发现管理方程的挑战
Derivative-based SINDy (DSINDy): Addressing the challenge of discovering governing equations from noisy data
论文作者
论文摘要
数据驱动动力学领域的最新进展允许使用状态测量发现ODE系统。一种方法，称为非线性动力学的稀疏识别（SINDY），假设该动力学在状态下的预定基础内是稀疏的，并通过稀疏性约束的线性回归找到了扩展系数。这种方法需要对状态时间导数进行准确的估计，这在没有其他约束的情况下不一定是在高噪声方面的可能性。我们提出了一种称为基于衍生物的Sindy（DSINDY）的方法，该方法结合了两种新型方法，以改善高噪声水平的ode恢复。首先，我们通过应用一个利用系统动力学基础的投影操作员来确定状态变量。其次，我们使用二阶锥体程序（SOCP）同时找到衍生物和管理方程。我们得出了基于投影的剥离步骤的理论结果，这使我们能够估算SOCP公式中使用的超参数的值。这种基本理论有助于限制所需的用户指定参数的数量。我们提出结果表明，我们的方法可改善范德尔振荡器，悬挂振荡器和Rössler吸引子的系统回收。
Recent advances in the field of data-driven dynamics allow for the discovery of ODE systems using state measurements. One approach, known as Sparse Identification of Nonlinear Dynamics (SINDy), assumes the dynamics are sparse within a predetermined basis in the states and finds the expansion coefficients through linear regression with sparsity constraints. This approach requires an accurate estimation of the state time derivatives, which is not necessarily possible in the high-noise regime without additional constraints. We present an approach called Derivative-based SINDy (DSINDy) that combines two novel methods to improve ODE recovery at high noise levels. First, we denoise the state variables by applying a projection operator that leverages the assumed basis for the system dynamics. Second, we use a second order cone program (SOCP) to find the derivative and governing equations simultaneously. We derive theoretical results for the projection-based denoising step, which allow us to estimate the values of hyperparameters used in the SOCP formulation. This underlying theory helps limit the number of required user-specified parameters. We present results demonstrating that our approach leads to improved system recovery for the Van der Pol oscillator, the Duffing oscillator, and the Rössler attractor.
