论文标题
稀疏的动态系统识别以及同时结构参数和初始条件估计
Sparse dynamical system identification with simultaneous structural parameters and initial condition estimation
论文作者
论文摘要
已经证明，非线性动力学（Sindy）的稀疏识别能够从数据中成功恢复管理方程。但是，这种方法假定初始条件是事先知道的，并且对噪声很敏感。在这项工作中，我们提出了一种积分的Sindy（Isindy）方法，以同时识别嘈杂的时间序列观测值的非线性普通微分方程（ODE）的模型结构和参数。首先，通过惩罚的样条平滑估算状态，然后替换为积分形式的数值离散求解器，从而导致伪线性回归。执行顺序阈值最小二乘从过度确定的候选特征集中提取最少的活动项，从而同时估算结构参数和初始条件，同时且与此同时，使所识别的动力学简化且可解释。模拟详细介绍了该方法的恢复精度和噪声的鲁棒性。示例包括逻辑方程，Lokta-Volterra系统和Lorenz系统。
Sparse Identification of Nonlinear Dynamics (SINDy) has been shown to successfully recover governing equations from data; however, this approach assumes the initial condition to be exactly known in advance and is sensitive to noise. In this work we propose an integral SINDy (ISINDy) method to simultaneously identify model structure and parameters of nonlinear ordinary differential equations (ODEs) from noisy time-series observations. First, the states are estimated via penalized spline smoothing and then substituted into the integral-form numerical discretization solver, leading to a pseudo-linear regression. The sequential threshold least squares is performed to extract the fewest active terms from the overdetermined set of candidate features, thereby estimating structural parameters and initial condition simultaneously and meanwhile, making the identified dynamics parsimonious and interpretable. Simulations detail the method's recovery accuracy and robustness to noise. Examples include a logistic equation, Lokta-Volterra system, and Lorenz system.
