Data-Driven Modeling and Prediction of Non-Linearizable Dynamics via Spectral Submanifolds

Data-driven Nonlinear Model Reduction to Spectral Submanifolds in Mechanical Systems

While data-driven model reduction techniques are well-established for linearizable mechanical systems, general approaches to reducing non-linearizable systems with multiple coexisting steady states have been unavailable. In this paper, we review such a data-driven nonlinear model reduction methodology based on spectral submanifolds (SSMs). As input, this approach takes observations of unforced nonlinear oscillations to construct normal forms of the dynamics reduced to very low dimensional invariant manifolds. These normal forms capture amplitude-dependent properties and are accurate enough to …

Fast data-driven model reduction for nonlinear dynamical systems

We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). We use observed data to locate a low-dimensional, attracting slow SSM and compute a maximally sparse approximation to the reduced dynamics on it. The recently released SSMLearn algorithm uses implicit optimization to fit a spectral submanifold to data and reduce the dynamics to the normal form. Here, we present two simplified algorithms, which reformulate manifold fitting and normal form computation as explicit problems under certain assumptions. …

基于作为谱子流形构造的惯性流形上混沌动力学的数据驱动建模与预测

Data-Driven Modeling and Forecasting of Chaotic Dynamics on Inertial Manifolds Constructed as Spectral Submanifolds

提出利用谱子流形（SSM）降低混沌系统维度的数据驱动方法，SSM作为低维惯性流形能准确预测短期混沌动力学并重现长期统计特征，在多个模型及屈曲梁实验中验证了其预测能力。

通过谱子流形实现延迟动力系统的数据驱动降维建模

Data-Driven Reduced Modeling of Delayed Dynamical Systems via Spectral Submanifolds

本文提出了一种基于谱子流形理论的数据驱动方法，用于减少非线性延迟系统的模型复杂度，通过比较基于方程和数据驱动的SSM降维方法，展示了该方法在处理延迟微分方程时的有效性，并应用于多个非线性延迟系统，得到无延迟的ODE模型。

主测地线格拉斯曼子流形上的多项式混沌展开用于代理建模与不确定性量化

Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds for Surrogate Modeling and Uncertainty Quantification

本文提出基于流形学习的代理建模框架，通过主测地线分析和多项式混沌展开，在高维随机系统中实现高效不确定性量化，并在四个测试案例中验证了其有效性。

数据驱动的非线性模型降阶：基于斜投影到谱子流形

Data-Driven Nonlinear Model Reduction to Spectral Submanifolds via Oblique Projection

针对强非正态动力系统，提出基于斜投影的SSM降阶方法，可从单一实验轨迹高效近似稳定叶理，实现精确降阶。