通过学习谱子流形上的最优投影，显著提升高维非线性系统的建模精度。
Taming High-Dimensional Dynamics: Learning Optimal Projections onto Spectral Submanifolds
- 基于谱子流形的纤维对齐投影，保留非线性几何结构
- 在180维机器人系统上实现轨迹追踪精度提升5倍
- 适合需要高精度建模的机器人控制与复杂系统研究
高维非线性系统在流体力学、先进机器人等领域建模与控制面临巨大挑战。现有降阶模型通常依赖正交投影，可能引发较大预测误差。本文推导出沿纤维方向投影至谱子流形的最优性，能保持非线性几何结构并最小化长期预测误差。我们提出一种数据驱动方法，从轨迹中学习这些投影，并在180维机器人系统上验证其有效性。所构建的降阶模型在模型预测控制下，轨迹跟踪精度相比当前最优方法最高提升五倍。
原文摘要 · Abstract (English)
High-dimensional nonlinear systems pose considerable challenges for modeling and control across many domains, from fluid mechanics to advanced robotics. Such systems are typically approximated with reduced-order models, which often rely on orthogonal projections, a simplification that may lead to large prediction errors. In this work, we derive optimality of fiber-aligned projections onto spectral submanifolds, preserving the nonlinear geometric structure and minimizing long-term prediction error. We propose a data-driven procedure to learn these projections from trajectories and demonstrate its effectiveness through a 180-dimensional robotic system. Our reduced-order models achieve up to fivefold improvement in trajectory tracking accuracy under model predictive control compared to the state of the art.
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