论文标题
用高斯流程对保守的拉格朗日系统的物理一致学习
Physically Consistent Learning of Conservative Lagrangian Systems with Gaussian Processes
论文作者
论文摘要
本文提出了一个物理上一致的高斯过程（GP），以识别不确定的拉格朗日系统。该功能空间是根据拉格朗日和微分方程结构的能量成分来量身定制的，可以在分析上保证物理和数学特性，例如能量保护和二次形式。 Cholesky分解的基质内核的新型表述允许概率保留正定性。在扭矩，速度和加速度中允许高斯噪声时，仅需要进行函数图的差分输入测量值。我们证明了该方法在数值模拟中的有效性。
This paper proposes a physically consistent Gaussian Process (GP) enabling the identification of uncertain Lagrangian systems. The function space is tailored according to the energy components of the Lagrangian and the differential equation structure, analytically guaranteeing physical and mathematical properties such as energy conservation and quadratic form. The novel formulation of Cholesky decomposed matrix kernels allow the probabilistic preservation of positive definiteness. Only differential input-to-output measurements of the function map are required while Gaussian noise is permitted in torques, velocities, and accelerations. We demonstrate the effectiveness of the approach in numerical simulation.
