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.

翻译：本文提出一种物理一致的 高斯过程（GP），用于识别不确定的拉格朗日系统。根据拉格朗日量的能量分量及微分方程结构对函数空间进行定制，从解析上保证了能量守恒及二次型等物理与数学性质。通过引入 Cholesky 分解矩阵核的新颖公式，实现了正定性的概率保持。该方法仅需函数映射的微分输入输出测量值，同时允许扭矩、速度和加速度中存在高斯噪声。我们通过数值仿真验证了该方法的有效性。