从位置数据直接学习机械系统动力学，无需速度信息。
Learning mechanical systems from real-world data using discrete forced Lagrangian dynamics
- 基于离散受力拉格朗日原理，分离保守与非保守动力学建模。
- 在人体运动和图像嵌入数据上实现精确动态重建与分离。
- 适合仅能获取位置数据的物理系统识别任务。
我们提出一种数据驱动方法，直接从位置测量值中学习机械系统的运动方程，无需速度数据。这在仅能获取位置信息（如动作捕捉、像素数据或低分辨率追踪）的系统辨识任务中尤为重要。该方法基于离散拉格朗日-达朗贝尔原理和受力离散欧拉-拉格朗日方程，构建物理基础的动力学模型。我们将动力学分解为保守与非保守两部分，分别由前馈神经网络学习。当无外力时，该方法退化为作用量原理的变分离散，自然保持哈密顿系统的辛结构。我们在多种合成与真实世界数据集上验证了方法的有效性，相较于基线方法表现更优。具体应用包括：(1) 实测人体运动数据；(2) 通过自编码器训练得到的图像序列隐空间嵌入。结果表明，该模型可忠实重构并分离保守与受力动力学，生成可解释且物理一致的预测。
原文摘要 · Abstract (English)
We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is particularly relevant in system identification tasks where only positional information is available, such as motion capture, pixel data or low-resolution tracking. Our approach takes advantage of the discrete Lagrange-d'Alembert principle and the forced discrete Euler-Lagrange equations to construct a physically grounded model of the system's dynamics. We decompose the dynamics into conservative and non-conservative components, which are learned separately using feed-forward neural networks. In the absence of external forces, our method reduces to a variational discretization of the action principle naturally preserving the symplectic structure of the underlying Hamiltonian system. We validate our approach on a variety of synthetic and real-world datasets, demonstrating its effectiveness compared to baseline methods. In particular, we apply our model to (1) measured human motion data and (2) latent embeddings obtained via an autoencoder trained on image sequences. We demonstrate that we can faithfully reconstruct and separate both the conservative and forced dynamics, yielding interpretable and physically consistent predictions.
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