In this paper, we introduce Symplectic ODE-Net (SymODEN), a deep learning framework which can infer the dynamics of a physical system, given by an ordinary differential equation (ODE), from observed state trajectories. To achieve better generalization with fewer training samples, SymODEN incorporates appropriate inductive bias by designing the associated computation graph in a physics-informed manner. In particular, we enforce Hamiltonian dynamics with control to learn the underlying dynamics in a transparent way, which can then be leveraged to draw insight about relevant physical aspects of the system, such as mass and potential energy. In addition, we propose a parametrization which can enforce this Hamiltonian formalism even when the generalized coordinate data is embedded in a high-dimensional space or we can only access velocity data instead of generalized momentum. This framework, by offering interpretable, physically-consistent models for physical systems, opens up new possibilities for synthesizing model-based control strategies.

翻译：本文提出辛普森ODE网络（SymODEN），一种能够从观测状态轨迹中推断物理系统动力学（由常微分方程描述）的深度学习框架。为实现少训练样本下的泛化能力提升，SymODEN通过设计符合物理规律的计算图引入适当的归纳偏置。具体而言，我们施加含控制的哈密顿动力学约束，以透明方式学习潜在动力学机制，从而可提取系统质量、势能等物理量的关键信息。此外，我们提出一种参数化方法，即使广义坐标数据嵌入高维空间或仅能获取速度数据而非广义动量，仍可强制执行哈密顿形式体系。该框架通过提供可解释且物理一致的物理系统模型，为综合基于模型的控制策略开辟了新途径。