Identifying the underlying dynamics of physical systems can be challenging when only provided with observational data. In this work, we consider systems that can be modelled as first-order ordinary differential equations. By assuming a certain pseudo-Hamiltonian formulation, we are able to learn the analytic terms of internal dynamics even if the model is trained on data where the system is affected by unknown damping and external disturbances. In cases where it is difficult to find analytic terms for the disturbances, a hybrid model that uses a neural network to learn these can still accurately identify the dynamics of the system as if under ideal conditions. This makes the models applicable in situations where other system identification models fail. Furthermore, we propose to use a fourth-order symmetric integration scheme in the loss function and avoid actual integration in the training, and demonstrate on varied examples how this leads to increased performance on noisy data.

翻译：仅凭观测数据识别物理系统的潜在动力学特性极具挑战性。本研究关注可建模为一阶常微分方程的系统。通过采用特定的伪哈密顿形式化方法，即便模型在存在未知阻尼和外部扰动的系统数据上训练，仍能学习到内部动力学的解析项。当难以找到扰动解析项时，采用神经网络学习扰动的混合模型仍可准确辨识系统在理想条件下的动力学特性。这使得模型能够应用于其他系统辨识模型失效的情境。此外，我们提出在损失函数中采用四阶对称积分格式，避免训练中的实际积分过程，并通过多组实例证明该方法能显著提升含噪数据的模型性能。