论文标题
通过Lipschitz正规化深神经网络的系统识别
System Identification Through Lipschitz Regularized Deep Neural Networks
论文作者
论文摘要
在本文中，我们使用神经网络从数据中学习控制方程。具体来说，我们直接使用神经网络直接从观察到的均匀时间采样数据中重建ODES $ \ dot {x}（t）= f（t，x（t））$的系统的右侧。与解决此问题的其他基于神经网络的方法相反，我们为我们的损失函数添加了Lipschitz正则化项。在综合示例中，我们从经验上观察到，与非规范化模型相比，这种正则化导致近似函数和更好的概括性能，无论是在轨迹和非对象数据上，尤其是在噪声的情况下。与稀疏回归方法相反，由于神经网络是通用近似器，因此我们不需要对ODE系统的任何先验知识。由于明智地应用了模型，因此它可以处理任何维度的系统，从而使其可用于现实世界数据。
In this paper we use neural networks to learn governing equations from data. Specifically we reconstruct the right-hand side of a system of ODEs $\dot{x}(t) = f(t, x(t))$ directly from observed uniformly time-sampled data using a neural network. In contrast with other neural network based approaches to this problem, we add a Lipschitz regularization term to our loss function. In the synthetic examples we observed empirically that this regularization results in a smoother approximating function and better generalization properties when compared with non-regularized models, both on trajectory and non-trajectory data, especially in presence of noise. In contrast with sparse regression approaches, since neural networks are universal approximators, we don't need any prior knowledge on the ODE system. Since the model is applied component wise, it can handle systems of any dimension, making it usable for real-world data.
