论文标题
受限的神经普通微分方程具有稳定性保证
Constrained Neural Ordinary Differential Equations with Stability Guarantees
论文作者
论文摘要
微分方程经常用于工程领域，例如对安全和绩效保证至关重要的工业系统的建模和控制。传统的基于物理的建模方法需要域专业知识，并且通常很难调整或适应新系统。在本文中，我们展示了如何用代数非线性作为具有不同程度的先验知识的深神经网络建模离散的普通微分方程（ODE）。我们根据对重量特征值施加的隐式约束来得出网络层的稳定性保证。此外，我们展示了如何使用障碍方法来处理其他不平等约束。我们证明了与带有双线性术语的地面真实动态相比，在开环模拟上评估的学习神经ODE的预测准确性。
Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches require domain expertise and are often difficult to tune or adapt to new systems. In this paper, we show how to model discrete ordinary differential equations (ODE) with algebraic nonlinearities as deep neural networks with varying degrees of prior knowledge. We derive the stability guarantees of the network layers based on the implicit constraints imposed on the weight's eigenvalues. Moreover, we show how to use barrier methods to generically handle additional inequality constraints. We demonstrate the prediction accuracy of learned neural ODEs evaluated on open-loop simulations compared to ground truth dynamics with bi-linear terms.
