神经端口-哈密顿微分代数方程用于电网的组合学习
Neural Port-Hamiltonian Differential Algebraic Equations for Compositional Learning of Electrical Networks
AI总结：
本文提出神经端口-哈密顿微分代数方程（N-PHDAE）用于电网组合学习，通过自动微分进行指标约简，在非线性电路和直流微电网实验中显著提升预测精度与约束满足度。
摘要：
我们为耦合动力系统开发了组合学习算法，特别关注电网。虽然深度学习已被证明能有效从数据中建模复杂关系，但系统组件之间的组合耦合通常会对状态变量引入代数约束，这对许多现有的数据驱动的动力系统建模方法构成了挑战。为了开发用于约束动力系统的深度学习模型，我们引入了神经端口-哈密顿微分代数方程（N-PHDAEs），该模型使用神经网络对端口-哈密顿DAE的微分和代数组件中的未知项进行参数化。为了训练这些模型，我们提出了一种使用自动微分进行指标约简的算法，自动将神经DAE转换为等价的神经常微分方程（N-ODEs）系统，对此已有成熟的模型推断和反向传播方法。模拟非线性电路动力学的实验证明了我们方法的优势：与基线N-ODE相比，所提出的N-PHDAE模型在长时间预测范围内实现了预测精度和约束满足度的一个数量级的改进。我们还通过在模拟直流微电网上的实验验证了我们方法的组合能力：我们为各个电网组件训练单独的N-PHDAE模型，然后将它们耦合以准确预测更大规模网络的行为。
英文摘要：
We develop compositional learning algorithms for coupled dynamical systems, with a particular focus on electrical networks. While deep learning has proven effective at modeling complex relationships from data, compositional couplings between system components typically introduce algebraic constraints on state variables, posing challenges to many existing data-driven approaches to modeling dynamical systems. Towards developing deep learning models for constrained dynamical systems, we introduce neural port-Hamiltonian differential algebraic equations (N-PHDAEs), which use neural networks to parameterize unknown terms in both the differential and algebraic components of a port-Hamiltonian DAE. To train these models, we propose an algorithm that uses automatic differentiation to perform index reduction, automatically transforming the neural DAE into an equivalent system of neural ordinary differential equations (N-ODEs), for which established model inference and backpropagation methods exist. Experiments simulating the dynamics of nonlinear circuits exemplify the benefits of our approach: the proposed N-PHDAE model achieves an order of magnitude improvement in prediction accuracy and constraint satisfaction when compared to a baseline N-ODE over long prediction time horizons. We also validate the compositional capabilities of our approach through experiments on a simulated DC microgrid: we train individual N-PHDAE models for separate grid components, before coupling them to accurately predict the behavior of larger-scale networks.
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