论文标题
耗散汉密尔顿神经网络：分别学习耗散和保守的动态
Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately
论文作者
论文摘要
理解自然对称性是理解我们复杂且不断变化的世界的关键。最近的工作表明，神经网络可以使用哈密顿神经网络（HNNS）直接从数据中学习此类对称性。但是，当在无法保存能量的数据集上接受培训时，HNNS挣扎。在本文中，我们询问是否可以同时识别和分解保守和耗散动力。我们提出了耗散的哈密顿神经网络（D-HNNS），该神经网络既可以参数化汉密尔顿和瑞利耗散函数。综上所述，它们代表了隐式的Helmholtz分解，该分解可以将耗散效应（例如摩擦）分开，例如能量保护。我们训练我们的模型将阻尼的质量弹力系统分解为摩擦和惯性术语，然后证明该分解可用于预测未见摩擦系数的动力学。然后，我们将模型应用于现实世界中的数据，包括大型嘈杂的海洋电流数据集，其中分解速度场可产生有用的科学见解。
Understanding natural symmetries is key to making sense of our complex and ever-changing world. Recent work has shown that neural networks can learn such symmetries directly from data using Hamiltonian Neural Networks (HNNs). But HNNs struggle when trained on datasets where energy is not conserved. In this paper, we ask whether it is possible to identify and decompose conservative and dissipative dynamics simultaneously. We propose Dissipative Hamiltonian Neural Networks (D-HNNs), which parameterize both a Hamiltonian and a Rayleigh dissipation function. Taken together, they represent an implicit Helmholtz decomposition which can separate dissipative effects such as friction from symmetries such as conservation of energy. We train our model to decompose a damped mass-spring system into its friction and inertial terms and then show that this decomposition can be used to predict dynamics for unseen friction coefficients. Then we apply our model to real world data including a large, noisy ocean current dataset where decomposing the velocity field yields useful scientific insights.
