Dissipative Hamiltonian Neural Networks：分别学习耗散和保守动力学
Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately
摘要：
理解自然对称性是理解我们这个复杂多变的世界的关键。最近的研究表明，神经网络可以使用哈密顿神经网络（HNN）直接从数据中学习这种对称性。但是，当在能量不守恒的数据集上训练时，HNN会遇到困难。在本文中，我们问是否有可能同时识别和分解保守和耗散动力学。我们提出了耗散哈密顿神经网络（D-HNNs），参数化的哈密顿和瑞利耗散函数。两者合计，他们代表了一个隐含的亥姆霍兹分解，可以分离耗散效应，如摩擦从对称性，如能量守恒。我们训练我们的模型分解成它的摩擦和惯性项阻尼质量弹簧系统，然后表明，这种分解可以用来预测看不见的摩擦系数的动态。然后，我们将我们的模型应用于现实世界的数据，包括一个大型的，嘈杂的洋流数据集，分解速度场产生有用的科学见解。
英文摘要：
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.
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