新架构让 Hamiltonian 神经网络无需已知广义动量即可学习
Learning momenta for Hamiltonian-based models
做物理信息神经网络的朋友看这篇：HNN 不再要求你提前写出广义动量公式，双摆和滚动圆盘上都验证过了。
Hamiltonian 神经网络（HNN）此前依赖目标系统广义动量的解析形式作为训练数据，限制了真实场景的应用。这篇 arXiv 论文提出扩展架构，能从状态及其导数的数据中同时学习广义动量、Hamiltonian 结构和系统动力学，即使动量解析形式未知、数据非序列化也可运行。作者在带阻尼的质量弹簧系统、双摆和非完整约束下的滚动圆盘三个经典例子上验证了性能。
Learning momenta for Hamiltonian-based models
There has been increasing interest in methodologies that incorporate physics priors into neural network architectures to enhance their modeling capabilities. Among these methodologies, Hamiltonian neural networks (HNNs) and their variants have gained considerable attention. These architectures explicitly encode Hamiltonian mechanics both in their structure and loss function, resulting in desirable properties and additional modeled information. A crucial limitation of HNNs is their reliance on data on the target system's generalized momenta. This severely hampers their applicability when the analytical form of the generalized momenta is unknown, which frequently is the case in real-world applications. The goal of the present work is to develop a general extension of Hamiltonian-based architectures that addresses this issue by simultaneously learning the system's generalized momenta, Hamiltonian structure, and dynamics from data. The proposed architecture learns the generalized momenta when their analytical form is unknown, and only (potentially non-sequential) data on the state and its derivatives is available. A dissipative mass-spring system, a double pendulum, and a rolling disk under nonholonomic constraints are considered as canonical examples to assess the performance of the proposed architecture.