Hamiltonian neural networks (HNNs) are state-of-the-art models that regress the vector field of a dynamical system under the learning bias of Hamilton's equations. A recent observation is that embedding a bias regarding the additive separability of the Hamiltonian reduces the regression complexity and improves regression performance. We propose separable HNNs that embed additive separability within HNNs using observational, learning, and inductive biases. We show that the proposed models are more effective than the HNN at regressing the Hamiltonian and the vector field. Consequently, the proposed models predict the dynamics and conserve the total energy of the Hamiltonian system more accurately.

翻译：哈密顿神经网络（HNNs）是在哈密顿方程的学习偏置下回归动力系统向量场的最先进模型。最近的一项观察表明，嵌入关于哈密顿量可加可分离性的偏置可以降低回归复杂度并提高回归性能。我们提出可分离HNNs，它通过观测偏置、学习偏置和归纳偏置，在HNNs内部嵌入可加可分离性。我们证明，所提出的模型在回归哈密顿量和向量场方面比HNN更有效。因此，所提出的模型能更准确地预测哈密顿系统的动力学并守恒其总能量。