拉格朗日与哈密顿神经网络及其在耗散系统中的应用
Lagrangian and Hamiltonian Neural Networks With a Dissipative System
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中文总结 AI 辅助
本研究将拉格朗日与哈密顿神经网络应用于含显式时间依赖的耗散系统，验证其能预测阻尼振荡器行为并学习潜在力学量，揭示时间依赖下的重要性质。
中文摘要 AI 辅助
我们研究了拉格朗日神经网络和哈密顿神经网络模型在具有显式时间依赖性的拉格朗日量、哈密顿量及总能量的耗散系统中的应用。为此，我们考虑了这些神经网络模型在模拟的带阻尼和不带阻尼的一维单组分谐振子系统上的表现。我们发现，拉格朗日方法和哈密顿方法均能预测阻尼振荡器系统的经验物理行为，并能不同程度地有效“学习”潜在的拉格朗日量和哈密顿量，正如先前在无阻尼振荡器系统中所示。这些研究阐明了拉格朗日力学和哈密顿力学的重要性质，包括在考虑无显式时间依赖性的系统时不显现的性质。
英文摘要
We investigate the applicability of Lagrangian and Hamiltonian Neural Network models to a dissipative system that has explicit time dependence in its Lagrangian, Hamiltonian, and total energy. To do so we consider these neural network models for simulated systems of a harmonic one-dimensional, one-component oscillator with damping, as well as without damping for comparison. We find that both the Lagrangian and Hamiltonian approaches are able to predict the empirical physical behavior of the damped oscillator systems and to effectively ``learn'' to varying degrees the underlying Lagrangians and Hamiltonians, as has previously been shown to be the case with undamped oscillator systems. These investigations elucidate important properties of Lagrangian and Hamiltonian mechanics, including properties that are not manifest when considering systems without explicit time dependence.
