Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems
Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems
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DOI：
10.1103/physreve.104.034312
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发表时间：
2021-07
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影响因子：
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通讯作者：
Shaan Desai;M. Mattheakis;David Sondak;P. Protopapas;Stephen J. Roberts
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作者：
Shaan Desai;M. Mattheakis;David Sondak;P. Protopapas;Stephen J. Roberts
准确地学习动态系统的时间行为需要具有精心选择的学习偏差的模型。最近的创新将哈密顿和拉格朗日形式嵌入到神经网络中，并显示出在预测物理系统轨迹方面相对于其他方法的显著改进。这些方法通常处理隐含地依赖于时间的自治系统或控制信号先验已知的系统。尽管取得了这样的成功，但许多现实世界的动力系统是非自治的，受到依赖于时间的力的驱动，并经历着能量耗散。在这项研究中，我们通过将端口-哈密顿形式嵌入到神经网络中来解决从这类非自治系统中学习的挑战，神经网络是一个可以捕获能量耗散和依赖于时间的控制力的通用框架。我们表明，所提出的端口-哈密顿神经网络可以有效地学习实际感兴趣的非线性物理系统的动力学，并准确地恢复潜在的稳态哈密顿量、依赖于时间的力和耗散系数。我们的网络的一个有希望的结果是它能够学习和预测混沌系统，如Duffing方程，对于这些系统，轨迹通常很难学习。
Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant improvement over other approaches in predicting trajectories of physical systems. These methods generally tackle autonomous systems that depend implicitly on time or systems for which a control signal is known a priori. Despite this success, many real world dynamical systems are nonautonomous, driven by time-dependent forces and experience energy dissipation. In this study, we address the challenge of learning from such nonautonomous systems by embedding the port-Hamiltonian formalism into neural networks, a versatile framework that can capture energy dissipation and time-dependent control forces. We show that the proposed port-Hamiltonian neural network can efficiently learn the dynamics of nonlinear physical systems of practical interest and accurately recover the underlying stationary Hamiltonian, time-dependent force, and dissipative coefficient. A promising outcome of our network is its ability to learn and predict chaotic systems such as the Duffing equation, for which the trajectories are typically hard to learn.