论文标题
哈密顿动力学系统的符号整合符号回归
Symplectically Integrated Symbolic Regression of Hamiltonian Dynamical Systems
论文作者
论文摘要
在这里，我们提出了符合性整合的符号回归（SISR），这是一种从数据中学习物理控制方程的新技术。 SISR使用具有突变的多层LSTM-RNN采用了深层符号回归方法，以概率地采样哈密顿符号表达式。使用符合性神经网络，我们开发了一种模型无关的方法，用于从数据中提取有意义的物理先验，这些方法可以直接施加到RNN输出中，从而限制了其搜索空间。使用四阶符号整合方案对RNN产生的汉密尔顿人进行了优化和评估。预测性能用于训练LSTM-RNN通过寻求风险的政策梯度方法来产生越来越更好的功能。利用这些技术，我们从振荡器，摆，两体和三体重力系统中提取正确的管理方程式，具有嘈杂且非常小的数据集。
Here we present Symplectically Integrated Symbolic Regression (SISR), a novel technique for learning physical governing equations from data. SISR employs a deep symbolic regression approach, using a multi-layer LSTM-RNN with mutation to probabilistically sample Hamiltonian symbolic expressions. Using symplectic neural networks, we develop a model-agnostic approach for extracting meaningful physical priors from the data that can be imposed on-the-fly into the RNN output, limiting its search space. Hamiltonians generated by the RNN are optimized and assessed using a fourth-order symplectic integration scheme; prediction performance is used to train the LSTM-RNN to generate increasingly better functions via a risk-seeking policy gradients approach. Employing these techniques, we extract correct governing equations from oscillator, pendulum, two-body, and three-body gravitational systems with noisy and extremely small datasets.
