论文标题
在连续时间对非线性动力学进行建模，并以衰减率和/或频率的感应偏差
Modeling Nonlinear Dynamics in Continuous Time with Inductive Biases on Decay Rates and/or Frequencies
论文作者
论文摘要
我们提出了一个基于神经网络的模型，用于连续时间的非线性动力学，可以对衰减率和/或频率施加电感偏见。诱导偏见有助于训练神经网络，尤其是在训练数据很小的情况下。所提出的模型基于Koopman操作员理论，其中使用衰减率和频率信息来限制Koopman操作员的特征值来描述Koopman空间中的线性进化。我们使用神经网络找到合适的Koopman空间，该空间通过使用不规则采样的时间序列数据来最大程度地减少多步骤预测和背景错误来训练。各种时间序列数据集的实验表明，在单个短训练序列下，所提出的方法比现有方法实现了更高的预测性能。
We propose a neural network-based model for nonlinear dynamics in continuous time that can impose inductive biases on decay rates and/or frequencies. Inductive biases are helpful for training neural networks especially when training data are small. The proposed model is based on the Koopman operator theory, where the decay rate and frequency information is used by restricting the eigenvalues of the Koopman operator that describe linear evolution in a Koopman space. We use neural networks to find an appropriate Koopman space, which are trained by minimizing multi-step forecasting and backcasting errors using irregularly sampled time-series data. Experiments on various time-series datasets demonstrate that the proposed method achieves higher forecasting performance given a single short training sequence than the existing methods.
