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.
翻译:我们提出一个连续时间的非线性动态神经网络模型,可以对衰变率和/或频率施加感应偏差; 诱导偏差有助于对神经网络进行培训,特别是在培训数据较少的情况下; 拟议的模型以Koopman操作员理论为基础,即使用衰变率和频率信息限制Koopman操作员描述Koopman空间线性演变的机能价值,从而限制Koopman操作员的衰变率和频率信息; 我们使用神经网络寻找适当的Koopman空间,通过尽可能减少多步骤预测和利用非常规抽样时间序列数据反射错误来培训。 对各种时间序列数据集的实验表明,在单短期培训序列情况下,拟议方法的预测性能高于现有方法。