Time series data is often composed of information at multiple time scales,
particularly in biomedical data. While numerous deep learning strategies exist
to capture this information, many make networks larger, require more data, are
more demanding to compute, and are difficult to interpret. This limits their
usefulness in real-world applications facing even modest computational or data
constraints and can further complicate their translation into practice. We
present a minimal, computationally efficient Time Scale Network combining the
translation and dilation sequence used in discrete wavelet transforms with
traditional convolutional neural networks and back-propagation. The network
simultaneously learns features at many time scales for sequence classification
with significantly reduced parameters and operations. We demonstrate advantages
in Atrial Dysfunction detection including: superior accuracy-per-parameter and
accuracy-per-operation, fast training and inference speeds, and visualization
and interpretation of learned patterns in atrial dysfunction detection on ECG
signals. We also demonstrate impressive performance in seizure prediction using
EEG signals. Our network isolated a few time scales that could be strategically
selected to achieve 90.9% accuracy using only 1,133 active parameters and
consistently converged on pulsatile waveform shapes. This method does not rest
on any constraints or assumptions regarding signal content and could be
leveraged in any area of time series analysis dealing with signals containing
features at many time scales.

通过结合传统的离散小波变换的转换和扩张序列，利用卷积神经网络和反向传播方法，我们提出了一种最小化、计算效率高的时间尺度网络，它可以同时学习多个时间尺度的特征，用于序列分类，并且具有显著减少参数和操作的优势。在心房功能障碍检测和癫痫预测方面表现出优异性能。

时间尺度网络：用于时间序列数据的浅层神经网络

Time Scale Network: A Shallow Neural Network For Time Series Data

Current physics-informed (standard or operator) neural networks still rely on
accurately learning the initial conditions of the system they are solving. In
contrast, standard numerical methods evolve such initial conditions without
needing to learn these. In this study, we propose to improve current
physics-informed deep learning strategies such that initial conditions do not
need to be learned and are represented exactly in the predicted solution.
Moreover, this method guarantees that when a DeepONet is applied multiple times
to time step a solution, the resulting function is continuous.

通过改进当前的物理信息神经网络深度学习策略，本研究提出了不需要学习初始条件且以精确预测解决方案为代表的方法。此外，该方法确保当多次应用 DeepONet 以进行解决方案的时间步进时，得到的函数是连续的。