SIAM Journal on Scientific Computing, Volume 43, Issue 3, Page A1607-A1624, January 2021.
We present a numerical framework for recovering unknown nonautonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the nonautonomous nature of the system, our method transforms the solution state into piecewise integration of the system over a discrete set of time instances. The time-dependent inputs are then locally parameterized by using a proper model, for example, polynomial regression, in the pieces determined by the time instances. This transforms the original system into a piecewise parametric system that is locally time invariant. We then design a deep neural network structure to learn the local models. Once the network model is constructed, it can be iteratively used over time to conduct global system prediction. We provide theoretical analysis of our algorithm and present a number of numerical examples to demonstrate the effectiveness of the method.

中文翻译：

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非自治系统的数据驱动学习

SIAM科学计算杂志，第43卷，第3期，第A1607-A1624页，2021年1月。
我们提出了一个数值框架，用于恢复依赖于时间的输入的未知非自治动力系统。为了避免由系统的非自治性质带来的困难，我们的方法将解决方案状态转换为在离散的时间实例集上的系统分段集成。然后，通过使用适当的模型（例如，多项式回归），在时间实例确定的片段中，对与时间相关的输入进行局部参数化。这将原始系统转换为局部时不变的分段参数系统。然后，我们设计一个深度神经网络结构来学习局部模型。一旦构建了网络模型，就可以随着时间的推移反复使用它来进行全局系统预测。