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arXiv 2203.06269cs.LGcs.CEcs.NAcs.SYeess.SYmath.NA
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基于时滞嵌入和学习微分算子的时间序列参数推断

Parameter Inference of Time Series by Delay Embeddings and Learning Differentiable Operators

Jacobs Technology Inc.(雅各布斯技术公司);DEVCOM-ARL U.S.Army Research Office(美国陆军作战能力发展司令部陆军研究实验室陆军研究办公室);Air Force Research Laboratory(美国空军研究实验室);University of California, Los Angeles(加州大学洛杉矶分校)

Alex Tong Lin, Adrian S. Wong, Robert Martin, Stanley J. Osher, Daniel Eckhardt

摘要:

本文提出了一种辨识动力系统参数的方法,称为ID-ODE --微分推断和观测延迟嵌入。在这种情况下,我们给出了一个带有系统参数标签的动力系统的轨迹数据集。我们的目标是识别新轨迹的系统参数。给定的轨迹可能包含也可能不包含系统的完整状态,我们可能只观察到一维时间序列。在后一种情况下,我们使用延迟嵌入来重建完整的状态,并且在充分条件下,Taken嵌入定理确保我们的重建与原始状态是同构的。这使得我们的方法可以在时间序列上工作。我们的方法首先使用以状态和系统参数作为变量输入的神经网络学习速度运算符(给定或重建)。然后,在新的轨迹上,我们将预测误差反向传播到系统参数输入,给我们一个梯度。然后,我们使用梯度下降来推断正确的系统参数。我们证明了我们的方法在许多数值例子:洛伦兹系统,Lorenz 96,Lotka-Volterra捕食者-猎物,和复合双摆。我们还将我们的算法应用于真实世界的数据集:霍尔效应推进器(HET)的推进。

英文摘要:

We provide a method to identify system parameters of dynamical systems, called ID-ODE -- Inference by Differentiation and Observing Delay Embeddings. In this setting, we are given a dataset of trajectories from a dynamical system with system parameter labels. Our goal is to identify system parameters of new trajectories. The given trajectories may or may not encompass the full state of the system, and we may only observe a one-dimensional time series. In the latter case, we reconstruct the full state by using delay embeddings, and under sufficient conditions, Taken's Embedding Theorem assures us the reconstruction is diffeomorphic to the original. This allows our method to work on time series. Our method works by first learning the velocity operator (as given or reconstructed) with a neural network having both state and system parameters as variable inputs. Then on new trajectories we backpropagate prediction errors to the system parameter inputs giving us a gradient. We then use gradient descent to infer the correct system parameter. We demonstrate the efficacy of our approach on many numerical examples: the Lorenz system, Lorenz96, Lotka-Volterra Predator-Prey, and the Compound Double Pendulum. We also apply our algorithm on a real-world dataset: propulsion of the Hall-effect Thruster (HET).

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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