潜微分同胚动态模态分解

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-08-05 DOI:10.1016/j.aml.2025.109701

Willem Diepeveen , Jon Schwenk , Andrea L. Bertozzi

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引用次数: 0

摘要

我们提出了一种新的用于分析非线性系统的数据约简方法——潜差分动态模态分解（LDDMD），它将动态模态分解（DMD）的可解释性与递归神经网络（rnn）的预测能力相结合。值得注意的是，LDDMD保持了简单性，这增强了可解释性，同时有效地建模和学习具有记忆的复杂非线性系统，从而实现准确的预测。该方法在水流预测中的成功应用说明了这一点。

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Latent Diffeomorphic Dynamic Mode Decomposition

We present Latent Diffeomorphic Dynamic Mode Decomposition (LDDMD), a new data reduction approach for the analysis of non-linear systems that combines the interpretability of Dynamic Mode Decomposition (DMD) with the predictive power of Recurrent Neural Networks (RNNs). Notably, LDDMD maintains simplicity, which enhances interpretability, while effectively modeling and learning complex non-linear systems with memory, enabling accurate predictions. This is exemplified by its successful application in streamflow prediction.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.