耦合编码解码卷积长短期记忆网络求解时变偏微分方程的参数识别问题
Coupled Encoder-Decoder ConvLSTM Structure for the Parameter Identification Problems of Time-Dependent Partial Differential Equations
DOI: 10.12677/aam.2025.142075, PDF,   
作者: 郭 琦：太原理工大学数学学院，山西 太原；贾宏恩*：太原理工大学数学学院，山西 太原；密码关键技术创新与融合应用实训实验室，山西 太原；王鸿斌：山西工学院通识教育学院，山西 朔州
关键词: 参数识别；编码；解码；ConvLSTM；时变偏微分方程；Parameter Identification； Encoder； Decoder； ConvLSTM； Time-Dependent PDE
摘要: 文章基于编码、解码结构提出了一种同时反演参数和求解偏微分方程的耦合编码解码卷积长短期记忆网络(ED-ConvLSTM)。编、解码结构中分别使用卷积层和转置卷积层，用于提取和恢复物理约束的空间信息。为了有效逼近时变偏微方程中的时间演化规律，ED-ConvLSTM引入编解码模块。通过几个数值试验证明所提出的耦合ED-ConvLSTM网络框架能够有效准确地预测场变量并且反演未知参数，特别是对于高噪声水平的输入序列。
Abstract: This paper proposes a coupled encoder-decoder ConvLSTM network (ED-ConvLSTM) based on an encoder and decoder to identify parameters and solve partial differential equations simultaneously. Convolutional and transposed convolutional layers are utilized in the encoder and decoder modules to extract and retrieve spatiotemporal information in physical laws. ConvLSTM modules are embedded into the encoder and decoder modules to accurately approximate the time evolution in time-dependent PDEs. Through intensive numerical examples, the coupled neural network can predict field variables and unknown parameters accurately and efficiently, especially for the input with large noise.
文章引用：郭琦, 贾宏恩, 王鸿斌. 耦合编码解码卷积长短期记忆网络求解时变偏微分方程的参数识别问题[J]. 应用数学进展, 2025, 14(2): 341-355. https://doi.org/10.12677/aam.2025.142075

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