Loss Function for Deep Learning to Model Dynamical Systems

作     者：Yoshida, Takahito Yaguchi, Takaharu Matsubara, Takashi 

作者机构：Osaka Univ Grad Sch Engn Sci Toyonaka 5600043 Japan Kobe Univ Grad Sch Syst Informat Kobe 6578501 Japan Hok kaido Univ Grad Sch Informat Sci & Technol Sapporo 0600808 Japan 

出 版 物：《IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS》 (IEICE Trans Inf Syst)

年 卷 期：2024年第E107D卷第11期

页      面：1458-1462页

核心收录：

学科分类：0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 0835[工学-软件工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：JST PRESTO [JP-MJPR21C7] JST CREST [JPMJCR1914] JST ASPIRE [JP-MJAP2329] JSPS KAKENHI [19H04172, 19K20344, 24K15105] 

主　　题：key deep learning physical system partial differential equation numerical error analysis 

摘      要：Accurately simulating physical systems is essential in various fields. In recent years, deep learning has been used to automatically build models of such systems by learning from data. One such method is the neural ordinary differential equation (neural ODE), which treats the output of a neural network as the time derivative of the system states. However, while this and related methods have shown promise, their training strategies still require further development. Inspired by error analysis techniques in numerical analysis while replacing numerical errors with modeling errors, we propose the error-analytic strategy to address this issue. Therefore, our strategy can capture long-term errors and thus improve the accuracy of long-term predictions.