Dynamic mode decomposition(DMD),as a data-driven method,has been frequently used to construct reduced-order models(ROMs)due to its good performance in time extrapolation.However,existing DMD-based ROMs suffer from hig...Dynamic mode decomposition(DMD),as a data-driven method,has been frequently used to construct reduced-order models(ROMs)due to its good performance in time extrapolation.However,existing DMD-based ROMs suffer from high storage and computational costs for high-dimensional problems.To mitigate this problem,we develop a new DMD-based ROM,i.e.,TDMD-GPR,by combining tensor train decomposition(TTD)and Gaussian process regression(GPR),where TTD is used to decompose the high-dimensional tensor into multiple factors,including parameterdependent and time-dependent factors.Parameter-dependent factor is fed into GPR to build the map between parameter value and factor vector.For any parameter value,multiplying the corresponding parameter-dependent factor vector and the timedependent factor matrix,the result describes the temporal behavior of the spatial basis for this parameter value and is then used to train the DMD model.In addition,incremental singular value decomposition is adopted to acquire a collection of important instants,which can further reduce the computational and storage costs of TDMD-GPR.The comparison TDMD and standard DMD in terms of computational and storage complexities shows that TDMD is more advantageous.The performance of the TDMD and TDMD-GPR is assessed through several cases,and the numerical results confirm the effectiveness of them.展开更多
Reinforcement Learning(RL)serves as a fundamental learning paradigm in the field of artificial intelligence,enabling decision-making policies through interactions with environments.However,traditional RL methods encou...Reinforcement Learning(RL)serves as a fundamental learning paradigm in the field of artificial intelligence,enabling decision-making policies through interactions with environments.However,traditional RL methods encounter challenges when dealing with large-scale or continuous state spaces due to the curse of dimensionality.Although Deep Reinforcement Learning(DRL)can handle complex environments,its lack of transparency and interpretability hinders its applicability due to the black box nature.Moreover,centralized data collection and processing methods pose privacy security risks.Federated learning offers a distributed approach that ensures privacy preservation while co-training models.However,existing federated reinforcement learning approaches have not adequately addressed communication and computation overhead issues.To address these challenges,this study proposes a tensor train decomposition-based federated reinforcement learning method that enhances efficiency and provides interpretability.By leveraging tensor to model state-action values and employing tensor decomposition techniques for dimensionality reduction,this method effectively reduces model parameters and communication overhead while maintaining strong interpretability,accelerates algorithm convergence speed.Experimental results validate the advantages of our proposed algorithm in terms of efficiency and reliability.展开更多
基金supported by the Taishan Scholars Program(tsqn202211059)the National Natural Science Foundation of China(12201592)+1 种基金the Shandong Provincial Natural Science Foundation(ZR2022QA006)Laoshan Laboratory(LSKJ202202302)。
文摘Dynamic mode decomposition(DMD),as a data-driven method,has been frequently used to construct reduced-order models(ROMs)due to its good performance in time extrapolation.However,existing DMD-based ROMs suffer from high storage and computational costs for high-dimensional problems.To mitigate this problem,we develop a new DMD-based ROM,i.e.,TDMD-GPR,by combining tensor train decomposition(TTD)and Gaussian process regression(GPR),where TTD is used to decompose the high-dimensional tensor into multiple factors,including parameterdependent and time-dependent factors.Parameter-dependent factor is fed into GPR to build the map between parameter value and factor vector.For any parameter value,multiplying the corresponding parameter-dependent factor vector and the timedependent factor matrix,the result describes the temporal behavior of the spatial basis for this parameter value and is then used to train the DMD model.In addition,incremental singular value decomposition is adopted to acquire a collection of important instants,which can further reduce the computational and storage costs of TDMD-GPR.The comparison TDMD and standard DMD in terms of computational and storage complexities shows that TDMD is more advantageous.The performance of the TDMD and TDMD-GPR is assessed through several cases,and the numerical results confirm the effectiveness of them.
基金supported by the National Natural Science Foundation of China(Nos.U23A20300 and 62207033)the Fundamental Research Funds for the Central Universities of South-Central Minzu University(No.CSZ23013).
文摘Reinforcement Learning(RL)serves as a fundamental learning paradigm in the field of artificial intelligence,enabling decision-making policies through interactions with environments.However,traditional RL methods encounter challenges when dealing with large-scale or continuous state spaces due to the curse of dimensionality.Although Deep Reinforcement Learning(DRL)can handle complex environments,its lack of transparency and interpretability hinders its applicability due to the black box nature.Moreover,centralized data collection and processing methods pose privacy security risks.Federated learning offers a distributed approach that ensures privacy preservation while co-training models.However,existing federated reinforcement learning approaches have not adequately addressed communication and computation overhead issues.To address these challenges,this study proposes a tensor train decomposition-based federated reinforcement learning method that enhances efficiency and provides interpretability.By leveraging tensor to model state-action values and employing tensor decomposition techniques for dimensionality reduction,this method effectively reduces model parameters and communication overhead while maintaining strong interpretability,accelerates algorithm convergence speed.Experimental results validate the advantages of our proposed algorithm in terms of efficiency and reliability.
