Although previous studies have made some clear leap in learning latent dynamics from high-dimensional representations,the performances in terms of accuracy and inference time of long-term model prediction still need t...Although previous studies have made some clear leap in learning latent dynamics from high-dimensional representations,the performances in terms of accuracy and inference time of long-term model prediction still need to be improved.In this study,a deep convolutional network based on the Koopman operator(CKNet)is proposed to model non-linear systems with pixel-level measurements for long-term prediction.CKNet adopts an autoencoder network architecture,consisting of an encoder to generate latent states and a linear dynamical model(i.e.,the Koopman operator)which evolves in the latent state space spanned by the encoder.The decoder is used to recover images from latent states.According to a multi-step ahead prediction loss function,the system matrices for approximating the Koopman operator are trained synchronously with the autoencoder in a mini-batch manner.In this manner,gradients can be synchronously transmitted to both the system matrices and the autoencoder to help the encoder self-adaptively tune the latent state space in the training process,and the resulting model is time-invariant in the latent space.Therefore,the proposed CKNet has the advantages of less inference time and high accuracy for long-term prediction.Experiments are per-formed on OpenAI Gym and Mujoco environments,including two and four non-linear forced dynamical systems with continuous action spaces.The experimental results show that CKNet has strong long-term prediction capabilities with sufficient precision.展开更多
综合能源系统在提高可再生能源利用率和为系统提供灵活性方面具有一定优势,如何厘清其物料流与能量流复杂耦合关系,建立优化运行策略是亟待解决的问题。以甲醇化工园区为例,构建甲醇化工园区综合能源系统(Methanol Chemical Park Integr...综合能源系统在提高可再生能源利用率和为系统提供灵活性方面具有一定优势,如何厘清其物料流与能量流复杂耦合关系,建立优化运行策略是亟待解决的问题。以甲醇化工园区为例,构建甲醇化工园区综合能源系统(Methanol Chemical Park Integrated Energy System, MCPIES),运用序贯模块法对甲醇生产过程进行模块化处理,通过依次求解生产过程中关键的物料流,确定甲醇生产过程的物料流平衡关系,在此基础上建立量化甲醇生产单元物料流与能量流耦合关系的数学模型,从而实现其优化运行调度;同时考虑MCPIES的生产柔性可调节特性,设置多个算例对比验证其柔性可调节特性对其日常生产运行经济性的影响。仿真计算结果显示,该策略可有效地降低园区的用能成本。展开更多
The errors in radar quantitative precipitation estimations consist not only of systematic biases caused by random noises but also spatially nonuniform biases in radar rainfall at individual rain-gauge stations. In thi...The errors in radar quantitative precipitation estimations consist not only of systematic biases caused by random noises but also spatially nonuniform biases in radar rainfall at individual rain-gauge stations. In this study, a real-time adjustment to the radar reflectivity rainfall rates （Z R） relationship scheme and the gauge-corrected, radar-based, estimation scheme with inverse distance weighting interpolation was devel- oped. Based on the characteristics of the two schemes, the two-step correction technique of radar quantitative precipitation estimation is proposed. To minimize the errors between radar quantitative precipitation es- timations and rain gauge observations, a real-time adjustment to the Z R relationship scheme is used to remove systematic bias on the time-domain. The gauge-corrected, radar-based, estimation scheme is then used to eliminate non-uniform errors in space. Based on radar data and rain gauge observations near the Huaihe River, the two-step correction technique was evaluated using two heavy-precipitation events. The results show that the proposed scheme improved not only in the underestimation of rainfall but also reduced the root-mean-square error and the mean relative error of radar-rain gauge pairs.展开更多
基金National Natural Science Foundation of China,Grant/Award Numbers:61825305,62003361,U21A20518China Postdoctoral Science Foundation,Grant/Award Number:47680。
文摘Although previous studies have made some clear leap in learning latent dynamics from high-dimensional representations,the performances in terms of accuracy and inference time of long-term model prediction still need to be improved.In this study,a deep convolutional network based on the Koopman operator(CKNet)is proposed to model non-linear systems with pixel-level measurements for long-term prediction.CKNet adopts an autoencoder network architecture,consisting of an encoder to generate latent states and a linear dynamical model(i.e.,the Koopman operator)which evolves in the latent state space spanned by the encoder.The decoder is used to recover images from latent states.According to a multi-step ahead prediction loss function,the system matrices for approximating the Koopman operator are trained synchronously with the autoencoder in a mini-batch manner.In this manner,gradients can be synchronously transmitted to both the system matrices and the autoencoder to help the encoder self-adaptively tune the latent state space in the training process,and the resulting model is time-invariant in the latent space.Therefore,the proposed CKNet has the advantages of less inference time and high accuracy for long-term prediction.Experiments are per-formed on OpenAI Gym and Mujoco environments,including two and four non-linear forced dynamical systems with continuous action spaces.The experimental results show that CKNet has strong long-term prediction capabilities with sufficient precision.
文摘综合能源系统在提高可再生能源利用率和为系统提供灵活性方面具有一定优势,如何厘清其物料流与能量流复杂耦合关系,建立优化运行策略是亟待解决的问题。以甲醇化工园区为例,构建甲醇化工园区综合能源系统(Methanol Chemical Park Integrated Energy System, MCPIES),运用序贯模块法对甲醇生产过程进行模块化处理,通过依次求解生产过程中关键的物料流,确定甲醇生产过程的物料流平衡关系,在此基础上建立量化甲醇生产单元物料流与能量流耦合关系的数学模型,从而实现其优化运行调度;同时考虑MCPIES的生产柔性可调节特性,设置多个算例对比验证其柔性可调节特性对其日常生产运行经济性的影响。仿真计算结果显示,该策略可有效地降低园区的用能成本。
基金supported bythe Special Fund for Basic Research and Operation of the Chinese Academy of Meteorological Sciences (GrantNo. 2011Y004)the Research and Development Special Fund for Public Welfare Industry (Meteorology+2 种基金Grant No.GYHY201006042)the National Natural Science Foundation of China (Grant No. 40975014)the Open Research Fund for State Key Laboratory of Hydroscience and Engineering of Tsinghua University (the search of basin QPE and QPF based on new generation of weather and numerical models)
文摘The errors in radar quantitative precipitation estimations consist not only of systematic biases caused by random noises but also spatially nonuniform biases in radar rainfall at individual rain-gauge stations. In this study, a real-time adjustment to the radar reflectivity rainfall rates （Z R） relationship scheme and the gauge-corrected, radar-based, estimation scheme with inverse distance weighting interpolation was devel- oped. Based on the characteristics of the two schemes, the two-step correction technique of radar quantitative precipitation estimation is proposed. To minimize the errors between radar quantitative precipitation es- timations and rain gauge observations, a real-time adjustment to the Z R relationship scheme is used to remove systematic bias on the time-domain. The gauge-corrected, radar-based, estimation scheme is then used to eliminate non-uniform errors in space. Based on radar data and rain gauge observations near the Huaihe River, the two-step correction technique was evaluated using two heavy-precipitation events. The results show that the proposed scheme improved not only in the underestimation of rainfall but also reduced the root-mean-square error and the mean relative error of radar-rain gauge pairs.
