Trust Region Methods For Nonconvex Stochastic Optimization Beyond Lipschitz Smoothness

In many important machine learning applications, the standard assumption of having a globally Lipschitz continuous gradient may fail to hold. This paper delves into a more general $(L_0, L_1)$-smoothness setting, which gains particular significance within the realms of deep neural networks and distributionally robust optimization (DRO). We demonstrate the significant advantage of trust region methods for stochastic nonconvex optimization under such generalized smoothness assumption. We show that first-order trust region methods can recover the normalized and clipped stochastic gradient as special cases and then provide a unified analysis to show their convergence to first-order stationary conditions. Motivated by the important application of DRO, we propose a generalized high-order smoothness condition, under which second-order trust region methods can achieve a complexity of $\mathcal{O}(\epsilon^{-3.5})$ for convergence to second-order stationary points. By incorporating variance reduction, the second-order trust region method obtains an even better complexity of $\mathcal{O}(\epsilon^{-3})$, matching the optimal bound for standard smooth optimization. To our best knowledge, this is the first work to show convergence beyond the first-order stationary condition for generalized smooth optimization. Preliminary experiments show that our proposed algorithms perform favorably compared with existing methods

The Inertial Energy Control Strategy of the Cascade H-Bridge Module applied in Photovoltaic System

This paper put forward the inertial control strategy based on the control of charge and discharge of supercapacitor and the trigger angle of H-bridge which integrates photovoltaic (PV) system. The whole cascade H-bridge structure is composed of traditional photovoltaic module, Boost/Buck circuit, supercapacitor (SC), and H-bridge circuit. First, the charging state and the inertial energy power support of the SC are analysed. Then the control strategy of the cascade H-bridge is proposed. To verify the efficiency of the control strategy, a cascade chain consists of 12 H-bridge unit was built in EMTP simulation software. Finally the simulation results prove that the newly developed SC-integrated cascade module can do inertial energy support well, which is important to the coordination between the power system and solar energy

Separation Method of Main and Foreign Water for the Measuring Weirs of Danjiangkou Earth-Rock Dam

Reservoir water and rainfall are the two main factors affecting the seepage of earth-rock dams, but the seepage measurement includes the seepage discharge caused by the reservoir water and rainfall. Only by obtaining the seepage discharge caused by the reservoir water can we evaluate the seepage safety state. In this paper, a statistical model for seepage monitoring of earth-rock dams is established. Normal distribution function and Rayleigh distribution function are used as the lag functions of reservoir water and rainfall, respectively. The grey wolf algorithm is used to solve the lag days, and the partial least square method is adopted to solve the regression coefficient of the statistical model. Then, the reservoir water (main water) and rainfall infiltration (foreign water) parts of the measuring weir are separated with the statistical model. The developed method is used to separate the main and foreign water parts of the three measuring weirs of the Danjiangkou earth-rock dam. The results show that the overall accuracy of the models is high (the multi-correlation coefficients are about 0.95), and the separated main and foreign water seepage discharge conforms to the seepage law of earth-rock dam, which verifies the effectiveness of the method

Separation Method of Main and Foreign Water for the Measuring Weirs of Danjiangkou Earth-Rock Dam

Reservoir water and rainfall are the two main factors affecting the seepage of earth-rock dams, but the seepage measurement includes the seepage discharge caused by the reservoir water and rainfall. Only by obtaining the seepage discharge caused by the reservoir water can we evaluate the seepage safety state. In this paper, a statistical model for seepage monitoring of earth-rock dams is established. Normal distribution function and Rayleigh distribution function are used as the lag functions of reservoir water and rainfall, respectively. The grey wolf algorithm is used to solve the lag days, and the partial least square method is adopted to solve the regression coefficient of the statistical model. Then, the reservoir water (main water) and rainfall infiltration (foreign water) parts of the measuring weir are separated with the statistical model. The developed method is used to separate the main and foreign water parts of the three measuring weirs of the Danjiangkou earth-rock dam. The results show that the overall accuracy of the models is high (the multi-correlation coefficients are about 0.95), and the separated main and foreign water seepage discharge conforms to the seepage law of earth-rock dam, which verifies the effectiveness of the method

Evaluation of the Effect of WRF Physical Parameterizations on Typhoon and Wave Simulation in the Taiwan Strait

Typhoons and typhoon waves can cause disasters in coastal areas around the world. The Taiwan Strait often experiences typhoons, especially in summer. Numerical models have been adopted to predict typhoons and reduce losses. The Weather Research and Forecasting (WRF) model is widely used in typhoon simulations, and the Simulating WAves Nearshore (SWAN) model performs well in wave simulations. However, significant uncertainty remains in terms of choosing suitable WRF physical parameterizations in different situations. To evaluate the effect of WRF physical parameterizations on wind and wave simulations, 27 simulation experiments were designed. Three typhoon events (Goni, Dujuan, and Meranti) with different tracks that influenced the Taiwan Strait were simulated. Three parameters (wind speed, wind direction and significant wave height) were assessed using Taylor diagrams, and it was found that the best simulation experiment changed according to typhoon tracks and physical parameters. In wind speed simulation, the best simulation experiment is 12 for typhoon Dujuan and 19 for typhoon Goni and Meranti. From the perspective of wind direction simulation, experiments 26, 23, and 2 performed best for typhoons Goni, Dujuan, and Meranti. And experiments 19, 1, and 20 had the best performances in significant wave height simulation for typhoons Goni, Dujuan, and Meranti. The WRF-SWAN model using the best simulation experiment reduced the error and exhibited good performance in the wind and wave simulations. Skill scores of three parameters were all over 70 for typhoon Goni and 80 for typhoon Dujuan and Meranti. The applicability of the best simulation experiments was demonstrated in typhoon simulations with similar tracks. The accuracy of the wave simulation depended on wind speed, wind direction, and their interaction. In addition, a scheme’s sensitivity changed with different typhoon tracks. This study provides references for designing physical parameterizations for use with the WRF-SWAN model, which may help to simulate typhoons and typhoon waves in the Taiwan Strait more accurately in the future

Guidelines for the use and interpretation of assays for monitoring autophagy

In 2008 we published the first set of guidelines for standardizing research in autophagy. Since then, research on this topic has continued to accelerate, and many new scientists have entered the field. Our knowledge base and relevant new technologies have also been expanding. Accordingly, it is important to update these guidelines for monitoring autophagy in different organisms. Various reviews have described the range of assays that have been used for this purpose. Nevertheless, there continues to be confusion regarding acceptable methods to measure autophagy, especially in multicellular eukaryotes. A key point that needs to be emphasized is that there is a difference between measurements that monitor the numbers or volume of autophagic elements (e.g., autophagosomes or autolysosomes) at any stage of the autophagic process vs. those that measure flux through the autophagy pathway (i.e., the complete process); thus, a block in macroautophagy that results in autophagosome accumulation needs to be differentiated from stimuli that result in increased autophagic activity, defined as increased autophagy induction coupled with increased delivery to, and degradation within, lysosomes (in most higher eukaryotes and some protists such as Dictyostelium) or the vacuole (in plants and fungi). In other words, it is especially important that investigators new to the field understand that the appearance of more autophagosomes does not necessarily equate with more autophagy. In fact, in many cases, autophagosomes accumulate because of a block in trafficking to lysosomes without a concomitant change in autophagosome biogenesis, whereas an increase in autolysosomes may reflect a reduction in degradative activity. Here, we present a set of guidelines for the selection and interpretation of methods for use by investigators who aim to examine macroautophagy and related processes, as well as for reviewers who need to provide realistic and reasonable critiques of papers that are focused on these processes. These guidelines are not meant to be a formulaic set of rules, because the appropriate assays depend in part on the question being asked and the system being used. In addition, we emphasize that no individual assay is guaranteed to be the most appropriate one in every situation, and we strongly recommend the use of multiple assays to monitor autophagy. In these guidelines, we consider these various methods of assessing autophagy and what information can, or cannot, be obtained from them. Finally, by discussing the merits and limits of particular autophagy assays, we hope to encourage technical innovation in the field

Guidelines for the use and interpretation of assays for monitoring autophagy

In 2008 we published the first set of guidelines for standardizing research in autophagy. Since then, research on this topic has continued to accelerate, and many new scientists have entered the field. Our knowledge base and relevant new technologies have also been expanding. Accordingly, it is important to update these guidelines for monitoring autophagy in different organisms. Various reviews have described the range of assays that have been used for this purpose. Nevertheless, there continues to be confusion regarding acceptable methods to measure autophagy, especially in multicellular eukaryotes. A key point that needs to be emphasized is that there is a difference between measurements that monitor the numbers or volume of autophagic elements (e.g., autophagosomes or autolysosomes) at any stage of the autophagic process vs. those that measure flux through the autophagy pathway (i.e., the complete process); thus, a block in macroautophagy that results in autophagosome accumulation needs to be differentiated from stimuli that result in increased autophagic activity, defined as increased autophagy induction coupled with increased delivery to, and degradation within, lysosomes (in most higher eukaryotes and some protists such as Dictyostelium) or the vacuole (in plants and fungi). In other words, it is especially important that investigators new to the field understand that the appearance of more autophagosomes does not necessarily equate with more autophagy. In fact, in many cases, autophagosomes accumulate because of a block in trafficking to lysosomes without a concomitant change in autophagosome biogenesis, whereas an increase in autolysosomes may reflect a reduction in degradative activity. Here, we present a set of guidelines for the selection and interpretation of methods for use by investigators who aim to examine macroautophagy and related processes, as well as for reviewers who need to provide realistic and reasonable critiques of papers that are focused on these processes. These guidelines are not meant to be a formulaic set of rules, because the appropriate assays depend in part on the question being asked and the system being used. In addition, we emphasize that no individual assay is guaranteed to be the most appropriate one in every situation, and we strongly recommend the use of multiple assays to monitor autophagy. In these guidelines, we consider these various methods of assessing autophagy and what information can, or cannot, be obtained from them. Finally, by discussing the merits and limits of particular autophagy assays, we hope to encourage technical innovation in the field