Capacity Control of ReLU Neural Networks by Basis-path Norm

Recently, path norm was proposed as a new capacity measure for neural networks with Rectified Linear Unit (ReLU) activation function, which takes the rescaling-invariant property of ReLU into account. It has been shown that the generalization error bound in terms of the path norm explains the empirical generalization behaviors of the ReLU neural networks better than that of other capacity measures. Moreover, optimization algorithms which take path norm as the regularization term to the loss function, like Path-SGD, have been shown to achieve better generalization performance. However, the path norm counts the values of all paths, and hence the capacity measure based on path norm could be improperly influenced by the dependency among different paths. It is also known that each path of a ReLU network can be represented by a small group of linearly independent basis paths with multiplication and division operation, which indicates that the generalization behavior of the network only depends on only a few basis paths. Motivated by this, we propose a new norm \emph{Basis-path Norm} based on a group of linearly independent paths to measure the capacity of neural networks more accurately. We establish a generalization error bound based on this basis path norm, and show it explains the generalization behaviors of ReLU networks more accurately than previous capacity measures via extensive experiments. In addition, we develop optimization algorithms which minimize the empirical risk regularized by the basis-path norm. Our experiments on benchmark datasets demonstrate that the proposed regularization method achieves clearly better performance on the test set than the previous regularization approaches

Sub-daily simulation of mountain flood processes based on the modified soil water assessment tool (SWAT) model

Floods not only provide a large amount of water resources, but they also cause serious disasters. Although there have been numerous hydrological studies on flood processes, most of these investigations were based on rainfall-type floods in plain areas. Few studies have examined high temporal resolution snowmelt floods in high-altitude mountainous areas. The Soil Water Assessment Tool (SWAT) model is a typical semi-distributed, hydrological model widely used in runoff and water quality simulations. The degree-day factor method used in SWAT utilizes only the average daily temperature as the criterion of snow melting and ignores the influence of accumulated temperature. Therefore, the influence of accumulated temperature on snowmelt was added by increasing the discriminating conditions of rain and snow, making that more suitable for the simulation of snowmelt processes in high-altitude mountainous areas. On the basis of the daily scale, the simulation of the flood process was modeled on an hourly scale. This research compared the results before and after the modification and revealed that the peak error decreased by 77% and the time error was reduced from +/- 11 h to +/- 1 h. This study provides an important reference for flood simulation and forecasting in mountainous areas

Structural dynamic response analysis on structure under tsunami bore impact

The forefront of the tsunami bore has extremely strong turbulent intensity, vorticity, and impact force. It generates tremendous impact effect on the coastal structures, which is the direct reason of the damage and destruction of the structures. On the basis of the computational fluid dynamic theory, this paper applied fluid volume method to capture the free surface motion of the tsunami waves and developed a 3D wave numerical model of an experiment of dam-break tsunami bore impact on a structure. The effectiveness of the model was also validated. The model was then applied to numerically analyze the dynamic impact effect of a tsunami bore on the structure of a full-scale reinforced concrete frame. It resolved the dynamic impact force of the tsunami bore on the structure and their interaction process. This study also employed finite element analysis to compare the static and dynamic response of the frame structure under the impact effect of the tsunami bore. The structural vibration characteristic and dynamic magnification factor of the structure under tsunami bore impact are confirmed, which could provide a reference for the design of anti-tsunami buildings

Accurate simulation of ice and snow runoff for the mountainous terrain of the Kunlun Mountains, China

While mountain runoff provides great potential for the development and life quality of downstream populations, it also frequently causes seasonal disasters. The accurate modeling of hydrological processes in mountainous areas, as well as the amount of meltwater from ice and snow, is of great significance for the local sustainable development, hydropower regulations, and disaster prevention. In this study, an improved model, the Soil Water Assessment Tool with added ice-melt module (SWATAI) was developed based on the Soil Water Assessment Tool (SWAT), a semi-distributed hydrological model, to simulate ice and snow runoff. A temperature condition used to determine precipitation types has been added in the SWATAI model, along with an elevation threshold and an accumulative daily temperature threshold for ice melt, making it more consistent with the runoff process of ice and snow. As a supplementary reference, the comparison between the normalized difference vegetation index (NDVI) and the quantity of meltwater were conducted to verify the simulation results and assess the impact of meltwater on the ecology. Through these modifications, the accuracy of the daily flow simulation results has been considerably improved, and the contribution rate of ice and snow melt to the river discharge calculated by the model increased by 18.73%. The simulation comparison of the flooding process revealed that the accuracy of the simulated peak flood value by the SWATAI was 77.65% higher than that of the SWAT, and the temporal accuracy was 82.93% higher. The correlation between the meltwater calculated by the SWATAI and the NDVI has also improved significantly. This improved model could simulate the flooding processes with high temporal resolution in alpine regions. The simulation results could provide technical support for economic benefits and reasonable reference for flood prevention