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Failure probability (FP) estimation problem is a crucial task in engineering. In this work we consider this problem in the situation that the underlying computer models are extremely expensive, which often arises in the practice, and in this setting, reducing the calls of computer model is of essential importance. We formulate the problem of estimating the failure probability with expensive computer models as an sequential experimental design for the limit state (i.e., the failure boundary) and propose a series of efficient adaptive design criteria to solve the design of experiment (DOE). Considering the remarkable achievements of neural networks, we aim to leverage this powerful tool for surrogate modeling and sampling purposes. In particular, the proposed method employs the deep neural network (DNN) as the surrogate of limit state function for efficiently reducing the calls of expensive computer experiment. A map from the Gaussian distribution to the posterior approximation of the limit state is learned by the normalizing flows for the ease of experimental design. Three normalizing-flows-based design criteria are proposed in this work for deciding the design locations based on the different assumption of generalization error. The accuracy and performance of the proposed method is demonstrated by both theory and practical examples. The relative error of FP estimation achieved by the proposed methods is consistently below ten percent. • Failure boundary detected by normalizing flows in Bayesian framework. • Sampling-based optimal design criteria with considering the generalization error. • Optimal experimental design without optimization. [ABSTRACT FROM AUTHOR]

In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar variable. The distribution of this performance variable is important in many uncertainty quantification problems, ranging from risk management to utility optimisation. In practice, this distribution usually cannot be derived analytically and has to be obtained numerically by simulations. To this end, standard Monte Carlo simulations are often used, however, they cannot efficiently reconstruct the tail of the distribution which is essential in many applications. One possible remedy is to use the Multicanonical Monte Carlo method, an adaptive importance sampling scheme. In this method, one draws samples from an importance sampling distribution in a nonstandard form in each iteration, which is usually done via Markov chain Monte Carlo (MCMC). MCMC is inherently serial and therefore struggles with parallelism. In this paper, we present a new approach, which uses the Sequential Monte Carlo sampler to draw from the importance sampling distribution, which is particularly suited for parallel implementation. With both mathematical and practical examples, we demonstrate the competitive performance of the proposed method. • Novel adaptation of Multicanonical Monte Carlo method for parallel implementation. • The proposed method fully reconstructs a performance function's distribution. • The proposed method uses Sequential Monte Carlo sampler, as such, it can be implemented in parallel. • The proposed method reduces computation time significantly compared to existing methods. [ABSTRACT FROM AUTHOR]

Farmland mulching is widely used to preserve soil moisture and increase crop yield in the semiarid region of the Loess Plateau. However, the effect of different farmland mulching on soil bacterial communities is not clear. Therefore, the impact of a 5-year field management practice (surface mulching) on the soil bacterial communities was studied in dryland farmland of the Loess Plateau by using Illumina sequencing of the 16S rRNA gene. The following treatments were investigated: (1) ridge-furrow mulching pattern; (2) flat plastic film mulching; (3) flat biodegradable film mulching; (4) flat straw mulching; and (5) control (CK), conventional flat planting without mulch. All farmland mulching increased the diversity of soil bacteria and the diversity was greatest under the plastic film treatment. The dominant phyla across all soil samples were Proteobacteria , Acidobacteria , and Actinobacteria. Cluster analyses showed that bacterial communities under mulching treatments were different from that of CK. The bacterial community composition of plastic film and straw mulching treatments, biodegradable film and ridge-furrow mulching treatments were similar at the phylum level. Spearman correlation analysis indicated that the response of bacterial alpha-diversity was mainly negatively associated with the soil organic carbon and total nitrogen. The Mantel test showed that the beta-diversity depended primarily on the soil total nitrogen and soil temperature. The changes of the bacterial community distribution were significantly related to the soil moisture, which varied significantly with a range of 9.8–17.3 between treatments. These results indicated that soil properties changed after long-term farmland mulching, and these changes were related to soil bacterial diversity and community structure. According to this study, flat plastic firm mulching was found to being a good option for increasing soil bacterial diversity and richness and thereby potentially stabilize functional stability of soil biological processes. • Effects of four mulching methods on soil bacterial communities were compared. • Farmland mulching increased the diversity of the soil bacterial community. • Bacterial alpha diversity response was mainly related to SOC and TN. • Bacterial community composition was highly sensitive to the soil moisture. • Flat plastic film mulching is recommended in semi-arid areas of the loess plateau. [ABSTRACT FROM AUTHOR]

The accurate and efficient management of water and nitrogen is essential for the effective intensive production of greenhouse watermelon. In order to determine the optimal application of water and nitrogen to promote the growth and yield of watermelon under the increasing CO 2 concentration in the future, we conducted an experiment with 12 treatments over two growing seasons in 2019 and 2020 to evaluate the effects of water and nitrogen coupling on the growth, photosynthesis, and yield of watermelon under carbon dioxide (CO 2) enrichment. The treatments included three irrigation levels, I 1 (80% evaporation (Ep)), I 2 (100% Ep), and I 3 (120% Ep); two nitrogen levels, N 1 (644.04 kg/ha) and N 2 (1288.09 kg/ha); and two CO 2 concentrations, C 1 (400 ppm) and C 2 (800 ppm). The experimental results show that except for intercellular CO 2 concentration (Ci) and chlorophyll, irrigation exhibited a promoting effect on other indicators in two years, and yield was most strongly improved with increased irrigation. The interaction of water and nitrogen dramatically affected the net photosynthetic rate (Pn), transpiration rate (Tr) and Ci in two years. Elevated CO 2 concentration alleviated the negative effect of low nitrogen on the number of leaves, dry matter accumulation, Pn, and Ci, with the biggest improvement on dry matter accumulation, changes of 35.7% and 17.9% for two years. Meanwhile, elevated CO 2 concentration also promoted Pn under low-irrigation, with increases of 36.9% and 31.1% in two years. Eight indicators of growth and photosynthesis were used to evaluate comprehensive growth based on Technique for order performance by similarity to ideal solution (TOPSIS), and dry matter accumulation achieved the largest combined weight of 0.241 and 0.232, followed by Pn. A positive correlation was found between comprehensive growth and yield. Different treatments were effective for overall promotion of growth and yield, with 115–120% Ep irrigation, 976.07–1288.09 kg/ha nitrogen fertilizer optimal for watermelon at 400 ppm CO 2 concentration and 114–120% Ep irrigation, 664.04–913.06 kg/ha nitrogen fertilizer best for 800 ppm CO 2. These results suggest for the expected future higher CO 2 concentrations, greenhouse watermelon production should reduce application of nitrogen fertilizers to save resources, but maintain full irrigation. • Net photosynthetic rate was strongly promoted in low-irrigation by CO 2 enrichment. • CO 2 enrichment dramatically improved the growth of watermelon under low nitrogen. • Eight growth and photosynthetic indicators are comprehensively evaluated by TOPSIS. • A linear relationship was found between comprehensive growth and yield. • The optimal water-nitrogen for watermelon of two CO 2 concentrations were determined. [ABSTRACT FROM AUTHOR]