A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

Physics-informed neural networks (PINNs) have shown to be an effective tool for solving forward and inverse problems of partial differential equations (PDEs). PINNs embed the PDEs into the loss of the neural network, and this PDE loss is evaluated at a set of scattered residual points. The distribution of these points are highly important to the performance of PINNs. However, in the existing studies on PINNs, only a few simple residual point sampling methods have mainly been used. Here, we present a comprehensive study of two categories of sampling: non-adaptive uniform sampling and adaptive nonuniform sampling. We consider six uniform sampling, including (1) equispaced uniform grid, (2) uniformly random sampling, (3) Latin hypercube sampling, (4) Halton sequence, (5) Hammersley sequence, and (6) Sobol sequence. We also consider a resampling strategy for uniform sampling. To improve the sampling efficiency and the accuracy of PINNs, we propose two new residual-based adaptive sampling methods: residual-based adaptive distribution (RAD) and residual-based adaptive refinement with distribution (RAR-D), which dynamically improve the distribution of residual points based on the PDE residuals during training. Hence, we have considered a total of 10 different sampling methods, including six non-adaptive uniform sampling, uniform sampling with resampling, two proposed adaptive sampling, and an existing adaptive sampling. We extensively tested the performance of these sampling methods for four forward problems and two inverse problems in many setups. Our numerical results presented in this study are summarized from more than 6000 simulations of PINNs. We show that the proposed adaptive sampling methods of RAD and RAR-D significantly improve the accuracy of PINNs with fewer residual points. The results obtained in this study can also be used as a practical guideline in choosing sampling methods

Enhanced Visible Light Photocatalytic Activity for TiO2 Nanotube Array Films by Codoping with Tungsten and Nitrogen

A series of W, N codoped TiO2 nanotube arrays with different dopant contents were fabricated by anodizing in association with hydrothermal treatment. The samples were characterized by scanning electron microscopy, X-ray diffraction, X-ray photoelectron spectroscopy, and ultraviolet-visible light diffuse reflection spectroscopy. Moreover, the photocatalytic activity of W and N codoped TiO2 nanotube arrays was evaluated by degradation of methylene blue under visible light irradiation.Comment: 8 pages, 5 figure

Risk assessment and source identification of coastal groundwater nitrate in northern China using dual nitrate isotopes combined with Bayesian mixing model

Due to the intensive and complicated human activities, the identification of nitrate pollution source of coastal aquifer is usually a challenge. This study firstly adopted stable isotope technique and stable isotope analysis in R (SIAR) model to identify the nitrate sources and contribution proportions of different sources in typical coastal groundwater of northern China. The results showed that about 91.5% of the groundwater samples illustrated significantly high nitrate concentrations exceeding the maximum WHO drinking water standard (50mg/l), reflecting the high risk of groundwater nitrate pollution in the coastal area. A total of 57 sampling sites were classified into three groups according to hierarchical cluster analysis (HCA). The N-15-NO3- and O-18-NO3- values of groundwater samples from Group C (including nine samples) were much higher than those from Group A (including 40 samples) and Group B (including 8 samples). SIAR results showed that NH4+ fertilizer was the dominant nitrate source for groundwater samples of Groups A and B while manure and sewage (M&amp;S) served as dominant source for Group C. This study provided essential information on the high risk and pollution sources of coastal groundwater nitrate of northern China.</p

Asymmetric Feature Fusion for Image Retrieval

In asymmetric retrieval systems, models with different capacities are deployed on platforms with different computational and storage resources. Despite the great progress, existing approaches still suffer from a dilemma between retrieval efficiency and asymmetric accuracy due to the limited capacity of the lightweight query model. In this work, we propose an Asymmetric Feature Fusion (AFF) paradigm, which advances existing asymmetric retrieval systems by considering the complementarity among different features just at the gallery side. Specifically, it first embeds each gallery image into various features, e.g., local features and global features. Then, a dynamic mixer is introduced to aggregate these features into compact embedding for efficient search. On the query side, only a single lightweight model is deployed for feature extraction. The query model and dynamic mixer are jointly trained by sharing a momentum-updated classifier. Notably, the proposed paradigm boosts the accuracy of asymmetric retrieval without introducing any extra overhead to the query side. Exhaustive experiments on various landmark retrieval datasets demonstrate the superiority of our paradigm

MicroRNA-939 restricts Hepatitis B virus by targeting Jmjd3-mediated and C/EBPα-coordinated chromatin remodeling

Multi-layered mechanisms of virus host interaction exist for chronic hepatitis B virus (HBV) infection, which have been typically manifested at the microRNA level. Our previous study suggested that miRNA-939 (miR-939) may play a potential role in regulating HBV replication. Here we further investigated the mechanism by which miR-939 regulates HBV life cycle. We found that miR-939 inhibited the abundance of viral RNAs without direct miRNA-mRNA base pairing, but via host factors. Expression profiling and functional validation identified Jmjd3 as a target responsible for miR-939 induced anti-HBV effect. Jmjd3 appeared to enhance the transcription efficiency of HBV enhancer II/core promoter (En II) in a C/EBPα-dependent manner. However, the demethylase activity of Jmjd3 was not required in this process. Rather, Jmjd3's transactivation activity depended on its interaction with C/EBPα. This coordinated action further recruited the Brm containing SWI/SNF chromatin remodeling complex which promoted the transcription of HBV RNAs. Taken together, we propose that the miR-939-Jmjd3 axis perturbs the accessibility of En II promoter to essential nuclear factors (C/EBPα and SWI/SNF complex) therefore leading to compromised viral RNA synthesis and hence restricted viral multiplication.</p