Image inpainting aims to fill the corrupted regions of an image while maintaining global consistency. Many image inpainting methods have made significant progress by incorporating reconstructed single-scale or multi-scale simplified image information as priors to provide explicit structural or textural assistance during the inpainting process. However, these methods typically design priors manually as predefined types of image information based on intuitive choices, overlooking the incomprehensible variations in information that image feature recovery at different scales tends to focus on, which inevitably reduces the efficiency of priors in assisting image feature recovery, and may result in suboptimal performance. To address this issue, we propose Multi-scale Adaptive Priors (MAPs), which dynamically adjust information based on assisting image features at each scale. MAPs are obtained through the MAPs Reconstructor (MAPs-R), which sequentially extracts, reconstructs, and adaptively aggregates multi-scale image representations from corrupted images. To explore MAPs’ potential in assisting inpainting, we designed the MAPs-based Inpainting Network (MAPs-IN), branching feature recovery at each decoder stage to focus on different information levels. Experimental results demonstrate that our proposed priors can more effectively assist in image feature inpainting and ultimately outperform other inpainting methods.

Although physics -informed neural networks (PINNs) have been successfully applied in a wide variety of science and engineering fields, they can fail to accurately predict the underlying solution in slightly challenging convection -diffusion -reaction problems. In this paper, we investigate the reason of this failure from a domain distribution perspective, and identify that learning multi -scale fields simultaneously makes the network unable to advance its training and easily get stuck in poor local minima. We show that the widespread experience of sampling more collocation points in high -loss regions hardly help optimize and may even worsen the results. These findings motivate the development of a novel curriculum learning method that encourages neural networks to prioritize learning on easier non -layer regions while downplaying learning on harder regions. The proposed method helps PINNs automatically adjust the learning emphasis and thereby facilitates the optimization procedure. Numerical results on typical benchmark equations show that the proposed curriculum learning approach mitigates the failure modes of PINNs and can produce accurate results for very sharp boundary and interior layers. Our work reveals that for equations whose solutions have large scale differences, paying less attention to high -loss regions can be an effective strategy for learning them accurately.

We present a new category of physics-informed neural networks called physics informed variational embedding generative adversarial network (PI-VEGAN), that effectively tackles the forward, inverse, and mixed problems of stochastic differential equations. In these scenarios, the governing equations are known, but only a limited number of sensor measurements of the system parameters are available. We integrate the governing physical laws into PI-VEGAN with automatic differentiation, while introducing a variational encoder for approximating the latent variables of the actual distribution of the measurements. These latent variables are integrated into the generator to facilitate accurate learning of the characteristics of the stochastic partial equations. Our model consists of three components, namely the encoder, generator, and discriminator, each of which is updated alternatively employing the stochastic gradient descent algorithm. We evaluate the effectiveness of PI-VEGAN in addressing forward, inverse, and mixed problems that require the concurrent calculation of system parameters and solutions. Numerical results demonstrate that the proposed method achieves satisfactory stability and accuracy in comparison with the previous physics-informed generative adversarial network (PI-WGAN).

Multi-view representation learning aims to integrate multiple data information from different views to improve the task performance. The information contained in multi-view data is usually complex. Not only do different views contain different information, but also different samples of the same view contain different information. In the multi-view representation learning, most existing methods either simply treat each view/sample with equal importance, or set fixed or dynamic weights for different views/samples, which is not accurate enough to capture the information of dimensions of each sample and causes information redundancy, especially for high-dimensional samples. In this paper, we propose a novel unsupervised multi-view representation learning method based on instance-wise feature selection. A main advantage of instance-wise feature selection in this paper is that one can dynamically select dimensions that favor both view-specific representation learning and view-shared representation learning for each sample, thereby improving the performance from the perspective of model input. The proposed method consists of selector network, view-specific network and view-shared network. Specifically, selector network is used to obtain the selection template, which selects different number of dimensions conducive to representation learning from different samples to solve the sample heterogeneity problem; the view-specific network and view-shared network are used to extract the view-specific and view-shared representations, respectively. The selector network, view-shared network, and view-specific network are optimized alternately. Extensive experiments on various multi-view datasets with clustering and multi-label classification tasks demonstrate that the proposed method outperforms the state-of-the-art multi-view learning methods.

Deep image inpainting research mainly focuses on constructing various neural network architectures or imposing novel optimization objectives. However, on the one hand, building a state-of-the-art deep inpainting model is an extremely complex task, and on the other hand, the resulting performance gains are sometimes very limited. We believe that besides the frameworks of inpainting models, lightweight traditional image processing techniques, which are often overlooked, can actually be helpful to these deep models. In this paper, we enhance the deep image inpainting models with the help of classical image complexity metrics. A knowledge-assisted index composed of missingness complexity and forward loss is presented to guide the batch selection in the training procedure. This index helps find samples that are more conducive to optimization in each iteration and ultimately boost the overall inpainting performance. The proposed approach is simple and can be plugged into many deep inpainting models by changing only a few lines of code. We experimentally demonstrate the improvements for several recently developed image inpainting models on various datasets.

Missing data imputation is a fundamental problem in data analysis, and many studies have been conducted to improve its performance by exploring model structures and learning procedures. However, data augmentation, as a simple yet effective method, has not received enough attention in this area. In this paper, we propose a novel data augmentation method called Missingness Augmentation (MisA) for generative imputation models. Our approach dynamically produces incomplete samples at each epoch by utilizing the generator's output, constraining the augmented samples using a simple reconstruction loss, and combining this loss with the original loss to form the final optimization objective. As a general augmentation technique, MisA can be easily integrated into generative imputation frameworks, providing a simple yet effective way to enhance their performance. Experimental results demonstrate that MisA significantly improves the performance of many recently proposed generative imputation models on a variety of tabular and image datasets. The code is available at \url{https://github.com/WYu-Feng/Missingness-Augmentation}.

Datasets with missing values are very common in real world applications. GAIN, a recently proposed deep generative model for missing data imputation, has been proved to outperform many state-of-the-art methods. But GAIN only uses a reconstruction loss in the generator to minimize the imputation error of the non-missing part, ignoring the potential category information which can reflect the relationship between samples. In this paper, we propose a novel unsupervised missing data imputation method named PC-GAIN, which utilizes potential category information to further enhance the imputation power. Specifically, we first propose a pre-training procedure to learn potential category information contained in a subset of low-missing-rate data. Then an auxiliary classifier is determined using the synthetic pseudo-labels. Further, this classifier is incorporated into the generative adversarial framework to help the generator to yield higher quality imputation results. The proposed method can improve the imputation quality of GAIN significantly. Experimental results on various benchmark datasets show that our method is also superior to other baseline approaches. Our code is available at https://github.com/WYu-Feng/pc-gain.