Tensor-view Topological Graph Neural Network

Graph classification is an important learning task for graph-structured data. Graph neural networks (GNNs) have recently gained growing attention in graph learning and have shown significant improvements in many important graph problems. Despite their state-of-the-art performances, existing GNNs only use local information from a very limited neighborhood around each node, suffering from loss of multi-modal information and overheads of excessive computation. To address these issues, we propose a novel Tensor-view Topological Graph Neural Network (TTG-NN), a class of simple yet effective topological deep learning built upon persistent homology, graph convolution, and tensor operations. This new method incorporates tensor learning to simultaneously capture Tensor-view Topological (TT), as well as Tensor-view Graph (TG) structural information on both local and global levels. Computationally, to fully exploit graph topology and structure, we propose two flexible TT and TG representation learning modules that disentangle feature tensor aggregation and transformation and learn to preserve multi-modal structure with less computation. Theoretically, we derive high probability bounds on both the out-of-sample and in-sample mean squared approximation errors for our proposed Tensor Transformation Layer (TTL). Real data experiments show that the proposed TTG-NN outperforms 20 state-of-the-art methods on various graph benchmarks.

SVBRDF Recovery From a Single Image With Highlights using a Pretrained Generative Adversarial Network

Spatially-varying bi-directional reflectance distribution functions (SVBRDFs) are crucial for designers to incorporate new materials in virtual scenes, making them look more realistic. Reconstruction of SVBRDFs is a long-standing problem. Existing methods either rely on extensive acquisition system or require huge datasets which are nontrivial to acquire. We aim to recover SVBRDFs from a single image, without any datasets. A single image contains incomplete information about the SVBRDF, making the reconstruction task highly ill-posed. It is also difficult to separate between the changes in color that are caused by the material and those caused by the illumination, without the prior knowledge learned from the dataset. In this paper, we use an unsupervised generative adversarial neural network (GAN) to recover SVBRDFs maps with a single image as input. To better separate the effects due to illumination from the effects due to the material, we add the hypothesis that the material is stationary and introduce a new loss function based on Fourier coefficients to enforce this stationarity. For efficiency, we train the network in two stages: reusing a trained model to initialize the SVBRDFs and fine-tune it based on the input image. Our method generates high-quality SVBRDFs maps from a single input photograph, and provides more vivid rendering results compared to previous work. The two-stage training boosts runtime performance, making it 8 times faster than previous work.

Targeted Source Detection for Environmental Data

In the face of growing needs for water and energy, a fundamental understanding of the environmental impacts of human activities becomes critical for managing water and energy resources, remedying water pollution, and making regulatory policy wisely. Among activities that impact the environment, oil and gas production, wastewater transport, and urbanization are included. In addition to the occurrence of anthropogenic contamination, the presence of some contaminants (e.g., methane, salt, and sulfate) of natural origin is not uncommon. Therefore, scientists sometimes find it difficult to identify the sources of contaminants in the coupled natural and human systems. In this paper, we propose a technique to simultaneously conduct source detection and prediction, which outperforms other approaches in the interdisciplinary case study of the identification of potential groundwater contamination within a region of high-density shale gas development.