Deep learning and data-driven approaches have shown great potential in scientific domains. The promise of data-driven techniques relies on the availability of a large volume of high-quality training datasets. Due to the high cost of obtaining data th
rough expensive physical experiments, instruments, and simulations, data augmentation techniques for scientific applications have emerged as a new direction for obtaining scientific data recently. However, existing data augmentation techniques originating from computer vision, yield physically unacceptable data samples that are not helpful for the domain problems that we are interested in. In this paper, we develop new physics-informed data augmentation techniques based on convolutional neural networks. Specifically, our generative models leverage different physics knowledge (such as governing equations, observable perception, and physics phenomena) to improve the quality of the synthetic data. To validate the effectiveness of our data augmentation techniques, we apply them to solve a subsurface seismic full-waveform inversion using simulated CO$_2$ leakage data. Our interest is to invert for subsurface velocity models associated with very small CO$_2$ leakage. We validate the performance of our methods using comprehensive numerical tests. Via comparison and analysis, we show that data-driven seismic imaging can be significantly enhanced by using our physics-informed data augmentation techniques. Particularly, the imaging quality has been improved by 15% in test scenarios of general-sized leakage and 17% in small-sized leakage when using an augmented training set obtained with our techniques.
The prevalence of graph-based data has spurred the rapid development of graph neural networks (GNNs) and related machine learning algorithms. Yet, despite the many datasets naturally modeled as directed graphs, including citation, website, and traffi
c networks, the vast majority of this research focuses on undirected graphs. In this paper, we propose MagNet, a spectral GNN for directed graphs based on a complex Hermitian matrix known as the magnetic Laplacian. This matrix encodes undirected geometric structure in the magnitude of its entries and directional information in their phase. A charge parameter attunes spectral information to variation among directed cycles. We apply our network to a variety of directed graph node classification and link prediction tasks showing that MagNet performs well on all tasks and that its performance exceeds all other methods on a majority of such tasks. The underlying principles of MagNet are such that it can be adapted to other spectral GNN architectures.
