ST-PCNN: Spatio-Temporal Physics-Coupled Neural Networks for Dynamics Forecasting

Ocean current, fluid mechanics, and many other spatio-temporal physical dynamical systems are essential components of the universe. One key characteristic of such systems is that certain physics laws -- represented as ordinary/partial differential equations (ODEs/PDEs) -- largely dominate the whole process, irrespective of time or location. Physics-informed learning has recently emerged to learn physics for accurate prediction, but they often lack a mechanism to leverage localized spatial and temporal correlation or rely on hard-coded physics parameters. In this paper, we advocate a physics-coupled neural network model to learn parameters governing the physics of the system, and further couple the learned physics to assist the learning of recurring dynamics. A spatio-temporal physics-coupled neural network (ST-PCNN) model is proposed to achieve three goals: (1) learning the underlying physics parameters, (2) transition of local information between spatio-temporal regions, and (3) forecasting future values for the dynamical system. The physics-coupled learning ensures that the proposed model can be tremendously improved by using learned physics parameters, and can achieve good long-range forecasting (e.g., more than 30-steps). Experiments, using simulated and field-collected ocean current data, validate that ST-PCNN outperforms existing physics-informed models.

Semisupervised Learning on Heterogeneous Graphs and its Applications to Facebook News Feed

Graph-based semi-supervised learning is a fundamental machine learning problem, and has been well studied. Most studies focus on homogeneous networks (e.g. citation network, friend network). In the present paper, we propose the Heterogeneous Embedding Label Propagation (HELP) algorithm, a graph-based semi-supervised deep learning algorithm, for graphs that are characterized by heterogeneous node types. Empirically, we demonstrate the effectiveness of this method in domain classification tasks with Facebook user-domain interaction graph, and compare the performance of the proposed HELP algorithm with the state of the art algorithms. We show that the HELP algorithm improves the predictive performance across multiple tasks, together with semantically meaningful embedding that are discriminative for downstream classification or regression tasks.

Validation of Matching

We introduce a technique to compute probably approximately correct (PAC) bounds on precision and recall for matching algorithms. The bounds require some verified matches, but those matches may be used to develop the algorithms. The bounds can be applied to network reconciliation or entity resolution algorithms, which identify nodes in different networks or values in a data set that correspond to the same entity. For network reconciliation, the bounds do not require knowledge of the network generation process.