In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and predicts its evolution using sparsely distributed data sites. Deep learning has shown promising results in modeling physical dynamics in recent years. However, most of the existing deep learning methods for modeling physical dynamics either focus on solving known PDEs or require data in a dense grid when the governing PDEs are unknown. In contrast, our method focuses on learning prediction models for unknown PDE-driven dynamics only from sparsely observed data. The proposed method is spatial dimension-independent and geometrically flexible. We demonstrate our method in the forecasting task for the two-dimensional wave equation and the Burgers-Fisher equation in multiple geometries with different boundary conditions, and the ten-dimensional heat equation.
Applying machine learning models to meteorological data brings many opportunities to the Geosciences field, such as predicting future weather conditions more accurately. In recent years, modeling meteorological data with deep neural networks has become a relevant area of investigation. These works apply either recurrent neural networks (RNN) or some hybrid approach mixing RNN and convolutional neural networks (CNN). In this work, we propose STConvS2S (Spatiotemporal Convolutional Sequence to Sequence Network), a deep learning architecture built for learning both spatial and temporal data depen…
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；Criteo AI Lab（Criteo人工智能实验室）
A recent line of work in the machine learning community addresses the problem of predicting high-dimensional spatiotemporal phenomena by leveraging specific tools from the differential equations theory. Following this direction, we propose in this article a novel and general paradigm for this task based on a resolution method for partial differential equations: the separation of variables. This inspiration allows us to introduce a dynamical interpretation of spatiotemporal disentanglement. It induces a principled model based on learning disentangled spatial and temporal representations of a ph…
Recently, air pollution is one of the most concerns for big cities. Predicting air quality for any regions and at any time is a critical requirement of urban citizens. However, air pollution prediction for the whole city is a challenging problem. The reason is, there are many spatiotemporal factors affecting air pollution throughout the city. Collecting as many of them could help us to forecast air pollution better. In this research, we present many spatiotemporal datasets collected over Seoul city in Korea, which is currently much suffered by air pollution problem as well. These datasets incl…
University of Notre Dame（圣母大学）；Condé Nast（康泰纳仕）；Wrocław University of Science and Technology（弗罗茨瓦夫理工大学）
User behavior modeling is important for industrial applications such as demographic attribute prediction, content recommendation, and target advertising. Existing methods represent behavior log as a sequence of adopted items and find sequential patterns; however, concrete location and time information in the behavior log, reflecting dynamic and periodic patterns, joint with the spatial dimension, can be useful for modeling users and predicting their characteristics. In this work, we propose a novel model based on graph neural networks for learning user representations from spatiotemporal behav…
University of Virginia（弗吉尼亚大学）；IBM Research（IBM研究院）；UT Austin（德克萨斯大学奥斯汀分校）
Multivariate time series forecasting focuses on predicting future values based on historical context. State-of-the-art sequence-to-sequence models rely on neural attention between timesteps, which allows for temporal learning but fails to consider distinct spatial relationships between variables. In contrast, methods based on graph neural networks explicitly model variable relationships. However, these methods often rely on predefined graphs that cannot change over time and perform separate spatial and temporal updates without establishing direct connections between each variable at every time…
Functional time series analysis, whether based on time of frequency domain methodology, has traditionally been carried out under the assumption of complete observation of the constituent series of curves, assumed stationary. Nevertheless, as is often the case with independent functional data, it may well happen that the data available to the analyst are not the actual sequence of curves, but relatively few and noisy measurements per curve, potentially at different locations in each curve's domain. Under this sparse sampling regime, neither the established estimators of the time series' dynamic…
This study addresses the issue of predicting the glaucomatous visual field loss from patient disease datasets. Our goal is to accurately predict the progress of the disease in individual patients. As very few measurements are available for each patient, it is difficult to produce good predictors for individuals. A recently proposed clustering-based method enhances the power of prediction using patient data with similar spatiotemporal patterns. Each patient is categorized into a cluster of patients, and a predictive model is constructed using all of the data in the class. Predictions are highly…
Accurate spatiotemporal modeling of conditions leading to moderate and large wildfires provides better understanding of mechanisms driving fire-prone ecosystems and improves risk management. We here develop a joint model for the occurrence intensity and the wildfire size distribution by combining extreme-value theory and point processes within a novel Bayesian hierarchical model, and use it to study daily summer wildfire data for the French Mediterranean basin during 1995--2018. The occurrence component models wildfire ignitions as a spatiotemporal log-Gaussian Cox process. Burnt areas are num…
Reliable 4D aircraft trajectory prediction, whether in a real-time setting or for analysis of counterfactuals, is important to the efficiency of the aviation system. Toward this end, we first propose a highly generalizable efficient tree-based matching algorithm to construct image-like feature maps from high-fidelity meteorological datasets - wind, temperature and convective weather. We then model the track points on trajectories as conditional Gaussian mixtures with parameters to be learned from our proposed deep generative model, which is an end-to-end convolutional recurrent neural network …
Emerging transportation modes, including car-sharing, bike-sharing, and ride-hailing, are transforming urban mobility but have been shown to reinforce socioeconomic inequities. Spatiotemporal demand prediction models for these new mobility regimes must therefore consider fairness as a first-class design requirement. We present FairST, a fairness-aware model for predicting demand for new mobility systems. Our approach utilizes 1D, 2D and 3D convolutions to integrate various urban features and learn the spatial-temporal dynamics of a mobility system, but we include fairness metrics as a form of …
Basketball games evolve continuously in space and time as players constantly interact with their teammates, the opposing team, and the ball. However, current analyses of basketball outcomes rely on discretized summaries of the game that reduce such interactions to tallies of points, assists, and similar events. In this paper, we propose a framework for using optical player tracking data to estimate, in real time, the expected number of points obtained by the end of a possession. This quantity, called \textit{expected possession value} (EPV), derives from a stochastic process model for the evol…
Accurately predicting when and where ambulance call-outs occur can reduce response times and ensure the patient receives urgent care sooner. Here we present a novel method for ambulance demand prediction using Gaussian process regression (GPR) in time and geographic space. The method exhibits superior accuracy to MEDIC, a method which has been used in industry. The use of GPR has additional benefits such as the quantification of uncertainty with each prediction, the choice of kernel functions to encode prior knowledge and the ability to capture spatial correlation. Measures to increase the uti…
Harvard T. H. Chan School of Public Health（哈佛大学陈曾熙公共卫生学院）
Fine particulate matter (PM$_{2.5}$) is one of the criteria air pollutants regulated by the Environmental Protection Agency in the United States. There is strong evidence that ambient exposure to (PM$_{2.5}$) increases risk of mortality and hospitalization. Large scale epidemiological studies on the health effects of PM$_{2.5}$ provide the necessary evidence base for lowering the safety standards and inform regulatory policy. However, ambient monitors of PM$_{2.5}$ (as well as monitors for other pollutants) are sparsely located across the U.S., and therefore studies based only on the levels of…
