Reservoir modeling is a critical process in the development of subsurface reservoirs, such as those found in oil and gas fields [1, 2]. Its primary objective is to characterize the spatial distribution of key reservoir properties, including porosity and permeability, which are essential for assessing reservoir reserves, evaluating properties, and determining overall potential [3, 4]. By integrating data from core samples, well logs, seismic surveys, and other sources, reservoir model offer a detailed representation of the spatial relationships between the essential reservoir properties. This modeling process is not only fundamental for understanding the current condition of the reservoir but also serves as the foundation for subsequent numerical simulations [5, 6] and the development of effective management strategies [7, 8]. Spatial interpolation is a widely used technique in reservoir modeling, involving the estimation of reservoir property distributions across a reservoir based on observations at discrete points [9].

Fitting a polynomial to observed data is an ubiquitous task in many signal processing and machine learning tasks, such as interpolation and prediction. In that context, input and output pairs are available and the goal is to find the coefficients of the polynomial. However, in many applications, the input may be partially known or not known at all, rendering conventional regression approaches not applicable. In this paper, we formally state the (potentially partial) blind regression problem, illustrate some of its theoretical properties, and propose algorithmic approaches to solve it. As a case-study, we apply our methods to a jitter-correction problem and corroborate its performance.

Sensors are the key to sensing the environment and imparting benefits to smart cities in many aspects, such as providing real-time air quality information throughout an urban area. However, a prerequisite is to obtain fine-grained knowledge of the environment. There is a limit to how many sensors can be installed in the physical world due to non-negligible expenses. In this paper, we propose to infer real-time information of any given location in a city based on historical and current observations from the available sensors (termed spatiotemporal inference). Our approach decouples the modeling of short-term and long-term patterns, relying on two major components. Firstly, unlike previous studies that separated the spatial and temporal relation learning, we introduce a joint spatiotemporal graph attention network that learns the short-term dependencies across both the spatial and temporal dimensions. Secondly, we propose an adaptive graph recurrent network with a time skip for capturing long-term patterns. The adaptive adjacency matrices are learned inductively first as the inputs of a recurrent network to learn dynamic dependencies. Experimental results on four public read-world datasets show that our method reduces state-of-the-art baseline mean absolute errors by 5%~12%.

There's a good chance you've seen a drone swarm. Maybe not in person, but probably televised during a New Year's celebration. A drone swarm occurs when a large number of the flying robots take to the skies in sync. It isn't a coincidence that they almost always fly in open outdoor areas. For these robotic fliers, it can be difficult to navigate in tight spaces without running into each other or environmental obstacles.