  Inferring the source information of greenhouse gases, such as methane, from
spatially sparse sensor observations is an essential element in mitigating
climate change. While it is well understood that the complex behavior of the
atmospheric dispersion of such pollutants is governed by the
Advection-Diffusion equation, it is difficult to directly apply the governing
equations to identify the source location and magnitude (inverse problem)
because of the spatially sparse and noisy observations, i.e., the pollution
concentration is known only at the sensor locations and sensors sensitivity is
limited. Here, we develop a multi-task learning framework that can provide
high-fidelity reconstruction of the concentration field and identify emission
characteristics of the pollution sources such as their location, emission
strength, etc. from sparse sensor observations. We demonstrate that our
proposed framework is able to achieve accurate reconstruction of the methane
concentrations from sparse sensor measurements as well as precisely pin-point
the location and emission strength of these pollution sources.
