Spatial-temporal source term estimation using deep neural network prior and its application to Chernobyl wildfires

The source term of atmospheric emissions of hazardous materials is a crucial aspect of the analysis of unintended release. Motivated by wildfires of regions contaminated by radioactivity, the focus is placed on the case of airborne transmission of material from 5 dimensions: spatial location described by longitude and latitude in a given area with potentially many sources, time profiles, height above ground level, and the size of particles carrying the material. Since the atmospheric inverse problem is typically ill-posed and the number of measurements is usually too low to estimate the whole 5D tensor, some prior information is necessary. For the first time in this domain, a method based on deep image prior utilizing the structure of a deep neural network to regularize the inversion is proposed. The network is initialized randomly without the need to train it on any dataset first. In tandem with variational optimization, this approach not only introduces smoothness in the spatial estimate of the emissions but also reduces the number of unknowns by enforcing a prior covariance structure in the source term. The strengths of this method are demonstrated on the case of ¹³⁷Cs emissions during the Chernobyl wildfires in 2020.