Bitumen extraction for the production of synthetic crude oil in Canada's Athabasca Oil Sands industry has recently come under spotlight for being a significant source of greenhouse gas emission. A major cause of concern is methane, a greenhouse gas produced by the anaerobic biodegradation of hydrocarbons in oil sands residues, or tailings, stored in settle basins commonly known as oil sands tailing ponds. In order to determine the methane emitting potential of these tailing ponds and have future methane projections, we use real-time weather data, mechanistic models developed from laboratory controlled experiments, and industrial reports to train a physics constrained machine learning model. Our trained model can successfully identify the directions of active ponds and estimate their emission levels, which are generally hard to obtain due to data sampling restrictions. We found that each active oil sands tailing pond could emit between 950 to 1500 tonnes of methane per year, whose environmental impact is equivalent to carbon dioxide emissions from at least 6000 gasoline powered vehicles. Although abandoned ponds are often presumed to have insignificant emissions, our findings indicate that these ponds could become active over time and potentially emit up to 1000 tonnes of methane each year. Taking an average over all datasets that was used in model training, we estimate that emissions around major oil sands regions would need to be reduced by approximately 12% over a year, to reduce the average methane concentrations to 2005 levels.

Diffusion probabilistic models have been successfully used to generate data from noise. However, most diffusion models are computationally expensive and difficult to interpret with a lack of theoretical justification. Random feature models on the other hand have gained popularity due to their interpretability but their application to complex machine learning tasks remains limited. In this work, we present a diffusion model-inspired deep random feature model that is interpretable and gives comparable numerical results to a fully connected neural network having the same number of trainable parameters. Specifically, we extend existing results for random features and derive generalization bounds between the distribution of sampled data and the true distribution using properties of score matching. We validate our findings by generating samples on the fashion MNIST dataset and instrumental audio data.

We propose a random feature model for approximating high-dimensional sparse additive functions called the hard-ridge random feature expansion method (HARFE). This method utilizes a hard-thresholding pursuit-based algorithm applied to the sparse ridge regression (SRR) problem to approximate the coefficients with respect to the random feature matrix. The SRR formulation balances between obtaining sparse models that use fewer terms in their representation and ridge-based smoothing that tend to be robust to noise and outliers. In addition, we use a random sparse connectivity pattern in the random feature matrix to match the additive function assumption. We prove that the HARFE method is guaranteed to converge with a given error bound depending on the noise and the parameters of the sparse ridge regression model. Based on numerical results on synthetic data as well as on real datasets, the HARFE approach obtains lower (or comparable) error than other state-of-the-art algorithms.