Scientific machine learning: bridging the gap between theory and practice in deep learning for computational science and engineering applications

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Scientific computing is essential to all areas of modern life. Whether it be forecasting extreme weather events, detecting and modelling virus outbreaks or producing high-fidelity medical images to better facilitate diagnoses, algorithms for scientific computing inform key decisions and policies that impact people and help create fairer, more equitable societies. Over the next five years, there is an unprecedented opportunity to rapidly advance this field through the incorporation of Machine Learning (ML) techniques. ML is poised to have a substantial impact on scientific computing and its many applications. Yet it also raises challenges. ML techniques are poorly understood from a theoretical perspective, and there is growing concern that existing techniques do not yet meet the traditional, rigorous standards of the field in terms of robustness and reliability. The overarching goal of this research program is to tackle these challenges. Its long-term vision is to help achieve the successful incorporation of ML as a paradigm-altering tool for scientific computing and its many applications. Specifically, its objectives are: 1) To develop robust, high-fidelity, computationally efficient and theoretically guaranteed end-to-end procedures for imaging complex environments based on neural networks and deep learning. This work is expected to bring significant improvements over current state-of-the-art methods, yielding tangible benefits in key imaging modalities such as light-field imaging (e.g. electro-optical and infrared systems, hyperspectral imaging, lensless imaging), medical imaging (e.g. MRI, X-Ray CT) and scientific imaging (e.g. electron microscopy, radio interferometry). 2) To design new data-driven techniques for large-scale, high-dimensional approximation that leverage low-dimensional structure in scientific datasets to significantly enhance performance. This work will lead to better methods and bring significant benefits in important scientific computing tasks such as uncertainty quantification and data-driven discovery of complex systems. 3) To establish new theoretical foundations for ML in scientific computing by providing both theoretical upper and lower bounds for stability and accuracy. This work will advance knowledge through a better understanding of the theoretical limits of learning in scientific computing problems, providing key benchmarks for future algorithmic developments by the research community. This program will provide training for many HQP in key areas of national importance. It will develop new, innovative ML algorithms that are applicable across a range of different problems in computational science and engineering, and advance knowledge through new theoretical foundations for robust and reliable ML in scientific computing. It will accelerate progress in this nascent, but rapidly developing field, develop key Canadian leadership and stimulate important technological improvements across a range of Canadian industries.