What's this course about?

Machine learning and uncertainty quantification (UQ) are ubiquitous in modern science and engineering applications. In the last two decades, UQ for complex physical processes has been developed rapidly with a focus on grid-based process models, such as finite element models, which are well-established in engineering applications. On the other hand, machine learning techniques have not traditionally been applied to physics-based models. The recent surge in data-driven models based on machine learning techniques such as deep learning is changing the computational science and engineering landscape. Novel hybrid models based on neural networks are emerging and are already enhancing traditional methods. In this seminar, we discuss theoretical and computational aspects that arise from combining PDE-based models and neural networks, e.g., neural networks for PDE approximation, molecular simulations, and fluid dynamics.