Julia (https://julialang.org/) is a generic programming language designed for high-performance computing. It solves the "two language problem" of scientific computing. Julia is dynamically typed like scripting language such as Python and can be compiled into native machine code. Besides, composability via multiple dispatches makes Julia ideal for integration across packages. SciML (https://sciml.ai/) is an open-source software for scientific machine learning based on the Julia language that combines machine learning and scientific computing by integrating numerous standalone packages.

Across engineering and scientific disciplines, machine learning is the main method for analyzing and identifying patterns in big data and making informed decisions around that data. Recently, a new area within artificial intelligence called scientific machine learning has emerged, which introduces physics laws into machine learning models. Scientific machine learning combines the areas of artificial intelligence and scientific computation. Because scientific machine learning algorithms are informed and constrained by physics laws, they do not rely only on data and can even make predictions where there is no data. However, there has been little work on probabilistic methods in scientific machine learning, meaning that current algorithms cannot model uncertainty in the data or the physics.

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Abstract: Scientific machine learning (SciML) is the burgeoning field combining scientific knowledge with machine learning for data-efficient predictive modeling. We will introduce SciML as the key to effective learning in many engineering applications, such as improving the fidelity of climate models to accelerating clinical trials. This will lead us to the question on the frontier of SciML: what about stiffness? Stiffness is a pervasive quality throughout engineering systems and the most common cause of numerical difficulties in simulation. We will see that handling stiffness in learning, and thus real-world models, requires new training techniques.