Title: Free boundary problems for compressible Euler gases
Abstract: A free boundary for a compressible Euler gas is the interface separating the gas domain from vacuum; this moves freely, depending on the state of the gas. Such problems arise in the study of stellar coronas, planetary atmospheres and even for Saturn’s rings. In this talk I will present recent work whose aim is to develop a complete Eulerian approach for this class of free boundary problems. This is joint work with Mihaela Ifrim.

Title: From the blackboard to the clinic: combining mechanism-driven models with machine learning for personalized medicine in ophthalmology
Abstract: Machine Learning (ML) aims at extracting information and knowledge from data. ML is naturally interdisciplinary, as it bridges fundamental techniques of data analysis, typically developed by mathematicians, statisticians and computer scientists, with the needs of actionable insights that are specific to the particular application domain. Mechanism-driven models are based on the principles of physics and physiology and allow for identification of cause-to-effect relationships among interplaying factors in a complex system. While invaluable for causality, mechanism-driven models are often based on simplifying assumptions to make them tractable for analysis and simulation; however, this often brings into question their relevance beyond theoretical explorations. The combination of mechanism-driven and data-driven models allows us to harness the advantages of both approaches, as mechanism-driven models excel at interpretability but suffer from a lack of scalability, while data-driven models are excellent at scale but suffer in terms of generalizability and insights for hypothesis generation. This combined, integrative approach represents the pillar of the interdisciplinary approach to data science that will be discussed in this talk, with application to glaucoma research. Glaucoma is the leading cause of irreversible blindness worldwide. Unfortunately, poor understanding of glaucoma risk factors has constrained currently approved treatments to intraocular pressure (IOP) reduction. Other factors such as vascular health, specifically blood pressure (BP), are known to alter risk of glaucoma onset and progression. BP and IOP vary by person, with both high and low BP being associated with the disease process. In this talk, we will show how combining mechanism-driven and data-driven methods can help quantify the relative contribution of BP as a risk factor in combination with IOP for a given individual to advance glaucoma management.