A connubio of Machine Learning and PDEs for Scientific Discovery in the Biological Sciences

In this talk, I will describe some problems at the intersection of data science and applied mathematics with particular focus on questions emerging in the study of the neuro-musculo-skeletal-environmental system. Many aspects of this system can be studied with (potentially different) combinations of machine learning and differential equations methods. An underlying theme of these problems is the partial understanding in mathematical terms of the phenomenon under study and the availability of some limited data, together with the need of combining information from different experimental sources. Another theme is that of the complexity of the models, which might be intrinsically geometric and include both continuous and discrete components, but that can sometimes be accurate even if expressed in terms of biologically motivated latent variables of reduced dimensions. If time permits, applications of some of these tools to problems in infectious diseases dynamics will also be discussed.