The solution of a number of challenging problems in materials science, biology and other complex systems will likely require the leveraging of optimal design of experiments, uncertainty quantification and a marriage of machine learning and domain knowledge.  I will discuss some recent and initial forays into this area.  In particular, I will describe some aspects the new DOE / National Cancer Institute initiative, Joint Design Of Advanced Computing Solutions For Cancer. I will also discuss some recent work on machine learning for coarse-grained theories in condensed matter as well as a high-level description of some computational methods that begin to make headway toward solving these problems. Finally, I will outline my thoughts on the future of mathematics and computer and computational science within the DOE complex.