This lecture will discuss recent results in computational physics, computer graphics, and learning/data science.  The first section will present a method for accurately simulating two-way solid-fluid coupling even when solids may be smaller than the size of a computational grid cell.  Next, a numerical method for simulating materials with large surface energy (such as liquid metals) will be discussed.  The third part of the lecture will introduce techniques for obtaining sparse semantic solutions to inverse and optimization problems, with a case study of inferring facial expressions from RGB images.  The lecture will conclude with future research directions at the interfaces of simulation, graphics, learning, and data.