Can we automate the process of scientific discovery? Can we distill observations into physically meaningful and predictive variables? My research group tackles these questions using a combination of physics-informed machine learning techniques with applications to fluid dynamics, granular materials, and nonlinear chaotic systems.
How do we define a point? Because I’ve never seen one, have you? It’s certainly not that drop of ink you put on a paper with a point-ed pen. If you look closer, it’s huge! A swarm of bacteria might be throwing a party on it. In fact, if you can see it, then it’s not a point.
In the last century, scientists and mathematicians have discovered many ways to combine what we know with what we don't. We no longer believe that the physical world can be explained and predicted with purely deterministic equations, as Newton and Laplace did.
Ideas emerge from the ceaseless storm of bursts in a complex network of cells. At least that’s what many scientists believe. If the world is purely physical, how else would it be? But the relationship between neurons and the abstract things they generate is wholly unknown. How can an infinite imagination with its colorful images and perfect shapes look so different from the squishy matter that creates it? After all, they both share the same space in my skull.