Latest Neural Nets Solve World's Hardest Equations Faster Than Ever Before

In high school physics, we learn about Newton's second law of motion -- force equals mass times acceleration -- through simple examples of a single force (say, gravity) acting on an object of some mass. In an idealized scenario where the only independent variable is time, the second law is effectively an "ordinary differential equation," which one can solve to calculate the position or velocity of the object at any moment in time. But in more involved situations, multiple forces act on the many moving parts of an intricate system over time. To model a passenger jet scything through the air, a seismic wave rippling through Earth or the spread of a disease through a population -- to say nothing of the interactions of fundamental forces and particles -- engineers, scientists and mathematicians resort to "partial differential equations" (PDEs) that can describe complex phenomena involving many independent variables. The problem is that partial differential equations -- as essential and ubiquitous as they are in science and engineering -- are notoriously difficult to solve, if they can be solved at all.