  In physics, there is a scalar function called the action which behaves like a
cost function. When minimized, it yields the "path of least action" which
represents the path a physical system will take through space and time. This
function is crucial in theoretical physics and is usually minimized
analytically to obtain equations of motion for various problems. In this paper,
we propose a different approach: instead of minimizing the action analytically,
we discretize it and then minimize it directly with gradient descent. We use
this approach to obtain dynamics for six different physical systems and show
that they are nearly identical to ground-truth dynamics. We discuss failure
modes such as the unconstrained energy effect and show how to address them.
Finally, we use the discretized action to construct a simple but novel quantum
simulation.
