Nature's Cost Function: Simulating Physics by Minimizing the Action
This work provides a novel computational method for physicists and researchers in computational physics, though it is incremental as it adapts existing gradient descent techniques to a physics context.
The paper tackled the problem of simulating physical systems by minimizing the action, a scalar function in physics, using gradient descent on a discretized version instead of analytical methods, and showed that this approach yields dynamics nearly identical to ground-truth for six systems, with concrete results like addressing failure modes such as the unconstrained energy effect.
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.