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Finding paths of least action with gradient descent (2023)
A blog by Sam Greydanus
In order to communicate this technique as clearly and concretely as possible, we’re going to apply it to a simple toy problem: a free body in a gravitational field. In the code below, we choose a path where the particle bounces around x=0 at random until time t=19 seconds, at which point it leaps up to its final state of x = x_num[-1]= 21.3 meters. This is a simple example, but we have investigated it in detail because it is illustrative of the broader “principle of least action” which defies natural human intuition and sculpts the very structure of our physical universe.
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