https://profoundphysics.com/lagrangian-mechanics-for-beginne... How you would translate from the discrete, relational approach to the continuous, analytic one?
For a first exercise, forget Dijkstra and just solve a maze by doing Value Iteration, and plot the cost-to-go at each step.
Then consider that this function doesn't have to take a graph vertex or grid cell, but could instead be some continuous function on R^n.
The next step usually is to learn about the Linear Quadratic Regulator problem, where the cost-to-go is a quadratic, and you get to do an iteration of "Value Iteration" by updating the quadratic coefficients.
To connect to physics, see how you'd write the Action Integral in these terms.
Hamilton-Jacobi-Bellman equation: https://en.wikipedia.org/wiki/Hamilton%E2%80%93Jacobi%E2%80%...
Pontryagin maximum principle: https://en.wikipedia.org/wiki/Pontryagin%27s_maximum_princip...
He reminds me of Jonathon Banks. I feel like I'm getting a physics lecture from Mike Ehrmantraut :)