Indexing numpy arrays only if within bounds
This problem smells like finite differences. Your best bet is to write a (fast, possibly recursive) loop for the inner points, and then loop over the boundary points separately, imposing the desired boundary conditions there. Obviously, the other way around also works: start by assigning boundary points, then loop over inner points.
That said, if you are having issues with speed (probably because your grid is gigantic), you may want to do a few optimizations, as 2d arrays in python are S L O W:

try reversing the order of looping: in python (NumPy, in case you are using that), 2d arrays are traversed by rows first. You may want to experiment with that at least.

try allocating your 2d thing as a big 1d chunk where its unique index is n = i + nx * j, with i,j your original 2d indices. Again, experiment with running the new index n along rows vs columns first.


These two suggestions combined should give you a massive speedup.
I have a 2d numpy array psi with shape (nx,ny). I want to create a new array phi of the same shape where for each element phi[i][j] I need to evaluate an expression containing psi[i][j] and neighboring elements psi[i-1][j],psi[i+1][j],psi[i][j+1] and psi[i][j-1],except for edge cases where any of these neighbors are not in the bounds of psi, treat that element as 0 in the expression.
I can implement this using nested for loops and checking for boundary conditions, but I would like to perform this operation as time efficient as possible. I've tried by assigning
phi[1:-1,1:-1] = f(psi[1:-1,1:-1], psi[0:-2,1:-1], psi[2:,1:-1], psi[1:-1,0:-2], psi[1:-1,2:])
but this does not cover edge cases which get messy, so if there were some conditional way to only reference when within bounds else just be 0 it might work. Or, of course, if there is an even more time efficient way that would be better.