Not yet but they are working on it

Theoretically, no. If you want to explain everything you'd have to put every subatomic particle into superposition to study it and then work your way backwards in accordance with every other particle.. and you'd have to do it for every single one. The amount of space that it would take to compute that is larger than the observable universe, and you can't catch up. Ergo, no, science cannot explain everything. It can extrapolate and give you consistent and correct predictions, but information literally cannot be processed fast enough at a universal scale.

This: https://en.wikipedia.org/wiki/Superposition_principle#Quantum_superposition
then scroll for Boundary value problems.

Oh, and then apply that to accumulating knowledge. It's just not possible.

The point is, by even trying to attempt it, you create more data than can be stored. It seems like a simplification, and it is for linear equations, but overall, writing it all out will ALWAYS take more space and energy in it's expression. This is also why a universal equation or constant or... something that reconciles quantum physics and space-time with standard physics is considered the holy grail.

Oh... this is also one of the reasons the multiverse idea has any credibility.