Does a spellcaster know when concentration ends on one of their spells?
For example, when a wizard casts invisibility, that target is invisible until they attack or after one hour. So if the character attacks and the spell ends is the wizard aware that their spell that they are concentrating on ended earlier than expected?
I can find no RAW, or any rulings at all, that can help answer this question. That being said, the following is speculation based on the entry on PHB page 205 that details ‘The Weave’ of magic.
In conjunction with how Wizards learn their magic, and the knowledge of the Arcane arts and the understanding they must have of the Weave in order to cast such magic, we can assume that yes: A wizard would know when the magic he cast a few turns ago that affected the Weave in such a way as to turn an ally invisible has lost its effect and thus become inert. I think this particularly holds true for concentration spells where the Wizard is actively maintaining the alteration to the Weave in order to sustain an effect.
When the spell ends, either through the Wizard deciding to end it, the spell running its full duration, or something ending it prematurely, I have no reason to believe this would be lost on the Wizard in question.
It would make absolutely sense for a caster to be aware when they lose concentration on a spell of their own.
"This guard hit me pretty hard, I can sense that Invisibility I gave to Tim in order to secretly enter the King's palace wore off! He must be in trouble now!"
The situation you describe is not the loss of concentration.
if the character attacks and the spell ends is the wizard aware ...
It's the very subject of the spell breaking it out of their own volition, something completely unrelated to the caster. Concentration is a different mechanism and, in this case, not the only one that can cause a spell to end sooner than its duration.
Ultimately, there are no rules specifying this so it's up to the DM to decide whether all casters in his world have a kind of "arcane sense" that allowed them to know exactly which of their spells are still operational and which aren't.
However, do keep in mind that accepting the above ruling can lead to some unexpected and possibly unwelcome situations. For instance, a mage casting a high duration spell, which ends on a trigger like Magic Mouth, in his sanctum/laboratory/tower/house so as to know exactly when someone entered it (triggering its ending).
The other answers say there doesn't seem to be anything in the PHB explicitly about whether you sense anything when a spell ends. Therefore, does it say anything implicitly?
Implicit Proof Ad Absurdum: If you weren't aware of whether your spell ended, then you wouldn't know to recast Haste when the target died, or recast Tasha's Hideous Laughter when the target took damage. You wouldn't know, so you would continue your concentration on such spells, and would be less likely to cast them. This is absurd and game-changing. Therefore, you are aware of when a "spell ends." Therefore, you are aware if spells you are concentrating on end.
For the same reasons, you know when your concentration ends (i.e., if you didn't then you might want to keep casting Haste every round, just in case, which is absurd.)
