Refund or Stop Paying Installments if You Quit Invisalign Mid-treatment?

Your treatment plan was a contract between you and your dentist to exchange an agreed amount of money for completed treatment. Your dentist has already paid Invisalign for the entire treatment and done the majority of the work even though you are only half way through treatment.
Do the right thing and finish the tereatment and pay the entire amount! Your dentist was nice enough to let you make payments. I get paid upfront for invisalign or the patient enters into a financial agreement with a 3rd party that charges interest.

It is common and prudent for orthodontists to recover their upfront costs at the beginning of treatment.  A large portion of our cost is incurred before you even get your aligners in the form of photographs, x-rays, teeth impressions, and lab fees.  It can be in the $1000-$2000 range.  If the remainder is spread over your estimated treatment time, then you are basically paying for treatment as you go.
That being said...you likely have a written contract with your doctor agreeing to pay for services over a period of time.  That is ... you are legally obligated to pay the entire fee whether you choose to wear the aligners or not.  To avoid any repercussions to yourself, it would be in your best interest to talk to him or her about your level of satisfaction and desire to stop treatment. 
If they feel that they have received appropriate compensation for the amount of work and materials that they have invested in the case, then they may be willing to adjust the contract to reflect that.  We do it all the time for people who move away in the middle of treatment.
But (this is your word of warning)

Don't expect them to be happy as orthodontists want it done right
Expect to sign a release form relieving them of any responsibility for adverse effects resulting from your decision.
Don't expect them to continue to see you to monitor the incomplete result
Don't expect them to give you retainers to maintain the correction - unless you pay for  them

It is still a good question and may be worth asking your doctor.  Good Luck.

In MY office, the fee is for the result.  If you are happy with what you have now, there would be no refund at all.
I would talk to your dentist or orthodontist to see what they think, but I would not expect a change in fee or refund.  The costs have already accrued and the aligners have been made, whether you decide to use them or not.
It would be like buying groceries to feed a large group.  If fewer people showed up, the costs didn't change.  All of the aligners have been created, so even though you haven't used them all, the dentist has already paid for them.