Our hardwood flooring on about 1500sq ft. down stairs is cupping and getting worse every day. About 6 weeks ago our hard wood floors were completed. The size of the flooring is 5". We feel confident that the installation was done accurately and that our problem is most likely comming from high moisture under the house. We have a 4ft. high crawl space lined with a thick plastic barrier from the ground. The whole house is insulated with open cell foam insulation. The concrete block curtain wall under the house is sprayed with closed cell foam insulation. There are two scuttle hole doors that have remained open under the house, opening to the porches which are ventilated by brick vents(perhaps our mistake was leaving these doors open). There is no type of insulation against the underneath side of the subfloor(perhaps a mistake). The hvac has been on since the day the hardwood entered the house back in February. They were allowed 6-8 weeks to acclimate before installation. May was an extreemly rainy month for us.
There is no obvious water under the house. The duck work is not sweating. The finish on the flooring ended up being 6 coats of polyurethane. The upstairs hardwoods still look great. We will be obtaining a wet bulb and barometer to check moisture levels under the house. It does however feel more humid under the house than in the house, but not a whole lot more humid than the outdoors.
Would buying a dehumidifier,completely sealing off under our house ,and equalizing the humidity levels indoors and underneath fix our problem? How likely is it that this would reverse the damage? If not, is the best option replacing the hardwoods or is it likely that the cupping could be sanded down?

Get someone to check the moisture content of the underneath part of the subfloor. Sounds like its pretty sealed up tight cept for that. De-humidify and wait before any attempt at sanding.

Hygrometers in the crawl space and inside the home placed on the floor.

Do you travel often, leaving the home unoccupied for days, or a week?

I agree with the other two posts. You need to find out the exact source of the moisture. So, take a RH reading underneath your home in the crawl space and another inside your home on the first floor. Also take moisture meter readings of the underside of the wood subflooring and framing members ( joists, posts, beams, girders, trusses, etc ). If you can, get moisture meter readings of the face of the wood flooring and then deeper down, into the flooring. I would make sure the polyethylene vapor barrier is working correctly. All seams need to be overlapped by 12" and "sealed" by weighting the seams with rock, gravel, bricks, sand, whatever. Tape will not work or last. The vapor barrier should lap up the foundation walls by 4 to 6" and again be held in place by gravel or similar. I suspect that the earth under your home is very wet. Since it appears that you have little to no foundation vents, the RH built up under the house and got into the subflooring, increasing it's MC. From there, into the finished flooring, causing the cupping.

Once you have located the source of the moisture and eliminated it, it is time to allow everything to equalize and dry out. This will take months. It may take a year. Monthly moisture meter readings should be taken to check on progress. After the flooring has dried out as much as it can, then repairs can begin. Re-nail any loose boards, fill any gaps with the appropriate filler and if the cupping has gone down to acceptable, then simply re-coat the floors. You could have them re-sanded as well if needed. But not before they are fully dried out.