Improve the performance of function approx for ac_opf problem in HGT

[cshjin]

init results:

With a single data, predict the pg of gen

true pg [7.7232, 8.9500, 8.9500, 5.0301, 5.0301, 5.9500, 5.9500]
pred pg [6.798503  6.798938  6.798938  6.7984858 6.7983723 6.7984943 6.7984943]

[cshjin]

Change the HGTConv with HAHConv

• single data

  true pg [7.7232, 8.9500, 8.9500, 5.0301, 5.0301, 5.9500, 5.9500]
  pred pg [7.740449  8.980435  6.2245636 6.2245636 6.224564  6.224564  6.224564 ]

• multi-data

  
  split 0 [1 2 3 4 5 6 7 8 9] [0]
  True pg [[7.7941985 8.95      8.95      5.05      5.05      6.05      6.05     ]]
  pred pg [[9.565271  9.148704  6.3749485 6.3749485 6.3749485 6.3749485 6.3749485]]

split 1 [0 2 3 4 5 6 7 8 9] [1] True pg [[7.7232 8.95 8.95 5.030133 5.030133 5.95 5.95 ]] pred pg [[6.3854384 8.949912 6.230029 6.230029 6.230029 6.230029 6.2300286]]

split 2 [0 1 3 4 5 6 7 8 9] [2] True pg [[7.7232 8.95 8.95 5.05 5.05 6.011201 6.0118766]] pred pg [[6.61629 8.946471 6.2282567 6.2282567 6.228257 6.2282567 6.228257 ]]

split 3 [0 1 2 4 5 6 7 8 9] [3] True pg [[7.7232 8.95 8.95 5.05 5.05 6.032817 6.033499]] pred pg [[6.956566 8.638954 6.6568613 6.6568613 6.6568613 6.6568613 6.6568613]]

split 4 [0 1 2 3 5 6 7 8 9] [4] True pg [[7.7283 8.95 8.95 5.05 5.05 6.05 6.05 ]] pred pg [[7.197293 8.949904 6.2300262 6.2300262 6.2300262 6.2300262 6.2300262]]

split 5 [0 1 2 3 4 6 7 8 9] [5] True pg [[7.8232 9.012909 9.012909 5.05 5.05 6.05 6.05 ]] pred pg [[6.16399 8.943898 6.2239866 6.2239866 6.223987 6.223987 6.223987 ]]

split 6 [0 1 2 3 4 5 7 8 9] [6] True pg [[7.7232 8.95 8.95 4.9644237 4.9644237 5.95 5.95 ]] pred pg [[7.6383343 8.949361 6.229678 6.229678 6.2296786 6.2296786 6.2296786]]

split 7 [0 1 2 3 4 5 6 8 9] [7] True pg [[7.7232 8.95 8.95 5.05 5.05 6.028692 6.0293646]] pred pg [[6.9769406 8.94991 6.2300186 6.2300186 6.2300186 6.230018 6.230018 ]]

split 8 [0 1 2 3 4 5 6 7 9] [8] True pg [[7.7232 8.95 8.95 5.05 5.05 6.0446453 6.045317 ]] pred pg [[6.8666754 8.912247 6.19369 6.19369 6.19369 6.19369 6.1936903]]

split 9 [0 1 2 3 4 5 6 7 8] [9] True pg [[7.8232 9.023437 9.023437 5.05 5.05 6.05 6.05 ]] pred pg [[6.8201632 8.949961 6.230077 6.230077 6.2300763 6.2300763 6.2300763]]

[cshjin]

Ignore the ac_opf problem for now. The Julia solver on ac_opf is not reliable.

Close for now.