Open V-Rang opened 6 months ago
uvilla
commented
6 months ago Thank you @V-Rang .
All results look good. I recommend we merge this into main, so we have a working base to which build off the rest.
Let's keep this issue open for future updates.
V-Rang
commented
6 months ago Changes made from previous results: commit: 1c390abdff998a094b7901207f9e497be2ca54d5
for the qpact example,
prior_param = {"gamma": 0.1, "delta": 2.}
instead of
prior_param = {"gamma": 0.05, "delta": 1.}
Following are the validation plots to check for correctness of modelVerify for the PACT and poisson examples. Plots are made for the following cases:
It cg_it cost misfit reg (g,dm) ||g||L2 alpha tolcg
1 1 3.296872e+04 3.251677e+04 4.519588e+02 -3.875949e+06 4.771534e+05 1.000000e+00 5.000000e-01
2 7 3.155966e+04 3.120122e+04 3.584371e+02 -7.643731e+04 6.649927e+03 3.125000e-02 1.180537e-01
3 3 2.796710e+04 2.739224e+04 5.748642e+02 -4.152889e+04 5.522025e+03 2.500000e-01 1.075772e-01
4 14 2.705065e+04 2.658544e+04 4.652047e+02 -6.089124e+04 4.465198e+03 3.125000e-02 9.673672e-02
5 4 2.533982e+04 2.465626e+04 6.835588e+02 -9.036735e+03 3.611779e+03 5.000000e-01 8.700247e-02
6 9 2.482851e+04 2.427916e+04 5.493458e+02 -4.471282e+04 3.667286e+03 6.250000e-02 8.766847e-02
7 15 2.437344e+04 2.374975e+04 6.236877e+02 -4.171283e+04 2.838350e+03 3.125000e-02 7.712656e-02
8 9 2.406868e+04 2.349112e+04 5.775573e+02 -6.462086e+03 2.730377e+03 1.250000e-01 7.564536e-02
9 17 2.377087e+04 2.312096e+04 6.499099e+02 -2.818587e+04 2.560199e+03 3.125000e-02 7.325004e-02
10 10 2.359262e+04 2.298338e+04 6.092321e+02 -5.662241e+03 2.567324e+03 1.250000e-01 7.335189e-02
11 17 2.329728e+04 2.261019e+04 6.870887e+02 -3.022134e+04 2.423973e+03 3.125000e-02 7.127461e-02
12 10 2.310403e+04 2.244562e+04 6.584048e+02 -5.547740e+03 2.434305e+03 6.250000e-02 7.142636e-02
13 10 2.295427e+04 2.224256e+04 7.117065e+02 -6.386892e+03 2.298275e+03 6.250000e-02 6.940200e-02
14 10 2.278479e+04 2.210582e+04 6.789732e+02 -6.207825e+03 2.378126e+03 6.250000e-02 7.059735e-02
15 10 2.265726e+04 2.192372e+04 7.335456e+02 -6.142784e+03 2.219152e+03 6.250000e-02 6.819688e-02
16 17 2.259393e+04 2.191548e+04 6.784472e+02 -6.743317e+03 2.304022e+03 6.250000e-02 6.948873e-02
17 17 2.242684e+04 2.169240e+04 7.344484e+02 -1.390302e+04 2.178747e+03 3.125000e-02 6.757318e-02
18 9 2.222491e+04 2.151035e+04 7.145604e+02 -3.331881e+03 2.198679e+03 1.250000e-01 6.788157e-02
19 17 2.207479e+04 2.131190e+04 7.628902e+02 -1.112544e+04 2.079360e+03 3.125000e-02 6.601396e-02
20 10 2.188162e+04 2.113709e+04 7.445320e+02 -2.818787e+03 2.094892e+03 1.250000e-01 6.626005e-02
21 5 9.019375e+03 4.307817e+03 4.711558e+03 -2.093940e+05 1.996465e+03 2.500000e-01 6.468474e-02
22 9 7.149101e+03 3.617456e+03 3.531645e+03 -5.194625e+04 1.014948e+03 6.250000e-02 4.612038e-02
23 16 5.383839e+03 2.844694e+03 2.539145e+03 -2.187967e+04 2.107345e+03 1.250000e-01 6.645671e-02
24 8 5.108703e+03 2.923998e+03 2.184705e+03 -7.448186e+03 1.791338e+03 2.500000e-01 6.127168e-02
25 3 4.051294e+03 1.909001e+03 2.142293e+03 -6.214051e+03 3.484868e+03 1.000000e+00 8.546026e-02
26 8 3.869729e+03 1.668682e+03 2.201047e+03 -1.343944e+05 1.619995e+03 7.812500e-03 5.826770e-02
27 5 3.514139e+03 1.533697e+03 1.980442e+03 -3.379007e+03 1.285266e+03 2.500000e-01 5.190002e-02
28 6 3.010683e+03 1.146314e+03 1.864369e+03 -3.052453e+03 1.871195e+03 2.500000e-01 6.262252e-02
29 17 2.954831e+03 1.115276e+03 1.839555e+03 -4.819727e+03 1.498399e+03 1.562500e-02 5.603828e-02
30 10 2.702201e+03 7.525594e+02 1.949642e+03 -1.091674e+03 1.409943e+03 1.000000e+00 5.435903e-02
31 12 2.541893e+03 6.355619e+02 1.906331e+03 -1.034107e+03 6.321756e+02 2.500000e-01 3.639903e-02
32 18 2.480316e+03 5.359777e+02 1.944338e+03 -8.076250e+02 5.560421e+02 1.250000e-01 3.413696e-02
33 11 2.371346e+03 5.316886e+02 1.839657e+03 -2.282551e+02 4.535901e+02 1.000000e+00 3.083208e-02
34 11 2.355402e+03 5.071336e+02 1.848268e+03 -2.860981e+01 1.197617e+02 1.000000e+00 1.584273e-02
35 13 2.354440e+03 5.038637e+02 1.850576e+03 -1.794025e+00 2.140523e+01 1.000000e+00 6.697781e-03
36 17 2.354424e+03 5.035916e+02 1.850833e+03 -2.974569e-02 2.456828e+00 1.000000e+00 2.269125e-03
Converged in 36 iterations.
Termination reason: Norm of the gradient less than tolerance
Final gradient norm: 0.0621147028625235
Final cost: 2354.424493453355
It cg_it cost misfit reg (g,dm) ||g||L2 alpha tolcg
1 1 3.296995e+04 3.251802e+04 4.519356e+02 -3.875723e+06 4.771542e+05 1.000000e+00 5.000000e-01
2 7 3.155839e+04 3.120018e+04 3.582100e+02 -7.666751e+04 6.652223e+03 3.125000e-02 1.180739e-01
3 3 2.796499e+04 2.739045e+04 5.745348e+02 -4.153938e+04 5.523031e+03 2.500000e-01 1.075869e-01
4 14 2.704973e+04 2.658494e+04 4.647847e+02 -6.097241e+04 4.463572e+03 3.125000e-02 9.671902e-02
5 4 2.534852e+04 2.466459e+04 6.839218e+02 -9.050234e+03 3.610608e+03 5.000000e-01 8.698829e-02
6 16 2.449498e+04 2.390083e+04 5.941553e+02 -4.713491e+04 3.671804e+03 3.125000e-02 8.772238e-02
7 15 2.404579e+04 2.337810e+04 6.676862e+02 -9.051502e+03 2.979350e+03 1.250000e-01 7.901898e-02
8 18 2.394606e+04 2.337364e+04 5.724192e+02 -1.335636e+04 2.705607e+03 6.250000e-02 7.530139e-02
9 17 2.366337e+04 2.301783e+04 6.455430e+02 -2.786584e+04 2.546911e+03 3.125000e-02 7.305963e-02
10 9 2.347865e+04 2.287297e+04 6.056806e+02 -5.722882e+03 2.563201e+03 1.250000e-01 7.329291e-02
11 17 2.318685e+04 2.250752e+04 6.793257e+02 -2.817525e+04 2.422086e+03 3.125000e-02 7.124680e-02
12 10 2.312548e+04 2.249397e+04 6.315054e+02 -5.363226e+03 2.428239e+03 1.250000e-01 7.133725e-02
13 17 2.280759e+04 2.208737e+04 7.202176e+02 -3.732720e+04 2.331012e+03 3.125000e-02 6.989449e-02
14 16 2.269148e+04 2.202200e+04 6.694851e+02 -6.422924e+03 2.330858e+03 6.250000e-02 6.989218e-02
15 16 2.268491e+04 2.191173e+04 7.731819e+02 -1.150701e+04 2.205185e+03 6.250000e-02 6.798188e-02
16 18 2.243215e+04 2.171989e+04 7.122566e+02 -1.502461e+04 2.374696e+03 3.125000e-02 7.054637e-02
17 4 2.137470e+04 2.047716e+04 8.975439e+02 -2.657031e+03 2.176034e+03 1.000000e+00 6.753105e-02
18 21 2.103745e+04 2.022861e+04 8.088414e+02 -1.943974e+04 2.456300e+03 6.250000e-02 7.174825e-02
19 19 2.078813e+04 1.991482e+04 8.733038e+02 -2.105607e+04 2.054072e+03 3.125000e-02 6.561127e-02
20 18 2.076780e+04 1.995535e+04 8.124550e+02 -2.829645e+03 1.914904e+03 1.250000e-01 6.334964e-02
21 5 8.349851e+03 4.072309e+03 4.277541e+03 -7.252027e+05 1.847368e+03 6.250000e-02 6.222248e-02
22 9 7.392673e+03 4.257577e+03 3.135096e+03 -1.089879e+05 9.980348e+02 3.125000e-02 4.573445e-02
23 8 6.361708e+03 3.212121e+03 3.149587e+03 -1.137715e+04 3.108112e+03 1.000000e+00 8.070844e-02
24 10 5.999214e+03 4.325820e+03 1.673394e+03 -1.006587e+04 2.486881e+03 5.000000e-01 7.219351e-02
25 6 4.322378e+03 2.451385e+03 1.870993e+03 -1.820136e+04 2.047321e+03 2.500000e-01 6.550336e-02
26 7 3.408702e+03 1.489883e+03 1.918819e+03 -3.371630e+04 2.067273e+03 6.250000e-02 6.582178e-02
27 8 2.904210e+03 1.102836e+03 1.801374e+03 -3.019679e+03 1.741981e+03 2.500000e-01 6.042162e-02
28 10 2.473420e+03 6.410852e+02 1.832335e+03 -8.240099e+02 1.361728e+03 1.000000e+00 5.342148e-02
29 8 2.372635e+03 5.314257e+02 1.841209e+03 -1.729121e+02 5.267813e+02 1.000000e+00 3.322659e-02
30 10 2.355748e+03 5.082983e+02 1.847450e+03 -2.868934e+01 1.695337e+02 1.000000e+00 1.884945e-02
31 12 2.353178e+03 5.043131e+02 1.848864e+03 -4.471165e+00 4.875016e+01 1.000000e+00 1.010785e-02
32 14 2.352970e+03 5.036071e+02 1.849363e+03 -3.869172e-01 1.106428e+01 1.000000e+00 4.815398e-03
33 18 2.352967e+03 5.035482e+02 1.849419e+03 -5.827122e-03 1.169999e+00 1.000000e+00 1.565898e-03
Converged in 33 iterations.
Termination reason: Norm of the gradient less than tolerance
Final gradient norm: 0.019329861759867107
Final cost: 2352.967129738087
It cg_it cost misfit reg (g,dm) ||g||L2 alpha tolcg
1 1 1.510023e+00 1.163090e+00 3.469327e-01 -1.233778e+01 1.720213e+01 1.000000e+00 5.000000e-01
2 1 1.318297e+00 6.116926e-01 7.066045e-01 -5.274990e-01 1.701795e+00 1.000000e+00 3.145303e-01
3 1 1.312508e+00 7.090180e-01 6.034896e-01 -2.078706e-02 2.782278e-01 1.000000e+00 1.271772e-01
4 1 1.311205e+00 6.644890e-01 6.467155e-01 -4.281429e-03 1.235148e-01 1.000000e+00 8.473608e-02
5 1 1.311015e+00 6.816581e-01 6.293570e-01 -6.445201e-04 5.437428e-02 1.000000e+00 5.622191e-02
6 2 1.310981e+00 6.744765e-01 6.365042e-01 -1.141230e-04 2.004328e-02 1.000000e+00 3.413448e-02
7 1 1.310975e+00 6.773678e-01 6.336075e-01 -1.820925e-05 8.418872e-03 1.000000e+00 2.212258e-02
8 1 1.310974e+00 6.761869e-01 6.347875e-01 -3.036375e-06 3.218755e-03 1.000000e+00 1.367895e-02
9 2 1.310974e+00 6.766668e-01 6.343075e-01 -5.024350e-07 1.468645e-03 1.000000e+00 9.239900e-03
10 2 1.310974e+00 6.764714e-01 6.345029e-01 -8.313884e-08 5.584325e-04 1.000000e+00 5.697630e-03
11 2 1.310974e+00 6.765509e-01 6.344234e-01 -1.375349e-08 2.280737e-04 1.000000e+00 3.641216e-03
12 2 1.310974e+00 6.765185e-01 6.344557e-01 -2.276719e-09 9.281822e-05 1.000000e+00 2.322873e-03
13 2 1.310974e+00 6.765317e-01 6.344426e-01 -3.767860e-10 3.775877e-05 1.000000e+00 1.481555e-03
Converged in 13 iterations.
Termination reason: Norm of the gradient less than tolerance
Final gradient norm: 1.536157472308261e-05
Final cost: 1.3109742417005774
It cg_it cost misfit reg (g,dm) ||g||L2 alpha tolcg
1 1 1.496400e+00 1.151556e+00 3.448446e-01 -1.226354e+01 1.714864e+01 1.000000e+00 5.000000e-01
2 1 1.305693e+00 6.045611e-01 7.011318e-01 -5.232803e-01 1.697806e+00 1.000000e+00 3.146510e-01
3 1 1.300027e+00 6.999198e-01 6.001076e-01 -2.019908e-02 2.753946e-01 1.000000e+00 1.267252e-01
4 1 1.298778e+00 6.566579e-01 6.421199e-01 -4.086709e-03 1.208338e-01 1.000000e+00 8.394203e-02
5 1 1.298599e+00 6.732131e-01 6.253857e-01 -6.060228e-04 5.325166e-02 1.000000e+00 5.572521e-02
6 2 1.298567e+00 6.663489e-01 6.322178e-01 -1.054426e-04 1.944718e-02 1.000000e+00 3.367546e-02
7 1 1.298562e+00 6.690905e-01 6.294713e-01 -1.655956e-05 8.037392e-03 1.000000e+00 2.164924e-02
8 1 1.298561e+00 6.679800e-01 6.305810e-01 -2.715871e-06 3.050890e-03 1.000000e+00 1.333824e-02
9 2 1.298561e+00 6.684276e-01 6.301332e-01 -4.420894e-07 1.378110e-03 1.000000e+00 8.964523e-03
10 2 1.298561e+00 6.682468e-01 6.303140e-01 -7.198797e-08 5.209175e-04 1.000000e+00 5.511498e-03
11 2 1.298561e+00 6.683198e-01 6.302411e-01 -1.171807e-08 2.109703e-04 1.000000e+00 3.507485e-03
12 2 1.298561e+00 6.682903e-01 6.302705e-01 -1.908626e-09 8.517799e-05 1.000000e+00 2.228686e-03
13 2 1.298561e+00 6.683022e-01 6.302586e-01 -3.108011e-10 3.437194e-05 1.000000e+00 1.415752e-03
Converged in 13 iterations.
Termination reason: Norm of the gradient less than tolerance
Final gradient norm: 1.3871005909740155e-05
Final cost: 1.298560860719057
V-Rang
commented
6 months ago commit: 411197e79494d27c5dcf84d96d11a60af0615bc7 Following are results for the dirichlet B.C. poisson example: poisson_dirichlet_example.py:
It cg_it cost misfit reg (g,dm) ||g||L2 alpha tolcg
1 1 2.210116e-01 2.209794e-01 3.220179e-05 -5.705780e-02 1.073671e+01 1.000000e+00 5.000000e-01
2 2 2.195079e-01 2.194459e-01 6.198675e-05 -3.006081e-03 2.285346e+00 1.000000e+00 4.613605e-01
3 4 2.183350e-01 2.179219e-01 4.131137e-04 -2.346012e-03 1.843750e+00 1.000000e+00 4.143959e-01
4 6 2.181011e-01 2.173819e-01 7.192358e-04 -4.675449e-04 9.063891e-01 1.000000e+00 2.905506e-01
5 7 2.180940e-01 2.173489e-01 7.451106e-04 -1.413515e-05 2.297253e-01 1.000000e+00 1.462746e-01
6 9 2.180940e-01 2.173429e-01 7.510416e-04 -1.235915e-07 2.219220e-02 1.000000e+00 4.546368e-02
7 11 2.180940e-01 2.173430e-01 7.510033e-04 -8.725152e-11 5.367020e-04 1.000000e+00 7.070189e-03
Converged in 7 iterations.
Termination reason: Norm of the gradient less than tolerance
Final gradient norm: 2.0616229359872946e-06
Final cost: 0.2180939716312415
It cg_it cost misfit reg (g,dm) ||g||L2 alpha tolcg
1 1 2.159406e-01 2.159049e-01 3.565489e-05 -6.331131e-02 1.145710e+01 1.000000e+00 5.000000e-01
2 2 2.152079e-01 2.151567e-01 5.114422e-05 -1.465300e-03 1.907459e+00 1.000000e+00 4.080283e-01
3 3 2.148228e-01 2.147183e-01 1.044897e-04 -7.703075e-04 1.635545e+00 1.000000e+00 3.778278e-01
4 6 2.145433e-01 2.141501e-01 3.931678e-04 -5.590322e-04 1.315141e+00 1.000000e+00 3.388042e-01
5 7 2.145405e-01 2.141397e-01 4.008192e-04 -5.613884e-06 1.351815e-01 1.000000e+00 1.086229e-01
6 10 2.145405e-01 2.141378e-01 4.026468e-04 -3.617218e-08 1.416015e-02 1.000000e+00 3.515577e-02
7 11 2.145405e-01 2.141378e-01 4.026401e-04 -6.779171e-12 1.085220e-04 1.000000e+00 3.077666e-03
Converged in 7 iterations.
Termination reason: Norm of the gradient less than tolerance
Final gradient norm: 5.145244891225999e-07
Final cost: 0.21454045138824673
uvilla
commented
6 months ago Something regarding the true parameter seems wrong in the Poisson Dirichlet BC example
V-Rang
commented
6 months ago commit: 231c29919667bf33ae31943e9d48435dc57fe36f
The previous post has results using m_true interpolated to be 0 over the mesh. The example has been revised using:
m_true.interpolate(lambda x: np.log(2 + 7*( ( (x[0] - 0.5)**2 + (x[1] - 0.5)**2)**0.5 > 0.2)) )
Following are revised results for the dirichlet B.C. poisson example: poisson_dirichlet_example.py:
It cg_it cost misfit reg (g,dm) ||g||L2 alpha tolcg
1 1 2.081549e+01 2.076407e+01 5.142130e-02 -2.327885e+01 2.314143e+02 1.000000e+00 5.000000e-01
2 2 4.767247e+00 4.106350e+00 6.608970e-01 -3.133430e+01 1.705423e+02 1.000000e+00 5.000000e-01
3 4 3.137648e+00 1.722906e+00 1.414742e+00 -3.311442e+00 4.131988e+01 1.000000e+00 4.225562e-01
4 5 3.037861e+00 1.554498e+00 1.483363e+00 -2.005600e-01 9.735901e+00 1.000000e+00 2.051129e-01
5 7 3.035789e+00 1.524561e+00 1.511228e+00 -4.158589e-03 1.640894e+00 1.000000e+00 8.420641e-02
6 9 3.035782e+00 1.525645e+00 1.510137e+00 -1.407674e-05 6.706989e-02 1.000000e+00 1.702428e-02
7 10 3.035782e+00 1.525544e+00 1.510238e+00 -8.118817e-08 5.597232e-03 1.000000e+00 4.918035e-03
8 11 3.035782e+00 1.525550e+00 1.510232e+00 -9.319779e-10 4.104822e-04 1.000000e+00 1.331840e-03
Converged in 8 iterations.
Termination reason: Norm of the gradient less than tolerance
Final gradient norm: 5.321298717835267e-05
Final cost: 3.0357821176877158
It cg_it cost misfit reg (g,dm) ||g||L2 alpha tolcg
1 1 2.070520e+01 2.065391e+01 5.129169e-02 -2.327944e+01 2.311846e+02 1.000000e+00 5.000000e-01
2 2 4.756430e+00 4.099402e+00 6.570276e-01 -3.114331e+01 1.700321e+02 1.000000e+00 5.000000e-01
3 4 3.131445e+00 1.719935e+00 1.411510e+00 -3.301555e+00 4.112825e+01 1.000000e+00 4.217846e-01
4 5 3.034989e+00 1.558796e+00 1.476192e+00 -1.939070e-01 9.608657e+00 1.000000e+00 2.038693e-01
5 7 3.032952e+00 1.528925e+00 1.504027e+00 -4.085692e-03 1.625483e+00 1.000000e+00 8.385168e-02
6 9 3.032945e+00 1.530024e+00 1.502921e+00 -1.371305e-05 6.613065e-02 1.000000e+00 1.691305e-02
7 10 3.032945e+00 1.529923e+00 1.503022e+00 -8.208561e-08 5.547424e-03 1.000000e+00 4.898535e-03
8 11 3.032945e+00 1.529929e+00 1.503016e+00 -9.622087e-10 4.211070e-04 1.000000e+00 1.349637e-03
Converged in 8 iterations.
Termination reason: Norm of the gradient less than tolerance
Final gradient norm: 5.4210885660070596e-05
Final cost: 3.032944864602089
V-Rang
commented
6 months ago commit: 6b24e130c2013f2e6276800e7e930c0bf7908f7c
Results for Poisson example on a square mesh with Dirichlet BC on top (u=1) and bottom (u=0) and Neumann BC on sides:
It cg_it cost misfit reg (g,dm) ||g||L2 alpha tolcg
1 1 2.106268e+00 1.774915e+00 3.313531e-01 -7.333175e+00 4.629337e+01 1.000000e+00 5.000000e-01
2 3 1.658591e+00 9.928253e-01 6.657658e-01 -9.008020e-01 1.279815e+01 1.000000e+00 5.000000e-01
3 4 1.652912e+00 9.776138e-01 6.752985e-01 -1.134766e-02 2.052329e+00 1.000000e+00 2.105543e-01
4 5 1.652713e+00 9.701717e-01 6.825415e-01 -3.981446e-04 3.109226e-01 1.000000e+00 8.195335e-02
5 6 1.652710e+00 9.707168e-01 6.819936e-01 -5.754615e-06 3.561622e-02 1.000000e+00 2.773732e-02
6 7 1.652710e+00 9.706608e-01 6.820496e-01 -1.679530e-08 1.772936e-03 1.000000e+00 6.188525e-03
7 9 1.652710e+00 9.706618e-01 6.820486e-01 -6.459187e-11 7.606230e-05 1.000000e+00 1.281815e-03
Converged in 7 iterations.
Termination reason: Norm of the gradient less than tolerance
Final gradient norm: 9.043502590837493e-06
Final cost: 1.6527103859730952
It cg_it cost misfit reg (g,dm) ||g||L2 alpha tolcg
1 1 2.106574e+00 1.782573e+00 3.240008e-01 -7.193400e+00 4.593610e+01 1.000000e+00 5.000000e-01
2 2 1.647535e+00 9.850315e-01 6.625039e-01 -9.233121e-01 1.341018e+01 1.000000e+00 5.000000e-01
3 5 1.641720e+00 9.692772e-01 6.724427e-01 -1.163518e-02 2.058922e+00 1.000000e+00 2.117107e-01
4 6 1.641679e+00 9.646987e-01 6.769799e-01 -8.053698e-05 1.426598e-01 1.000000e+00 5.572805e-02
5 6 1.641678e+00 9.646532e-01 6.770252e-01 -2.096055e-07 6.521994e-03 1.000000e+00 1.191552e-02
6 7 1.641678e+00 9.646461e-01 6.770324e-01 -3.100893e-10 2.836787e-04 1.000000e+00 2.485057e-03
Converged in 6 iterations.
Termination reason: Norm of the gradient less than tolerance
Final gradient norm: 1.236504498323809e-05
Final cost: 1.6416784640711513
git commit hash: commit 13388d1f620c2c4ae849d84d0e3ef7fea40216db
Following are the validation plots to check for correctness of modelVerify for the PACT and poisson examples. Plots are made for the following cases:
qPACT Problem:
Number of processes = 1
Finite difference check with misfit only = True
Finite difference check with misfit only = False
output of iNCG
image of True parameter and estimated parameter
Number of processes = 4
Finite difference check with misfit only = True
Finite difference check with misfit only = False
output of iNCG
image of True parameter and estimated parameter
Poisson Example with Robin BC
Number of processes = 1
Finite difference check with misfit_only = True
Finite difference check with misifit_only = False
output of iNCG
image of True parameter and estimated parameter
Number of processes = 4
Finite difference check with misfit_only = True
Finite difference check with misfit_only = False
output of iNCG
image of True parameter and estimated parameter