implemented MLE for alpha and beta with the M+K kernel

optimal_alpha_beta/beam.pro

+gpinit =
+{
+  type = GPInit;
+
+  mesh =
+  {
+    type = gmsh;
+    file = beam_fine2.msh;
+  };
+
+  coarseMesh =
+  {
+    type = gmsh;
+    file = beam_coarse.msh;
+  };
+
+  nodeGroups = [ lb, rb, tm ];
+
+  lb =
+  {
+    xtype = min;
+    ytype = min;
+  };
+
+  rb =
+  {
+    xtype = max;
+    ytype = min;
+  };
+
+  tm =
+  {
+    ytype = max;
+    xtype = mid;
+  };
+};
+
+gpsolver =
+{
+  type = GPSolver;
+
+  nsteps = 1;
+  storeMatrix = True;
+  storeConstraints = True;
+  getUnitMassMatrix = True;
+};
+
+gpsampler =
+{
+  type = GPSampler;
+
+  nsample = 3;
+  seed = 0;
+};
+
+model =
+{
+  type = Multi;
+
+  models = [ elastic, gp, diri, neum ];
+
+  elastic =
+  {
+    type = XElastic;
+
+    elements = all;
+
+    young = 10000.;
+    thickness = 0.2;
+    poisson = 0.2;
+    rho = 1;
+    state = plane_stress;
+
+    shape =
+    {
+      type = Triangle3;
+      intScheme = Gauss1;
+    };
+  };
+
+  gp =
+  {
+    type = GP;
+
+    obsNoise = 1e-10;
+    alpha = opt;
+
+    prior = M+K;
+    alpha = 1;
+    beta = 1;
+
+    shape =
+    {
+      type = Triangle3;
+      intScheme = Gauss1;
+    };
+  };
+
+  diri =
+  {
+    type = Dirichlet;
+
+    groups = [ lb, lb, rb ];
+    dofs   = [ dx, dy, dy ];
+    values = [ 0., 0., 0. ];
+  };
+
+  neum =
+  {
+    type = Neumann;
+
+    groups = [ tm ];
+    dofs   = [ dy ];
+    values = [ -1. ];
+  };
+};