Updated Domain inverse

- USA Problem with forward problem and inverse problem

examples/inverse_problems_2d/domain_inverse_cd2d/USA/cd2d_inverse_usa_example.py

@@ -10,7 +10,9 @@ def usa_boundary(x, y):
     """
     This function will return the boundary value for given component of a boundary
     """
-    val = 20 * np.exp(-0.1 * y) * np.cos(x)
+    # val = 20 * np.exp(-0.1 * y) * np.cos(x)
+    val = np.exp(-0.1 * y) * np.cos(x)
+
     return val
 
 
@@ -22,15 +24,25 @@ def rhs(x, y):
     # return -y * np.sin(x * y) * np.tanh(8 * x * y) + 8 * y * np.cos(x * y) / np.cosh(8 * x * y)**2 + 10 * (x**2 + y**2) * \
     #       (16 * np.sin(x * y) / np.cosh(8 * x * y)**2 + np.cos(x * y) * np.tanh(8 * x * y) + 128 * np.cos(x * y) * np.tanh(8 * x * y) / np.cosh(8 * x * y)**2) * np.sin(x) * np.cos(y)
 
-    return (196.0 - 396.0 * np.sin(x) ** 2) * np.exp(-0.2 * y)
+    # return (196.0 - 396.0 * np.sin(x) ** 2) * np.exp(-0.2 * y)
+
+    return (
+        (
+            -0.1 * x * np.sin(x * y) * np.cos(x)
+            - y * np.sin(x) * np.sin(x * y)
+            + 1.99 * np.cos(x) * np.cos(x * y)
+        )
+        * np.exp(-0.1 * y)
+        * np.sin(x)
+    )
 
 
 def exact_solution(x, y):
     """
     This function will return the exact solution at a given point
     """
 
-    val = 20 * np.exp(-0.1 * y) * np.cos(x)
+    val = np.exp(-0.1 * y) * np.cos(x)
 
     return val
 
@@ -67,5 +79,5 @@ def get_inverse_params_actual_dict(x, y):
     This function will return a dictionary of inverse parameters
     """
     # Initial Guess
-    eps = 10 * np.exp(-0.1 * y) * np.cos(x)
+    eps = np.sin(x) * np.cos(x * y)
     return {"eps": eps}

examples/inverse_problems_2d/domain_inverse_cd2d/USA/input_inverse_domain.yaml

@@ -1,6 +1,6 @@
 # input file for inverse problems (domain)
 experimentation:
-  output_path: "output/usa"
+  output_path: "output/usa_2"
 
 geometry:
   mesh_generation_method: "external"
@@ -22,18 +22,18 @@ geometry:
     boundary_sampling_method: "uniform"  # "uniform"
 
 fe:
-  fe_order: 5 
+  fe_order: 4 
   fe_type: "jacobi"   #"jacobi"
   quad_order:  5    
   quad_type: "gauss-jacobi"  # "gauss-jacobi,
 
 pde:
   beta: 10
 model:
-  model_architecture: [2, 30,30,30,30, 2] # output is made as 2 to accomodate the inverse param in the output
+  model_architecture: [2, 30,30,30, 2] # output is made as 2 to accomodate the inverse param in the output
   activation: "tanh"
   use_attention: False
-  epochs: 100000
+  epochs: 20000
   dtype: "float32"
   set_memory_growth: True
   learning_rate:

examples/inverse_problems_2d/domain_inverse_cd2d/USA/rhs.ipynb

@@ -12,8 +12,8 @@
     "x, y, u, eps = sp.symbols('x y u eps')\n",
     "\n",
     "# Define the function\n",
-    "u = 20 * sp.exp (-0.1 * y) * sp.cos (x)\n",
-    "eps = 10 * sp.cos(x) * sp.exp(-0.1 * y)\n",
+    "u =  sp.exp (-0.1 * y) * sp.cos (x)\n",
+    "eps =  sp.cos(x*y) * sp.sin(x)\n",
     "# compute the gradients\n",
     "u_x = sp.diff(u, x)\n",
     "u_y = sp.diff(u, y)\n",
@@ -38,7 +38,36 @@
     "import inspect\n",
     "\n",
     "# obtain the source code of the function\n",
-    "print(inspect.getsource(f_func))\n"
+    "source_code = inspect.getsource(f_func)\n",
+    "\n",
+    "# create a dictionary \n",
+    "\n",
+    "replace_dict = {\"exp\": \"np.exp\", \"cos\": \"np.cos\", \"sin\": \"np.sin\", \"sqrt\": \"np.sqrt\", \"log\": \"np.log\"}\n",
+    "\n",
+    "# replace the keys with the values in the source code\n",
+    "for key, value in replace_dict.items():\n",
+    "    source_code = source_code.replace(key, value)\n",
+    "\n",
+    "# print the source code\n",
+    "print(source_code)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x = np.linspace(-1, 1, 100)\n",
+    "y = np.linspace(-1, 1, 100)\n",
+    "\n",
+    "X, Y = np.meshgrid(x, y)\n",
+    "\n",
+    "U = np.cos(X*Y) * np.sin(X)\n",
+    "\n",
+    "plt.contourf(X, Y, U)\n",
+    "plt.colorbar()\n",
+    "plt.show()"
    ]
   },
   {