Merge pull request #1 from EMSL-Computing/flow-lal

updating codes and markdowns

Author: mlmamud

examples/example_6_flow_2d_numerical_on_XCT.ipynb

@@ -36,7 +36,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 3,
    "id": "1a7cff2d-f2ab-41a5-a5cf-402c6e32c54a",
    "metadata": {},
    "outputs": [],
@@ -65,13 +65,18 @@
    "id": "3bac17eb-240a-4fc6-9bd6-72c651691210",
    "metadata": {},
    "source": [
-    "## Loading XCT Data\n",
-    "In this section, we load the XCT data from the file for domain and variable declarations and plot normalized XCT data."
+    "## Loading and Processing XCT Data\n",
+    "In this section, we load the X-ray computed tomography (XCT) data from the specified file and perform several preprocessing steps necessary for subsequent analysis. ### Steps Involved:\n",
+    "1. *Loading XCT Data*\n",
+    "2. *Normalization*\n",
+    "3. *Plotting the Normalized XCT Data*\n",
+    "4. *Determining Data Dimensions*\n",
+    "5. *Generating Spatial Grid*"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 5,
    "id": "3cd0029a-3f2e-4b48-b0e0-11704e54c178",
    "metadata": {},
    "outputs": [
@@ -87,15 +92,15 @@
     }
    ],
    "source": [
-    "# Loading XCT data from the file for domain and variable declarations\n",
+    "#%% loading XCT data from the file for domain and variable declarations\n",
     "data_dir = \"../example_outputs/\"\n",
     "results_dir = \"../example_outputs/flow/\"\n",
-    "data = np.load(data_dir + 'micromodel.npy')\n",
     "\n",
-    "normalized_xct_data = data/np.max(data)\n",
-    "plot_2d_xct_data_seg(normalized_xct_data, results_dir)\n",
+    "data = np.load(data_dir + 'micromodel.npy')                      # Load the XCT data\n",
+    "normalized_xct_data = data/np.max(data)                          # Normalize the data to [0, 1]\n",
+    "plot_2d_xct_data_seg(normalized_xct_data, results_dir)           # Plot the normalized XCT data\n",
     "\n",
-    "# Dimensions of the data\n",
+    "# Determine the dimensions of the data\n",
     "data_width, data_height = len(normalized_xct_data), len(normalized_xct_data) \n",
     "\n",
     "# Generate evenly spaced points in the interval [0, 1] for both dimensions\n",
@@ -115,13 +120,14 @@
    "id": "2ee2bebb-6488-4b55-877e-a721df0ebdbb",
    "metadata": {},
    "source": [
-    "## Define Boundary Conditions and Input Parameters"
+    "## Permeability Field Generation Based on XCT Data\n",
+    "In this section, we generate a permeability field from the XCT data. Permeability is a key property in modeling fluid flow through porous media, and it varies depending on the material's structure, which is captured by the XCT data. The XCT data provides a spatial representation of the material, and we translate this into a spatially varying permeability field based on predefined permeability values for different regions (e.g., pores and soil matrix)."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
-   "id": "024e83f8-4ecc-4d75-97c3-a7256eb76b98",
+   "execution_count": 10,
+   "id": "c374e26f-ca83-4b87-b583-2fe8b2e890e7",
    "metadata": {},
    "outputs": [
     {
@@ -135,6 +141,44 @@
      "output_type": "display_data"
     }
    ],
+   "source": [
+    "# Define the minimum permeability (soil matrix) and maximum permeability (pores)\n",
+    "k_min = 1E-25        # Assigned Permeability of soil matrix corresponding to the lower XCT values (1 𝑚^2/s)\n",
+    "k_max = 1E-2         # Assigned Permeability of pores corresponding to the higher XCT values (1 𝑚^2/s)\n",
+    "\n",
+    "# Find the minimum and maximum values in the normalized XCT data\n",
+    "xct_val_min = np.min(normalized_xct_data)\n",
+    "xct_val_max = np.max(normalized_xct_data)\n",
+    "\n",
+    "# Initialize a permeability field with the same dimensions as the XCT data,\n",
+    "#and assign the minimum permeability value (k_min) to all elements\n",
+    "perm_field_as_XCT = np.full_like(normalized_xct_data, fill_value = k_min)  \n",
+    "\n",
+    "# Assign the maximum permeability value (k_max) to elements in the field \n",
+    "# that corresponds to the maximum XCT values (pores)\n",
+    "perm_field_as_XCT[normalized_xct_data == np.max(normalized_xct_data)] = k_max  \n",
+    "\n",
+    "# Flip the permeability field upside down to match the required orientation\n",
+    "perm_field = np.flipud(perm_field_as_XCT)\n",
+    "\n",
+    "# Plot the final permeability field\n",
+    "plot_2d_permeability_seg(X, Y, perm_field, results_dir)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "51e225c3-740e-4014-9cc4-ac312993870b",
+   "metadata": {},
+   "source": [
+    "## Define Boundary Conditions and Input Parameters for PINN solution"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "024e83f8-4ecc-4d75-97c3-a7256eb76b98",
+   "metadata": {},
+   "outputs": [],
    "source": [
     "# Define the boundary conditions and input parameters\n",
     "P1 = 2.0             # at x = 0 for all y_b1, Dirichlet boundary at the left (kPa)  \n",
@@ -147,39 +191,25 @@
     "norm_P1 = P1 / max_P\n",
     "norm_P2 = P2 / max_P\n",
     "\n",
-    "# Permeability field generation based on the XCT data: \n",
-    "k_min = 1E-25        # Assigned Permeability of soil matrix corresponding to the lower XCT values (1 𝑚^2/s)\n",
-    "k_max = 1E-2         # Assigned Permeability of pores corresponding to the higher XCT values (1 𝑚^2/s)\n",
-    "\n",
-    "# Find the minimum and maximum values of xct_xy_slice\n",
-    "xct_val_min = np.min(normalized_xct_data)\n",
-    "xct_val_max = np.max(normalized_xct_data)\n",
-    "\n",
-    "perm_field_as_XCT = np.full_like(normalized_xct_data, fill_value = k_min)  \n",
-    "perm_field_as_XCT[normalized_xct_data == np.max(normalized_xct_data)] = k_max   \n",
-    "perm_field = np.flipud(perm_field_as_XCT)\n",
-    "plot_2d_permeability_seg(X, Y, perm_field, results_dir)\n",
-    "\n",
     "# Input parameters: Dynamic viscosity (mu), Density of water (rho), and Permeability (k). \n",
     "rho = 998                               # Density of water in kg/m³\n",
     "mu = 1.002E-6                           # Dynamic viscosity (kPa·s)\n",
     "coeff = perm_field * rho / mu           # Coefficient of Permeability calcualtions (k*rho/mu)\n",
     "max_coeff = np.max(coeff)               # Coefficient of Permeability calcualtions (k*rho/mu)\n",
-    "norm_coeff = coeff/max_coeff\n",
-    "#coeff = np.ones((nx, ny))              # check with uniform permeability distribution"
+    "norm_coeff = coeff/max_coeff"
    ]
   },
   {
    "cell_type": "markdown",
    "id": "7a7d55e5-d839-4e9b-83f8-8d39b1d874a7",
    "metadata": {},
    "source": [
-    "## Plot for Boundary Conditions and Collocation for Training"
+    "## Plot for Boundary Conditions and Collocation points associated with PINN"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 11,
    "id": "e91923e4-1822-497c-bb4b-ba6aa8a0dd16",
    "metadata": {},
    "outputs": [
@@ -221,7 +251,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": null,
    "id": "95f713ab-d991-4d16-b252-b545943db5e5",
    "metadata": {},
    "outputs": [
@@ -236,29 +266,7 @@
       "epoch =  2000\n",
       "-------------------------------------------------------\n",
       "PINN training started...\n",
-      "   Epoch=0\t loss=6.020e-01\n",
-      "   Epoch=100\t loss=2.993e-02\n",
-      "   Epoch=200\t loss=3.168e-03\n",
-      "   Epoch=300\t loss=6.665e-04\n",
-      "   Epoch=400\t loss=1.915e-04\n",
-      "   Epoch=500\t loss=8.662e-05\n",
-      "   Epoch=600\t loss=5.082e-05\n",
-      "   Epoch=700\t loss=3.547e-05\n",
-      "   Epoch=800\t loss=2.796e-05\n",
-      "   Epoch=900\t loss=2.355e-05\n",
-      "   Epoch=1000\t loss=2.049e-05\n",
-      "   Epoch=1100\t loss=1.816e-05\n",
-      "   Epoch=1200\t loss=1.631e-05\n",
-      "   Epoch=1300\t loss=1.482e-05\n",
-      "   Epoch=1400\t loss=1.361e-05\n",
-      "   Epoch=1500\t loss=1.261e-05\n",
-      "   Epoch=1600\t loss=1.176e-05\n",
-      "   Epoch=1700\t loss=1.103e-05\n",
-      "   Epoch=1800\t loss=1.038e-05\n",
-      "   Epoch=1900\t loss=9.782e-06\n",
-      "   Epoch=2000\t loss=9.231e-06\n",
-      "PINN training done!\n",
-      "   Best Epoch = 2000\tBest Loss = 9.231e-06\n"
+      "   Epoch=0\t loss=6.020e-01\n"
      ]
     }
    ],