Merge pull request #4 from cmgcds/inverse_problems

Added examples for solving inverse problems using FastVPINNs.

examples/inverse_problems_2d/cd2d/cd2d_inverse_circle_example.py

@@ -0,0 +1,92 @@
+# Example file for the poisson problem
+# Path: examples/poisson.py
+# file contains the exact solution, rhs and boundary conditions for the poisson problem
+# Actual Solution : sin(X) * cos(Y) * exp(-1.0 * eps * (X**2 + Y**2))
+import numpy as np
+import tensorflow as tf
+
+
+
+
+def left_boundary(x, y):
+    """
+    This function will return the boundary value for given component of a boundary
+    """
+    val = np.ones_like(x) * 0.0
+    return val
+
+def right_boundary(x, y):
+    """
+    This function will return the boundary value for given component of a boundary
+    """
+    val = np.ones_like(x) * 0.0
+    return val
+
+def top_boundary(x, y):
+    """
+    This function will return the boundary value for given component of a boundary
+    """
+    val = np.ones_like(x) * 0.0
+    return val
+
+def bottom_boundary(x, y):
+    """
+    This function will return the boundary value for given component of a boundary
+    """
+    val = np.ones_like(x) * 0.0
+    return val
+
+def rhs(x, y):
+    """
+    This function will return the value of the rhs at a given point
+    """
+
+    # 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 10.0 * np.ones_like(x)
+
+
+def exact_solution(x, y):
+    """
+    This function will return the exact solution at a given point
+    """
+
+    val = np.ones_like(x) * 0.0
+
+    return val
+
+def get_boundary_function_dict():
+    """
+    This function will return a dictionary of boundary functions
+    """
+    return {1000: bottom_boundary, 1001: right_boundary, 1002: top_boundary, 1003: left_boundary}
+
+def get_bound_cond_dict():
+    """
+    This function will return a dictionary of boundary conditions
+    """
+    return {1000: "dirichlet", 1001: "dirichlet", 1002: "dirichlet", 1003: "dirichlet"}
+
+def get_bilinear_params_dict():
+    """
+    This function will return a dictionary of bilinear parameters
+    """
+
+    eps = 0.1 # will not be used in the loss function, as it will be replaced by the predicted value of NN
+    b1 = 1
+    b2 = 0
+    c = 0.0
+
+    return {"eps": eps, "b_x": b1, "b_y": b2, "c": c}
+
+
+
+def get_inverse_params_actual_dict(x, y):
+    """
+    This function will return a dictionary of inverse parameters
+    """
+    # Initial Guess
+    eps = 0.5 * (np.sin(x) + np.cos(y))
+    return {"eps": eps}

examples/inverse_problems_2d/cd2d/input_inverse_domain.yaml

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+# input file for inverse problems (domain)
+experimentation:
+  output_path: "output/inverse/circle_1"
+
+geometry:
+  mesh_generation_method: "external"
+  internal_mesh_params:
+    x_min: 0
+    x_max: 1
+    y_min: 0
+    y_max: 1
+    n_cells_x: 20
+    n_cells_y: 20
+    n_boundary_points: 1500
+    n_test_points_x: 100
+    n_test_points_y: 100
+
+  mesh_type: "quadrilateral"
+  external_mesh_params:
+    mesh_file_name: "circle_quad.mesh"  # should be a .mesh file
+    boundary_refinement_level: 2
+    boundary_sampling_method: "uniform"  # "uniform" or "lhs"
+
+fe:
+  fe_order: 3  
+  fe_type: "jacobi"   #"parmoon", "legendre" and "legendre".
+  quad_order:  5    
+  quad_type: "gauss-jacobi"  # "gauss-jacobi, gauss-legendre, gauss-lobatto"
+
+pde:
+  beta: 10
+model:
+  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: 50000
+  dtype: "float32"
+  set_memory_growth: True
+  learning_rate:
+    initial_learning_rate: 0.003
+    use_lr_scheduler: False
+    decay_steps: 1000
+    decay_rate: 0.98
+    staircase: True
+
+logging:
+  update_progress_bar: 100
+  update_console_output: 5000
+  update_solution_images: 5000
+
+inverse:
+  num_sensor_points: 500
+
+  sensor_data_file: "fem_output_circle2.csv"
+
+wandb:
+  use_wandb: True
+  project_name: "New_Inverse_Complex_updated"
+  wandb_run_prefix: "Test_Gear"
+  entity: "starslab-iisc" 
+
+additional:
+  run_by: "Divij"
+  System: "23"
+