tmp commit - toward 0.0.1

problems/laplacian_optimal_control_parametric.py

@@ -0,0 +1,55 @@
+import numpy as np
+import torch
+from pina.problem import Problem
+from pina.segment import Segment
+from pina.parametricproblem2d import ParametricProblem2D
+
+bc = {
+    'y': (
+        (Segment((0, 0), (4, 0)), lambda x: torch.ones(x.shape[0], 1)),
+        (Segment((4, 0), (4, 1)), lambda x: torch.ones(x.shape[0], 1)),
+        (Segment((4, 1), (0, 1)), lambda x: torch.ones(x.shape[0], 1)),
+        (Segment((0, 1), (0, 0)), lambda x: torch.ones(x.shape[0], 1)),
+    ),
+    'p': (
+        (Segment((0, 0), (4, 0)), lambda x: torch.zeros(x.shape[0], 1)),
+        (Segment((4, 0), (4, 1)), lambda x: torch.zeros(x.shape[0], 1)),
+        (Segment((4, 1), (0, 1)), lambda x: torch.zeros(x.shape[0], 1)),
+        (Segment((0, 1), (0, 0)), lambda x: torch.zeros(x.shape[0], 1)),
+    )
+}
+
+# optimal control parameters and data
+alpha = 1e-5
+# yd = 10*x[:, 0]*(1-x[:, 0])*x[:, 1]*(1-x[:, 1])
+# three variables 
+# state y = f[0]
+# control u = f[1]
+# adjoint p = f[2]
+
+# the three variables
+
+def adjoint_eq(x, f):
+    grad_x, grad_y = Problem.grad(f['p'], x)[:, :2].T
+    grad_xx = Problem.grad(grad_x, x)[:, 0]
+    grad_yy = Problem.grad(grad_y, x)[:, 1]
+    return - grad_xx - grad_yy  - f['y'] + 1*(x[:, 0] <= 1) + x[:, 2]*(x[:, 0] > 1)
+
+def control_eq(x, f):
+    return alpha*f['u'] - f['p']
+
+def state_eq(x, f):
+    grad_x, grad_y = Problem.grad(f['y'], x)[:, :2].T
+    grad_xx = Problem.grad(grad_x, x)[:, 0]
+    grad_yy = Problem.grad(grad_y, x)[:, 1]
+    return - grad_xx - grad_yy  - f['u']
+
+def equation(x, f):
+    return state_eq(x, f) + control_eq(x, f) + adjoint_eq(x, f)
+
+laplace = ParametricProblem2D(
+        variables=['y', 'u', 'p'], 
+        bc=bc,
+        domain_bound=np.array([[0, 4],[0, 1]]),
+        params_bound=np.array([[0.5, 2.5]]))
+laplace.equation = equation