Added files

pinns_practice/basic_pinn.py

@@ -0,0 +1,67 @@
+import torch
+import torch.nn as nn
+import matplotlib.pyplot as plt
+
+class BasicPINN(nn.Module):
+    def __init__(self):
+        super().__init__()
+        self.net = nn.Sequential(
+            nn.Linear(1, 20),
+            nn.Tanh(), # for RELU 2 derivative is always 0, so use Tanh
+            nn.Linear(20, 20),
+            nn.Tanh(),
+            nn.Linear(20, 1)
+        )
+
+    def forward(self, x):
+        x =self.net(x)
+        return x
+
+model = BasicPINN()
+optimizer = torch.optim.Adam(model.parameters(), lr=0.01)
+
+for epoch in range(2000):
+    optimizer.zero_grad()
+
+    t_physics = torch.rand(100, 1).requires_grad_(True)  # requires_grad=True important for derivatives
+
+    y_pred = model(t_physics)
+
+    # y = e ^ (-2t)
+    # dy/dt = -2y
+
+    # Calculating derivative dy/dt
+    # We use PyTorch auto-differentiation to find the rate of change of y_pred with respect to t_physics.
+    dy_dt = torch.autograd.grad(
+        outputs=y_pred, # What we differentiate, y
+        inputs=t_physics, # What we differentiate with respect to, (time, t)
+        grad_outputs=torch.ones_like(y_pred), # vector from 1, for 100 examples, calculates gradients independently
+        create_graph=True, # history of calculations, critical for PINNs
+    )[0]
+
+    # Physical Loss dy/dt + 2y = 0
+    physical_loss = torch.mean((dy_dt + 2 * y_pred) ** 2)
+
+    # Initial condition, t = 0 -> 1.0
+    t_0 = torch.zeros(1, 1)
+    y_0_pred = model(t_0)
+    initial_condition_loss = torch.mean((y_0_pred - 1.0) ** 2)
+
+    loss = physical_loss + initial_condition_loss
+    loss.backward()
+    optimizer.step()
+
+    if epoch % 200 == 0:
+        print(f"Epoch {epoch}, Loss: {loss.item():.5f}")
+
+t_test = torch.linspace(0, 2, 100).view(-1, 1)
+with torch.no_grad():
+    y_test_pred = model(t_test)
+
+
+y_exact = torch.exp(-2 * t_test)
+plt.plot(t_test.numpy(), y_test_pred.numpy(), label="PINN model", color="red", linestyle="--")
+plt.plot(t_test.numpy(), y_exact.numpy(), label="Exact solution (Math)", alpha=0.5)
+plt.legend()
+plt.title("Solving the differential equation!!")
+plt.show()