Change M(c) to mimick ACCC

calculations/PMM.py

@@ -24,16 +24,19 @@ train_ks = torch.tensor(train_data['k'].to_numpy(), dtype=torch.complex128)
 N = 5
 
 # initialize random Hamiltonians
-H0 = torch.randn(N, N, dtype=torch.complex128)
+H0 = 0.1 * torch.randn(N, N, dtype=torch.complex128)
-H0 = (H0 + torch.transpose(H0, 0, 1)).requires_grad_() # symmetric
+H0 = (H0 + H0.T).requires_grad_() # symmetric
-H1 = torch.randn(N, N, dtype=torch.complex128)
+H1 = 0.1 * torch.randn(N, N, dtype=torch.complex128)
-H1 = (H1 + torch.transpose(H1, 0, 1)).requires_grad_() # symmetric
+H1 = (H1 + H1.T).requires_grad_() # symmetric
 
-def enforce_ep():  # enforce exceptional point at c=0
+def get_H(c):
+    H = H0 + np.sqrt(complex(c)) * H1
+    return H
+
+def enforce_ep():  # enforce threshold point at c=0
     with torch.no_grad():
-        H0[0:2, :] = 0
+        H0[0, :] = 0
-        H0[:, 0:2] = 0
+        H0[:, 0] = 0
-        H0[0, 1] = 1
 
 enforce_ep()
 
@@ -50,31 +53,20 @@ c_steps = np.delete(c_steps, 0) # remove the first point (c=0)
 optimizer = torch.optim.Adam([H0, H1])
 
 # Training loop
-epochs = 200000
+epochs = 20000
 for epoch in range(epochs):
     ks = torch.empty(len(train_data), dtype=torch.complex128)
-    kvs = torch.empty(len(train_data), dtype=torch.complex128)
     current_k = 0.0 # start at the threshold
-    current_kv = 0.0 # start at the threshold
     for c in c_steps:
-        H = H0 + c * H1
+        H = get_H(c)
         evals = torch.linalg.eigvals(H)
         current_k = evals[torch.argmin(torch.abs(evals - current_k))]
-        evals = evals[evals != current_k] # remove selected k
-        current_kv = evals[torch.argmin(torch.abs(evals - current_kv))]
         if np.any(c == train_cs):
             index = np.where(c == train_cs)[0][0]
             ks[index] = current_k
-            kvs[index] = current_kv
 
     loss = ((ks - train_ks).abs() ** 2).sum()
 
-    # push virtual states towards (-)bound and then to the imaginary axis
-    if epoch/epochs < 0.25:
-        loss += ((kvs + train_ks).abs() ** 2).sum()
-    else:
-        loss += (kvs.imag ** 2).sum()
-
     if epoch % 1000 == 0:
         print(f"Training {(epoch+1)/epochs:.1%} \t Loss: {loss}")
 
@@ -82,8 +74,6 @@ for epoch in range(epochs):
     optimizer.zero_grad()
     loss.backward()
     optimizer.step()
-
-    # Enforce exceptional point constraints
     enforce_ep()
 
 # %%
@@ -93,7 +83,7 @@ exact_k = torch.tensor(df['k'].values, dtype=torch.complex128)
 pred_ks = np.empty(len(df), dtype=np.complex128)
 with torch.no_grad():
     for (index, (c, k)) in enumerate(zip(all_c, exact_k)):
-        H = H0 + c * H1
+        H = get_H(c)
         evals = torch.linalg.eigvals(H)
         i = torch.argmin(torch.abs(evals - k)) # TODO: more robust way to identify the eigenvector
         pred_ks[index]= evals[i]
@@ -144,7 +134,7 @@ ax.set_title('c = ?')
 
 # Animation function
 def update(c):
-    H = H0 + c * H1
+    H = get_H(c)
     evals = torch.linalg.eigvals(H).detach().numpy()
     sc.set_offsets(np.c_[np.real(evals), np.imag(evals)])
     ax.set_title(f'c = {c:.2f}')