82 lines
2.4 KiB
Python
82 lines
2.4 KiB
Python
#%%
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import pandas as pd
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import torch
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import numpy as np
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#%%
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df = pd.read_csv('../temp/2body_data.csv').sort_values(by='c')
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df['E'] = df['re_E'] + 1j * df['im_E']
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train_data = df[df['re_E'] < 0]
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target_data = df[df['re_E'] > 0]
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train_cs = train_data['c'].to_numpy()
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train_Es = torch.tensor(train_data['E'].to_numpy(), dtype=torch.complex128)
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#%%
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# hyperparameters
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N = 9
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# initialize random Hamiltonians
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H0 = torch.randn(N, N, dtype=torch.complex128)
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H0 = (H0 + torch.transpose(H0, 0, 1)).requires_grad_() # symmetric
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H1 = torch.randn(N, N, dtype=torch.complex128)
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H1 = (H1 + torch.transpose(H1, 0, 1)).requires_grad_() # symmetric
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#%%
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# training
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# generate a set of c values to follow by subdividing the training cs
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subdivisions = 3
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c_steps = np.concatenate([np.linspace(start, stop, subdivisions, endpoint=False) for (start, stop) in zip(train_cs, train_cs[1:])])
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c_steps = np.append(c_steps, train_cs[-1])
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lr = 0.05
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epochs = 100000
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for epoch in range(epochs):
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Es = torch.empty(len(train_data), dtype=torch.complex128)
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current_E = 0.0 # start at the threshold
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for c in c_steps:
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H = H0 + c * H1
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evals = torch.linalg.eigvals(H)
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current_E = evals[torch.argmin(torch.abs(evals - current_E))]
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if np.any(c == train_cs):
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index = np.where(c == train_cs)[0][0]
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Es[index] = current_E
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loss = ((Es - train_Es).abs() ** 2).sum()
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if epoch % 1000 == 0:
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print(f"Training {(epoch+1)/epochs:.1%} \t Loss: {loss}")
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if H0.grad is not None:
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H0.grad.zero_()
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if H1.grad is not None:
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H1.grad.zero_()
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loss.backward()
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with torch.no_grad():
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H0 -= lr * H0.grad
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H1 -= lr * H1.grad
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# %%
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# evaluate for all points
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all_c = torch.tensor(df['c'].values, dtype=torch.float64)
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exact_E = torch.tensor(df['E'].values, dtype=torch.complex128)
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pred_Es = torch.empty(len(df), dtype=torch.complex128)
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with torch.no_grad():
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for (index, (c, E)) in enumerate(zip(all_c, exact_E)):
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H = H0 + c * H1
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evals = torch.linalg.eigvals(H)
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i = torch.argmin(torch.abs(evals - E)) # TODO: more robust way to identify the eigenvector
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pred_Es[index]= evals[i]
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# %%
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# plot the results
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import matplotlib.pyplot as plt
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plt.scatter(train_data['re_E'], train_data['im_E'], label='training')
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plt.scatter(target_data['re_E'], target_data['im_E'], label='target')
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plt.scatter(pred_Es.real, pred_Es.imag, marker='x', label='predicted')
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plt.legend()
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# %%
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