7_ml_force_field.ipynb

{"cells":[{"cell_type":"markdown","source":"> ไฟล์ Python Notebook สำหรับหนังสือ \"การเรียนรู้ของเครื่องสำหรับเคมีควอนตัม\" โดย รังสิมันต์ เกษแก้ว","metadata":{"tags":[],"cell_id":"81b4483452a549b381cacacbd858a1ca","is_collapsed":false,"formattedRanges":[],"deepnote_cell_type":"text-cell-callout"}},{"cell_type":"markdown","source":"> This is a Python notebook for \"Machine Learning for Quantum Chemistry\" book by Rangsiman Ketkaew","metadata":{"tags":[],"cell_id":"c00178b987cc4bb48fa1973750a402d6","is_collapsed":false,"formattedRanges":[],"deepnote_cell_type":"text-cell-callout"}},{"cell_type":"markdown","source":"## ฝึกสอนโมเดล Neural Network สำหรับใช้เป็น Force Field ในการทำนายพลังงานและแรง (Machine Learning Force Field)","metadata":{"tags":[],"cell_id":"d5ec142bd4fd44a0bbd0c1771ad60210","deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"import numpy as np\nimport ase\nfrom ase.calculators.lj import LennardJones\nimport matplotlib.pyplot as plt\nfrom dscribe.descriptors import SOAP","metadata":{"tags":[],"cell_id":"f68dad61382e4e37b8890e30aff565a4","source_hash":"957c39ab","execution_start":1671622610776,"execution_millis":1425,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[],"execution_count":1},{"cell_type":"markdown","source":"### 1. สร้าง Dataset","metadata":{"tags":[],"cell_id":"821f291aef1b4800881faa25f35fff6d","deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"# Setting up the SOAP descriptor\nsoap = SOAP(\n    species=[\"H\"],\n    periodic=False,\n    rcut=5.0,\n    sigma=0.5,\n    nmax=3,\n    lmax=0,\n)\n\n# Generate dataset of Lennard-Jones energies and forces\nn_samples = 200\ntraj = []\nn_atoms = 2\nenergies = np.zeros(n_samples)\nforces = np.zeros((n_samples, n_atoms, 3))\nr = np.linspace(2.5, 5.0, n_samples)\nfor i, d in enumerate(r):\n    a = ase.Atoms('HH', positions = [[-0.5 * d, 0, 0], [0.5 * d, 0, 0]])\n    a.set_calculator(LennardJones(epsilon=1.0 , sigma=2.9))\n    traj.append(a)\n    energies[i] = a.get_total_energy()\n    forces[i, :, :] = a.get_forces()\n\t\n# Plot the energies to validate them\nfig, ax = plt.subplots(figsize=(8, 5))\nplt.subplots_adjust(left=0.1, right=0.95, top=0.95, bottom=0.1)\nline, = ax.plot(r, energies)\nplt.xlabel(\"Distance (Å)\")\nplt.ylabel(\"Energy (eV)\")\nplt.show()\n\n# Create the SOAP desciptors and their derivatives for all samples. One center\n# is chosen to be directly between the atoms.\nderivatives, descriptors = soap.derivatives(\n    traj,\n    positions=[[[0, 0, 0]]] * len(r),\n    method=\"analytical\"\n)\n\n# Save to disk for later training\nnp.save(\"r.npy\", r)\nnp.save(\"E.npy\", energies)\nnp.save(\"D.npy\", descriptors)\nnp.save(\"dD_dr.npy\", derivatives)\nnp.save(\"F.npy\", forces)","metadata":{"tags":[],"cell_id":"f94fc257f9a342a698dc8059efa3ade0","source_hash":"7cc4c311","execution_start":1671622706817,"execution_millis":356,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"data":{"text/plain":"<Figure size 800x500 with 1 Axes>","image/png":"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\n"},"metadata":{"image/png":{"width":746,"height":488}},"output_type":"display_data"}],"execution_count":2},{"cell_type":"markdown","source":"### 2. นำเข้าชุดข้อมูลและเตรียม Input สำหรับฝึกสอนโมเดล","metadata":{"tags":[],"cell_id":"83da73583c48474087e314b0d8b98b40","deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"import torch\nfrom matplotlib import pyplot as plt\nfrom sklearn.preprocessing import StandardScaler\nfrom sklearn.model_selection import train_test_split\nfrom sklearn.metrics import mean_absolute_error\ntorch.manual_seed(7)","metadata":{"tags":[],"cell_id":"8a2b7fad64ea4580b76741e704e0a78d","source_hash":"7f8ad401","execution_start":1671622724077,"execution_millis":1766,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"name":"stderr","text":"/shared-libs/python3.9/py/lib/python3.9/site-packages/tqdm/auto.py:22: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n  from .autonotebook import tqdm as notebook_tqdm\n","output_type":"stream"},{"output_type":"execute_result","execution_count":3,"data":{"text/plain":"<torch._C.Generator at 0x7f0c2ce69290>"},"metadata":{}}],"execution_count":3},{"cell_type":"code","source":"# Load the dataset\nD_numpy = np.load(\"D.npy\")[:, 0, :]  # We only have one SOAP center \nn_samples, n_features = D_numpy.shape\nE_numpy = np.array([np.load(\"E.npy\")]).T\nF_numpy = np.load(\"F.npy\")\ndD_dr_numpy = np.load(\"dD_dr.npy\")[:, 0, :, :, : ]  # We only have one SOAP center \nr_numpy = np.load(\"r.npy\")\n\n# Select equally spaced points for training\nn_train = 30\nidx = np.linspace(0, len(r_numpy) - 1, n_train).astype(int)\nD_train_full = D_numpy[idx]\nE_train_full = E_numpy[idx]\nF_train_full = F_numpy[idx]\nr_train_full = r_numpy[idx]\ndD_dr_train_full = dD_dr_numpy[idx]\n\n# Standardize input for improved learning. Fit is done only on training data,\n# scaling is applied to both descriptors and their derivatives on training and\n# test sets.\nscaler = StandardScaler().fit(D_train_full)\nD_train_full = scaler.transform(D_train_full)\nD_whole = scaler.transform(D_numpy)\ndD_dr_whole = dD_dr_numpy / scaler.scale_[None, None, None, :]\ndD_dr_train_full = dD_dr_train_full / scaler.scale_[None, None, None, :]\n\n# Calculate the variance of energy and force values for the training set. These\n# are used to balance their contribution to the MSE loss\nvar_energy_train = E_train_full.var()\nvar_force_train = F_train_full.var()\n\n# Subselect 20% of validation points for early stopping.\nD_train, D_valid, E_train, E_valid, F_train, F_valid, dD_dr_train, dD_dr_valid = train_test_split(\n    D_train_full,\n    E_train_full,\n    F_train_full,\n    dD_dr_train_full,\n    test_size=0.2,\n    random_state=7,\n)\n\n# Create tensors for pytorch\nD_whole = torch.Tensor(D_whole)\nD_train = torch.Tensor(D_train)\nD_valid = torch.Tensor(D_valid)\nE_train = torch.Tensor(E_train)\nE_valid = torch.Tensor(E_valid)\nF_train = torch.Tensor(F_train)\nF_valid = torch.Tensor(F_valid)\ndD_dr_train = torch.Tensor(dD_dr_train)\ndD_dr_valid = torch.Tensor(dD_dr_valid)","metadata":{"tags":[],"cell_id":"92938f021b5b44d1b043c02707608724","source_hash":"7c8cd842","execution_start":1671622763771,"execution_millis":8,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[],"execution_count":4},{"cell_type":"markdown","source":"### 3. สร้างโมเดลและกำหนด Loss Function","metadata":{"tags":[],"cell_id":"4f3f62c05a00470882b1a8f1208047ee","deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"class FFNet(torch.nn.Module):\n    \"\"\"A simple feed-forward network with one hidden layer, randomly\n    initialized weights, sigmoid activation and a linear output layer.\n    \"\"\"\n    def __init__(self, n_features, n_hidden, n_out):\n        super(FFNet, self).__init__()\n        self.linear1 = torch.nn.Linear(n_features, n_hidden)\n        torch.nn.init.normal_(self.linear1.weight, mean=0, std=1.0)\n        self.sigmoid = torch.nn.Sigmoid()\n        self.linear2 = torch.nn.Linear(n_hidden, n_out)\n        torch.nn.init.normal_(self.linear2.weight, mean=0, std=1.0)\n\n    def forward(self, x):\n        x = self.linear1(x)\n        x = self.sigmoid(x)\n        x = self.linear2(x)\n\n        return x\n\n\ndef energy_force_loss(E_pred, E_train, F_pred, F_train):\n    \"\"\"Custom loss function that targets both energies and forces.\n    \"\"\"\n    energy_loss = torch.mean((E_pred - E_train)**2) / var_energy_train\n    force_loss = torch.mean((F_pred - F_train)**2) / var_force_train\n    return energy_loss + force_loss\n\n# Initialize model\nmodel = FFNet(n_features, n_hidden=5, n_out=1)\n\n# The Adam optimizer is used for training the model parameters\noptimizer = torch.optim.Adam(model.parameters(), lr=1e-2)","metadata":{"tags":[],"cell_id":"f1f58bb62bfe4c6eae2196e3df2cb080","source_hash":"22bdec99","execution_start":1671622788420,"execution_millis":0,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[],"execution_count":5},{"cell_type":"markdown","source":"### 4. ฝึกสอนโมเดล (Training)","metadata":{"tags":[],"cell_id":"48ee5ac5bec948b0bd352c53a80ff507","deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"# Train!\nn_max_epochs = 5000\nbatch_size = 2\npatience = 20\ni_worse = 0\nold_valid_loss = float(\"Inf\")\nbest_valid_loss = float(\"Inf\")\n\n# We explicitly require that the gradients should be calculated for the input\n# variables. PyTorch will not do this by default as it is typically not needed.\nD_valid.requires_grad = True\n\n# Epochs\nfor i_epoch in range(n_max_epochs):\n\n    # Batches\n    permutation = torch.randperm(D_train.size()[0])\n    for i in range(0, D_train.size()[0], batch_size):\n\n        indices = permutation[i:i+batch_size]\n        D_train_batch, E_train_batch = D_train[indices], E_train[indices]\n        D_train_batch.requires_grad = True\n        F_train_batch, dD_dr_train_batch = F_train[indices], dD_dr_train[indices]\n\n        # Forward pass: Predict energies from the descriptor input\n        E_train_pred_batch = model(D_train_batch)\n\n        # Get derivatives of model output with respect to input variables. The\n        # torch.autograd.grad-function can be used for this, as it returns the\n        # gradients of the input with respect to outputs. It is very important\n        # to set the create_graph=True in this case. Without it the derivatives\n        # of the NN parameters with respect to the loss from the force error\n        # will not be populated (=the force error will not affect the\n        # training), but the model will still run fine without errors.\n        df_dD_train_batch = torch.autograd.grad(\n            outputs=E_train_pred_batch,\n            inputs=D_train_batch,\n            grad_outputs=torch.ones_like(E_train_pred_batch),\n            create_graph=True,\n        )[0]\n\n        # Get derivatives of input variables (=descriptor) with respect to atom\n        # positions = forces\n        F_train_pred_batch = -torch.einsum('ijkl,il->ijk', dD_dr_train_batch, df_dD_train_batch)\n\n        # Zero gradients, perform a backward pass, and update the weights.\n        # D_train_batch.grad.data.zero_()\n        optimizer.zero_grad()\n        loss = energy_force_loss(E_train_pred_batch, E_train_batch, F_train_pred_batch, F_train_batch)\n        loss.backward()\n        optimizer.step()\n            \n    # Check early stopping criterion and save best model\n    E_valid_pred = model(D_valid)\n    df_dD_valid = torch.autograd.grad(\n        outputs=E_valid_pred,\n        inputs=D_valid,\n        grad_outputs=torch.ones_like(E_valid_pred),\n    )[0]\n    F_valid_pred = -torch.einsum('ijkl,il->ijk', dD_dr_valid, df_dD_valid)\n    valid_loss = energy_force_loss(E_valid_pred, E_valid, F_valid_pred, F_valid)\n    if valid_loss < best_valid_loss:\n        # print(\"Saving at epoch {}\".format(i_epoch))\n        torch.save(model.state_dict(), \"best_model.pt\")\n        best_valid_loss = valid_loss\n    if valid_loss >= old_valid_loss:\n        i_worse += 1\n    else:\n        i_worse = 0\n    if i_worse > patience:\n        print(\"Early stopping at epoch {}\".format(i_epoch))\n        break\n    old_valid_loss = valid_loss\n\n    if i_epoch % 500 == 0:\n        print(\"  Finished epoch: {} with loss: {}\".format(i_epoch, loss.item()))","metadata":{"tags":[],"cell_id":"7cf315a91bd14de6b1ad8b5ad58d08c5","source_hash":"e9808c7","execution_start":1671622811764,"execution_millis":110963,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"name":"stdout","text":"  Finished epoch: 0 with loss: 21.220672607421875\n  Finished epoch: 500 with loss: 0.0004732480738312006\n  Finished epoch: 1000 with loss: 0.01046457514166832\n  Finished epoch: 1500 with loss: 4.018305116915144e-05\n  Finished epoch: 2000 with loss: 8.0366779002361e-05\n  Finished epoch: 2500 with loss: 1.7976299204747193e-05\n  Finished epoch: 3000 with loss: 0.00024088378995656967\n  Finished epoch: 3500 with loss: 0.0008821815135888755\n  Finished epoch: 4000 with loss: 8.457103103864938e-05\n  Finished epoch: 4500 with loss: 5.806452827528119e-05\n","output_type":"stream"}],"execution_count":6},{"cell_type":"markdown","source":"### 5. วิเคราะห์โมเดล","metadata":{"tags":[],"cell_id":"68f209ce993244ce884f871aee08d977","deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"# Way to tell pytorch that we are entering the evaluation phase\nmodel.load_state_dict(torch.load(\"best_model.pt\"))\nmodel.eval()","metadata":{"tags":[],"cell_id":"6eddad3d172a412faeb3c2ae83c121b1","source_hash":"af55b873","execution_start":1671622922795,"execution_millis":5,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"output_type":"execute_result","execution_count":8,"data":{"text/plain":"FFNet(\n  (linear1): Linear(in_features=6, out_features=5, bias=True)\n  (sigmoid): Sigmoid()\n  (linear2): Linear(in_features=5, out_features=1, bias=True)\n)"},"metadata":{}}],"execution_count":8},{"cell_type":"code","source":"# Calculate energies and force for the entire range\nE_whole = torch.Tensor(E_numpy)\nF_whole = torch.Tensor(F_numpy)\ndD_dr_whole = torch.Tensor(dD_dr_whole)\nr_whole = r_numpy\nD_whole.requires_grad = True\nE_whole_pred = model(D_whole)\ndf_dD_whole = torch.autograd.grad(\n    outputs=E_whole_pred,\n    inputs=D_whole,\n    grad_outputs=torch.ones_like(E_whole_pred),\n)[0]\n\nF_whole_pred = -torch.einsum('ijkl,il->ijk', dD_dr_whole, df_dD_whole)","metadata":{"tags":[],"cell_id":"bac730955e3c44f7acb87670ef5ffc4e","source_hash":"2a986b27","execution_start":1671622922806,"execution_millis":1,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[],"execution_count":9},{"cell_type":"code","source":"F_whole_pred","metadata":{"tags":[],"cell_id":"02c99dfe174b4a10af3dbd968d4bb7e6","source_hash":"b39f135d","execution_start":1671622922808,"execution_millis":4,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"output_type":"execute_result","execution_count":10,"data":{"text/plain":"tensor([[[-9.4200e+01, -0.0000e+00, -0.0000e+00],\n         [ 9.4200e+01, -0.0000e+00, -0.0000e+00]],\n\n        [[-9.6559e+01, -0.0000e+00, -0.0000e+00],\n         [ 9.6559e+01, -0.0000e+00, -0.0000e+00]],\n\n        [[-9.1401e+01, -0.0000e+00, -0.0000e+00],\n         [ 9.1401e+01, -0.0000e+00, -0.0000e+00]],\n\n        ...,\n\n        [[ 3.4931e-02, -0.0000e+00, -0.0000e+00],\n         [-3.4931e-02, -0.0000e+00, -0.0000e+00]],\n\n        [[ 1.5592e-02, -0.0000e+00, -0.0000e+00],\n         [-1.5592e-02, -0.0000e+00, -0.0000e+00]],\n\n        [[-3.6762e-03, -0.0000e+00, -0.0000e+00],\n         [ 3.6762e-03, -0.0000e+00, -0.0000e+00]]])"},"metadata":{}}],"execution_count":10},{"cell_type":"markdown","source":"### 6. พลอตกราฟพลังงานและแรงที่ทำนายได้ และกราฟการฝึกสอน","metadata":{"tags":[],"cell_id":"5c1e86926ac9403f9661bc06e89a98ca","deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"# Plot energies for the whole range\nE_whole_pred = E_whole_pred.detach().numpy()\nE_whole = E_whole.detach().numpy()\norder = np.argsort(r_whole)\n\nfig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(10, 10))\nax1.plot(r_whole[order], E_whole[order], label=\"True\", linewidth=3, linestyle=\"-\")\nax1.plot(r_whole[order], E_whole_pred[order], label=\"Predicted\", linewidth=3, linestyle=\"-\")\nax1.set_ylabel('Energy', size=15)\nmae_energy = mean_absolute_error(E_whole_pred, E_whole)\nax1.text(0.95, 0.5, \"MAE: {:.2} eV\".format(mae_energy), size=16, horizontalalignment='right', verticalalignment='center', transform=ax1.transAxes)\n\n# Plot forces for whole range\nF_x_whole_pred = F_whole_pred.detach().numpy()[order, 0, 0]\nF_x_whole = F_whole[:, 0, 0][order]\nax2.plot(r_whole[order], F_x_whole, label=\"True\", linewidth=3, linestyle=\"-\")\nax2.plot(r_whole[order], F_x_whole_pred, label=\"Predicted\", linewidth=3, linestyle=\"-\")\nax2.set_xlabel('Distance', size=15)\nax2.set_ylabel('Forces', size=15)\nmae_force = mean_absolute_error(F_x_whole_pred, F_x_whole)\nax2.text(0.95, 0.5, \"MAE: {:.2} eV/Å\".format(mae_force), size=16, horizontalalignment='right', verticalalignment='center', transform=ax2.transAxes)\n\n# Plot training points\nF_x_train_full = F_train_full[:, 0, 0]\nax1.scatter(r_train_full, E_train_full, marker=\"o\", color=\"k\", s=20, label=\"Training points\", zorder=3)\nax2.scatter(r_train_full, F_x_train_full, marker=\"o\", color=\"k\", s=20, label=\"Training points\", zorder=3)\n\n# Show plot\nax1.legend(fontsize=12)\nplt.subplots_adjust(left=0.08, right=0.97, top=0.97, bottom=0.08, hspace=0)\nplt.show()","metadata":{"tags":[],"cell_id":"0f7be8ac64174b67b39160fc0b9c5fc4","source_hash":"5ec4cdba","execution_start":1671622929145,"execution_millis":323,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"data":{"text/plain":"<Figure size 1000x1000 with 2 Axes>","image/png":"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\n"},"metadata":{"image/png":{"width":983,"height":959}},"output_type":"display_data"}],"execution_count":11},{"cell_type":"markdown","source":"<a 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> </img>\nCreated in <span style='font-weight:600;margin-left:4px;'>Deepnote</span></a>","metadata":{"tags":[],"created_in_deepnote_cell":true,"deepnote_cell_type":"markdown"}}],"nbformat":4,"nbformat_minor":0,"metadata":{"deepnote":{},"orig_nbformat":2,"deepnote_notebook_id":"b8b3abca5db4407d9706ed2dc4a406c7","deepnote_execution_queue":[]}}