From 1e8c0b3757bbb259946135c96950840f643e0ead Mon Sep 17 00:00:00 2001 From: Michele Ceriotti Date: Tue, 25 May 2021 09:13:31 +0200 Subject: [PATCH 01/12] Added (untested) RKHS solver --- bindings/rascal/models/krr.py | 21 +++++++++++++++++---- 1 file changed, 17 insertions(+), 4 deletions(-) diff --git a/bindings/rascal/models/krr.py b/bindings/rascal/models/krr.py index e9fccc3fa..9a7256578 100644 --- a/bindings/rascal/models/krr.py +++ b/bindings/rascal/models/krr.py @@ -354,6 +354,7 @@ def train_gap_model( X_sparse, y_train, self_contributions, + solver="Normal", grad_train=None, lambdas=None, jitter=1e-8, @@ -463,11 +464,23 @@ def train_gap_model( F /= lambdas[1] / delta Y = np.vstack([Y, F]) - KMM[np.diag_indices_from(KMM)] += jitter + if solver == "Normal": + # Finds the KRR weights using the normal equations + K = KMM + np.dot(KNM.T, KNM) + Y = np.dot(KNM.T, Y) + weights = np.linalg.lstsq(K, Y, rcond=jitter)[0] + elif solver == "RKHS": + # Finds the weights by computing explicitly the RKHS and + # solving a least-square model + eva, eve = np.linalg.eigh(KMM) + eva = eva[::-1] + eve = eve[:,::-1] + nrkhs = len(np.where(eva>jitter)[0]) + PKT = eve[:,:nrkhs] @ np.diag(1.0/eva[:nrkhs]) + KNM = KNM @ PKT + + weights = PKT @ np.linalg.lstsq(KNM.T, Y, rcond = 1.0/eva[0]) - K = KMM + np.dot(KNM.T, KNM) - Y = np.dot(KNM.T, Y) - weights = np.linalg.lstsq(K, Y, rcond=None)[0] model = KRR(weights, kernel, X_sparse, self_contributions) # avoid memory clogging From 06acbb52df46e830d281b917765870c66232b8b9 Mon Sep 17 00:00:00 2001 From: Michele Ceriotti Date: Tue, 25 May 2021 10:30:37 +0200 Subject: [PATCH 02/12] Tried and tested RKHS solver (at least on zundel example) --- bindings/rascal/models/krr.py | 25 +++- examples/zundel_i-PI.ipynb | 261 ++++++++-------------------------- 2 files changed, 79 insertions(+), 207 deletions(-) diff --git a/bindings/rascal/models/krr.py b/bindings/rascal/models/krr.py index 9a7256578..0ce71ad46 100644 --- a/bindings/rascal/models/krr.py +++ b/bindings/rascal/models/krr.py @@ -429,6 +429,15 @@ def train_gap_model( jitter : double, optional small jitter for the numerical stability of solving the linear system, by default 1e-8 + solver: string, optional + method used to solve the sparse KRR equations. + "Normal" uses a least-squares solver for the normal equations: + (K_NM.T@K_NM + K_MM)^(-1) K_NM.T@Y + "RKHS" computes first the reproducing kernel features by diagonalizing K_MM + and computing P_NM = K_NM @ U_MM @ Lam_MM^(-1.2) and then solves the linear + problem for those (which is usually better conditioned) + (P_NM.T@P_NM + 1)^(-1) P_NM.T@Y + by default, "Normal" Returns ------- @@ -466,25 +475,29 @@ def train_gap_model( if solver == "Normal": # Finds the KRR weights using the normal equations - K = KMM + np.dot(KNM.T, KNM) + K = KMM + np.dot(KNM.T, KNM) Y = np.dot(KNM.T, Y) weights = np.linalg.lstsq(K, Y, rcond=jitter)[0] + del K + elif solver == "RKHS": # Finds the weights by computing explicitly the RKHS and # solving a least-square model eva, eve = np.linalg.eigh(KMM) eva = eva[::-1] eve = eve[:,::-1] - nrkhs = len(np.where(eva>jitter)[0]) + + # drop eigenvectors smaller than the jitter + nrkhs = len(np.where(eva/eva[0]>jitter)[0]) PKT = eve[:,:nrkhs] @ np.diag(1.0/eva[:nrkhs]) - KNM = KNM @ PKT + PNM = KNM @ PKT - weights = PKT @ np.linalg.lstsq(KNM.T, Y, rcond = 1.0/eva[0]) + weights = PKT @ np.linalg.solve( PNM.T@PNM + np.eye(nrkhs), PNM.T @ Y) + del PKT, PNM model = KRR(weights, kernel, X_sparse, self_contributions) # avoid memory clogging - del K, KMM - K, KMM = [], [] + del KMM return model diff --git a/examples/zundel_i-PI.ipynb b/examples/zundel_i-PI.ipynb index de6b26db5..53b310aaa 100644 --- a/examples/zundel_i-PI.ipynb +++ b/examples/zundel_i-PI.ipynb @@ -83,7 +83,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": { "init_cell": true }, @@ -128,17 +128,9 @@ }, { "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "dict_keys(['numbers', 'positions', 'forces'])\n" - ] - } - ], + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "# Load the first N structures of the zundel dataset\n", "N_dataset = 1000\n", @@ -151,7 +143,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": { "init_cell": true }, @@ -189,14 +181,14 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": { "code_folding": [] }, "outputs": [], "source": [ "# Number of structures to train the model with\n", - "n = 800\n", + "n = 900\n", "\n", "global_species = set()\n", "for frame in frames:\n", @@ -216,7 +208,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -226,13 +218,13 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Atomic energy baseline\n", "atom_energy_baseline = np.mean(energies)/(frames[0].get_global_number_of_atoms())\n", - "energy_baseline = {np.int(species): atom_energy_baseline for species in global_species}" + "energy_baseline = {int(species): atom_energy_baseline for species in global_species}" ] }, { @@ -248,7 +240,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -292,32 +284,9 @@ }, { "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "742829ccfc204504a6374bd03d0a63b6", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "HBox(children=(IntProgress(value=0, max=800), HTML(value='')))" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "Execution: 0.2071518898010254 s\n" - ] - } - ], + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "managers = []\n", "for f in tqdm(frames_train):\n", @@ -339,23 +308,11 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": null, "metadata": { "code_folding": [] }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The number of pseudo points selected by central atom species is: {1: 250, 8: 125}\n", - "Selecting species: 1\n", - "Reconstruction RMSE=1.157e-02\n", - "Selecting species: 8\n", - "Reconstruction RMSE=1.020e-02\n" - ] - } - ], + "outputs": [], "source": [ "# select the sparse points for the sparse kernel method with CUR on the whole training set\n", "n_sparse = {1:250, 8:125}\n", @@ -376,32 +333,9 @@ }, { "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "6e18e28e49de4ddcbfb49acf29b0e7a5", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "HBox(children=(IntProgress(value=0, description='Computing kernel matrix', max=800, style=ProgressStyle(descri…" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "Execution: 6.5608484745025635 s\n" - ] - } - ], + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "zeta = 2\n", "\n", @@ -413,7 +347,7 @@ "KNM = compute_KNM(tqdm(frames_train, leave=True, desc=\"Computing kernel matrix\"), X_sparse, kernel, soap)\n", "\n", "model = train_gap_model(kernel, frames_train, KNM, X_sparse, y_train, energy_baseline, \n", - " grad_train=-f_train, lambdas=[1e-12, 1e-12], jitter=1e-13)\n", + " grad_train=-f_train, lambdas=[1e-13, 1e-12], jitter=1e-12, solver=\"RKHS\")\n", "\n", "# save the model to a file in json format for future use\n", "dump_obj('zundel_model.json', model)\n", @@ -438,23 +372,23 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ - "n = 800\n", + "n = 900\n", "model = load_obj('zundel_model.json')\n", "ids = np.loadtxt('Structure_indices.txt')" ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ - "train_ids = [np.int(i) for i in ids[:n]]\n", - "test_ids = [np.int(i) for i in ids[n:]] \n", + "train_ids = [int(i) for i in ids[:n]]\n", + "test_ids = [int(i) for i in ids[n:]] \n", "\n", "frames_train = [frames[ii] for ii in train_ids]\n", "frames_test = [frames[ii] for ii in test_ids]\n", @@ -462,7 +396,9 @@ "y_train = [energies[ii] for ii in train_ids]\n", "y_train = np.array(y_train)\n", "y_test = [energies[ii] for ii in test_ids]\n", - "y_test = np.array(y_test)" + "y_test = np.array(y_test)\n", + "\n", + "f_test = extract_forces(frames_test, 'forces')" ] }, { @@ -474,31 +410,9 @@ }, { "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "a90dd7b7f71045d8af5183258fbfa785", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "HBox(children=(IntProgress(value=0, max=200), HTML(value='')))" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n" - ] - } - ], + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "# make predictions on the test set\n", "y_pred = []\n", @@ -516,15 +430,6 @@ "f_pred = np.array(f_pred)" ] }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [], - "source": [ - "f_test = extract_forces(frames_test, 'forces')" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -544,58 +449,30 @@ }, { "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "RMSE = 18.520980475974834 meV\n", - "Sigma test set = 0.274800153468654 eV\n", - "%RMSE = 6.739799902654528 %\n" - ] - } - ], + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "from rascal.utils import get_score\n", "\n", "score = get_score(y_pred, y_test)\n", "RMSE = score['RMSE']\n", "sigma_test = np.std(y_test)\n", + "\n", + "score = get_score(f_test.flatten(), f_pred.flatten())\n", + "fRMSE = score['RMSE']\n", + "\n", "print(\"RMSE = \", RMSE*1000.0, \"meV\")\n", "print(\"Sigma test set = \", sigma_test, \" eV\")\n", - "print(\"%RMSE = \", RMSE/sigma_test*100.0, \" %\")" + "print(\"%RMSE = \", RMSE/sigma_test*100.0, \" %\")\n", + "print(\"force RMSE = \", fRMSE, \"eV/A\")" ] }, { "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0, 0.5, 'reference energies [eV]')" - ] - }, - "execution_count": 16, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "plt.scatter(y_test, y_pred, s=5.0, c = 'black')\n", "lims = [\n", @@ -604,7 +481,7 @@ "]\n", "\n", "# now plot both limits against eachother\n", - "plt.plot(lims, lims, 'k-', zorder=0, color='red')\n", + "plt.plot(lims, lims, 'r-', zorder=0)\n", "plt.title(\"correlation plot\")\n", "plt.xlabel(\"predicted energies [eV]\")\n", "plt.ylabel(\"reference energies [eV]\")" @@ -654,34 +531,9 @@ }, { "cell_type": "code", - "execution_count": 19, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "[Text(0.5, 0, 'time [ps]')]" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "#Plotting the results of the simulations\n", "try:\n", @@ -692,7 +544,7 @@ "\n", "Nframes = len(lines)\n", "steps = np.zeros((Nframes, 1), dtype=float)\n", - "time = np.zeros((Nframes, 1), dtype=float)\n", + "times = np.zeros((Nframes, 1), dtype=float)\n", "KE = np.zeros((Nframes, 1), dtype=float)\n", "PE = np.zeros((Nframes, 1), dtype=float)\n", "Pressure = np.zeros((Nframes, 1), dtype=float)\n", @@ -700,7 +552,7 @@ "i = 0\n", "for x in lines: \n", " steps[i] = float(x.split()[0])\n", - " time[i] = float(x.split()[1])\n", + " times[i] = float(x.split()[1])\n", " KE[i] = float(x.split()[4])\n", " PE[i] = float(x.split()[5])\n", " Pressure[i] = float(x.split()[6])\n", @@ -710,16 +562,23 @@ "f.subplots_adjust(hspace=0)\n", "f.suptitle('T = 250 K', fontweight='bold')\n", "\n", - "axs[0].plot(time, (KE - KE[0]), linewidth = 1.5, label = r'$\\Delta PE$')\n", - "axs[0].plot(time, (PE - PE[0]), linewidth = 1.5, label = r'$\\Delta KE$')\n", + "axs[0].plot(times, (KE - KE[0]), linewidth = 1.5, label = r'$\\Delta PE$')\n", + "axs[0].plot(times, (PE - PE[0]), linewidth = 1.5, label = r'$\\Delta KE$')\n", "axs[0].set(ylabel= 'Energy [eV]')\n", "axs[0].set_ylim(-0.5, 0.5)\n", "axs[0].legend(ncol = 2, mode='expand', prop={'size': 12}, loc=\"lower center\")\n", "\n", - "axs[1].plot(time, Pressure, linewidth = 1.5, color = 'red')\n", + "axs[1].plot(times, Pressure, linewidth = 1.5, color = 'red')\n", "axs[1].set(ylabel= 'MD Pressure [bar]')\n", "axs[1].set(xlabel= 'time [ps]')" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -739,7 +598,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.10" + "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, From ac41bd80c25405aeba0e5e26fe0226138488fd73 Mon Sep 17 00:00:00 2001 From: Michele Ceriotti Date: Tue, 25 May 2021 10:48:49 +0200 Subject: [PATCH 03/12] Mini-cleaning --- bindings/rascal/models/krr.py | 20 ++++++++++---------- 1 file changed, 10 insertions(+), 10 deletions(-) diff --git a/bindings/rascal/models/krr.py b/bindings/rascal/models/krr.py index 0ce71ad46..48fdf67f1 100644 --- a/bindings/rascal/models/krr.py +++ b/bindings/rascal/models/krr.py @@ -430,7 +430,7 @@ def train_gap_model( small jitter for the numerical stability of solving the linear system, by default 1e-8 solver: string, optional - method used to solve the sparse KRR equations. + method used to solve the sparse KRR equations. "Normal" uses a least-squares solver for the normal equations: (K_NM.T@K_NM + K_MM)^(-1) K_NM.T@Y "RKHS" computes first the reproducing kernel features by diagonalizing K_MM @@ -475,24 +475,24 @@ def train_gap_model( if solver == "Normal": # Finds the KRR weights using the normal equations - K = KMM + np.dot(KNM.T, KNM) + K = KMM + np.dot(KNM.T, KNM) Y = np.dot(KNM.T, Y) weights = np.linalg.lstsq(K, Y, rcond=jitter)[0] del K - + elif solver == "RKHS": # Finds the weights by computing explicitly the RKHS and - # solving a least-square model + # solving a least-square model eva, eve = np.linalg.eigh(KMM) eva = eva[::-1] - eve = eve[:,::-1] - + eve = eve[:, ::-1] + # drop eigenvectors smaller than the jitter - nrkhs = len(np.where(eva/eva[0]>jitter)[0]) - PKT = eve[:,:nrkhs] @ np.diag(1.0/eva[:nrkhs]) - PNM = KNM @ PKT + nrkhs = len(np.where(eva / eva[0] > jitter)[0]) + PKT = eve[:, :nrkhs] @ np.diag(1.0 / eva[:nrkhs]) + PNM = KNM @ PKT - weights = PKT @ np.linalg.solve( PNM.T@PNM + np.eye(nrkhs), PNM.T @ Y) + weights = PKT @ np.linalg.solve(PNM.T @ PNM + np.eye(nrkhs), PNM.T @ Y) del PKT, PNM model = KRR(weights, kernel, X_sparse, self_contributions) From 3805fea0b63dd685532988229138674f680543a4 Mon Sep 17 00:00:00 2001 From: Michele Ceriotti Date: Tue, 25 May 2021 15:44:47 +0200 Subject: [PATCH 04/12] Better solver for the RKHS mode --- bindings/rascal/models/krr.py | 10 +++++++--- 1 file changed, 7 insertions(+), 3 deletions(-) diff --git a/bindings/rascal/models/krr.py b/bindings/rascal/models/krr.py index 48fdf67f1..f652e347f 100644 --- a/bindings/rascal/models/krr.py +++ b/bindings/rascal/models/krr.py @@ -490,9 +490,13 @@ def train_gap_model( # drop eigenvectors smaller than the jitter nrkhs = len(np.where(eva / eva[0] > jitter)[0]) PKT = eve[:, :nrkhs] @ np.diag(1.0 / eva[:nrkhs]) - PNM = KNM @ PKT - - weights = PKT @ np.linalg.solve(PNM.T @ PNM + np.eye(nrkhs), PNM.T @ Y) + #PNM = KNM @ PKT + #weights = PKT @ np.linalg.solve(PNM.T @ PNM + np.eye(nrkhs), PNM.T @ Y) + PNM = np.vstack([KNM, PKT.T]) + print(Y.shape) + YP = np.vstack([Y, np.zeros((nrkhs,1))]) + weights = np.linalg.lstsq(PNM, YP, rcond=None)[0] + del PKT, PNM model = KRR(weights, kernel, X_sparse, self_contributions) From f3de49564859157d99c9dd9f0c09efd0d4a5691e Mon Sep 17 00:00:00 2001 From: Michele Ceriotti Date: Tue, 25 May 2021 16:02:55 +0200 Subject: [PATCH 05/12] Try to commit without stripping the zundel notebook --- .gitattributes | 2 + examples/zundel_i-PI.ipynb | 224 +++++++++++++++++++++++++++++++------ 2 files changed, 192 insertions(+), 34 deletions(-) diff --git a/.gitattributes b/.gitattributes index 305a9b048..90e9e7a1b 100644 --- a/.gitattributes +++ b/.gitattributes @@ -1,2 +1,4 @@ *.ipynb filter=nbstripout *.ipynb diff=ipynb + +examples/zundel_i-PI.ipynb filter= diff= diff --git a/examples/zundel_i-PI.ipynb b/examples/zundel_i-PI.ipynb index 53b310aaa..256b5066b 100644 --- a/examples/zundel_i-PI.ipynb +++ b/examples/zundel_i-PI.ipynb @@ -83,7 +83,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "init_cell": true }, @@ -112,9 +112,17 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "/local/home/ceriotti/lavoro/code/librascal/examples/i-PI/zundel\n" + ] + } + ], "source": [ "cd i-PI/zundel/" ] @@ -128,9 +136,17 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "dict_keys(['numbers', 'positions', 'forces'])\n" + ] + } + ], "source": [ "# Load the first N structures of the zundel dataset\n", "N_dataset = 1000\n", @@ -143,7 +159,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": { "init_cell": true }, @@ -181,7 +197,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": { "code_folding": [] }, @@ -208,7 +224,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ @@ -218,7 +234,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ @@ -240,7 +256,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "metadata": {}, "outputs": [], "source": [ @@ -284,9 +300,32 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "9895891cb60d4e2391e07e8a47a85a77", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "HBox(children=(FloatProgress(value=0.0, max=900.0), HTML(value='')))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Execution: 0.26677918434143066 s\n" + ] + } + ], "source": [ "managers = []\n", "for f in tqdm(frames_train):\n", @@ -308,11 +347,23 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": { "code_folding": [] }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The number of pseudo points selected by central atom species is: {1: 250, 8: 125}\n", + "Selecting species: 1\n", + "Reconstruction RMSE=1.370e-02\n", + "Selecting species: 8\n", + "Reconstruction RMSE=1.218e-02\n" + ] + } + ], "source": [ "# select the sparse points for the sparse kernel method with CUR on the whole training set\n", "n_sparse = {1:250, 8:125}\n", @@ -333,9 +384,33 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "d98e88b929614517bc7c1ca0d82e1bd6", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "HBox(children=(FloatProgress(value=0.0, description='Computing kernel matrix', max=900.0, style=ProgressStyle(…" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "(19800, 1)\n", + "Execution: 9.232456684112549 s\n" + ] + } + ], "source": [ "zeta = 2\n", "\n", @@ -372,7 +447,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -383,7 +458,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -410,9 +485,31 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "41069a3272dc442397cc262d89019f46", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "HBox(children=(FloatProgress(value=0.0), HTML(value='')))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], "source": [ "# make predictions on the test set\n", "y_pred = []\n", @@ -449,9 +546,20 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "RMSE = 11.224114363408386 meV\n", + "Sigma test set = 0.2749245567889843 eV\n", + "%RMSE = 4.082616152773631 %\n", + "force RMSE = 0.08338680841929573 eV/A\n" + ] + } + ], "source": [ "from rascal.utils import get_score\n", "\n", @@ -470,9 +578,32 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'reference energies [eV]')" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "#Plotting the results of the simulations\n", "try:\n", From ee5991a6bcf7ce25fda3b71372ee9b2e276e988c Mon Sep 17 00:00:00 2001 From: Michele Ceriotti Date: Wed, 26 May 2021 08:45:06 +0200 Subject: [PATCH 06/12] Better comments --- bindings/rascal/models/krr.py | 10 +++++++--- 1 file changed, 7 insertions(+), 3 deletions(-) diff --git a/bindings/rascal/models/krr.py b/bindings/rascal/models/krr.py index f652e347f..e62fd8b3e 100644 --- a/bindings/rascal/models/krr.py +++ b/bindings/rascal/models/krr.py @@ -490,10 +490,14 @@ def train_gap_model( # drop eigenvectors smaller than the jitter nrkhs = len(np.where(eva / eva[0] > jitter)[0]) PKT = eve[:, :nrkhs] @ np.diag(1.0 / eva[:nrkhs]) - #PNM = KNM @ PKT - #weights = PKT @ np.linalg.solve(PNM.T @ PNM + np.eye(nrkhs), PNM.T @ Y) + + # This would be the direct LR solution + # PNM = KNM @ PKT + # weights = PKT @ np.linalg.solve(PNM.T @ PNM + np.eye(nrkhs), PNM.T @ Y) + + # ... but instead we use an alternative (equivalent) formulation discussed + # in Foster et al. JMLR (2009) PNM = np.vstack([KNM, PKT.T]) - print(Y.shape) YP = np.vstack([Y, np.zeros((nrkhs,1))]) weights = np.linalg.lstsq(PNM, YP, rcond=None)[0] From faeda4ae7a056c9d420de1eb963987f63ba0f78b Mon Sep 17 00:00:00 2001 From: Michele Ceriotti Date: Wed, 26 May 2021 08:45:47 +0200 Subject: [PATCH 07/12] Black --- bindings/rascal/models/krr.py | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/bindings/rascal/models/krr.py b/bindings/rascal/models/krr.py index e62fd8b3e..ba46154f7 100644 --- a/bindings/rascal/models/krr.py +++ b/bindings/rascal/models/krr.py @@ -490,17 +490,17 @@ def train_gap_model( # drop eigenvectors smaller than the jitter nrkhs = len(np.where(eva / eva[0] > jitter)[0]) PKT = eve[:, :nrkhs] @ np.diag(1.0 / eva[:nrkhs]) - - # This would be the direct LR solution + + # This would be the direct LR solution # PNM = KNM @ PKT - # weights = PKT @ np.linalg.solve(PNM.T @ PNM + np.eye(nrkhs), PNM.T @ Y) - - # ... but instead we use an alternative (equivalent) formulation discussed + # weights = PKT @ np.linalg.solve(PNM.T @ PNM + np.eye(nrkhs), PNM.T @ Y) + + # ... but instead we use an alternative (equivalent) formulation discussed # in Foster et al. JMLR (2009) PNM = np.vstack([KNM, PKT.T]) - YP = np.vstack([Y, np.zeros((nrkhs,1))]) + YP = np.vstack([Y, np.zeros((nrkhs, 1))]) weights = np.linalg.lstsq(PNM, YP, rcond=None)[0] - + del PKT, PNM model = KRR(weights, kernel, X_sparse, self_contributions) From feaa3ce743cad2e6245234d8485f80880935cd7c Mon Sep 17 00:00:00 2001 From: Michele Ceriotti Date: Thu, 27 May 2021 10:46:53 +0200 Subject: [PATCH 08/12] Added a "QR" mode for the example --- bindings/rascal/models/krr.py | 26 +++++++++++++++++--------- 1 file changed, 17 insertions(+), 9 deletions(-) diff --git a/bindings/rascal/models/krr.py b/bindings/rascal/models/krr.py index ba46154f7..ffd1cc9c7 100644 --- a/bindings/rascal/models/krr.py +++ b/bindings/rascal/models/krr.py @@ -479,7 +479,14 @@ def train_gap_model( Y = np.dot(KNM.T, Y) weights = np.linalg.lstsq(K, Y, rcond=jitter)[0] del K - + if solver == "QR": + # Finds the KRR weights solving am extended system, see e.g + # Foster et al. JMLR (2009) + V = np.linalg.cholesky(KMM) + A = np.vstack([KNM, V.T]) + b = np.vstack([Y, np.zeros((len(KMM),1))]) + weights = np.linalg.lstsq(A, b, rcond=jitter)[0] + del V, A, b elif solver == "RKHS": # Finds the weights by computing explicitly the RKHS and # solving a least-square model @@ -489,19 +496,20 @@ def train_gap_model( # drop eigenvectors smaller than the jitter nrkhs = len(np.where(eva / eva[0] > jitter)[0]) - PKT = eve[:, :nrkhs] @ np.diag(1.0 / eva[:nrkhs]) - + print("Retaining ", nrkhs, " RKHS components out of ", len(eva)) + PKT = eve[:, :nrkhs] @ np.diag(1.0 / np.sqrt(eva[:nrkhs])) + # This would be the direct LR solution + # PKT = eve[:, :nrkhs] @ np.diag(1.0 / np.sqrt(eva[:nrkhs])) # PNM = KNM @ PKT # weights = PKT @ np.linalg.solve(PNM.T @ PNM + np.eye(nrkhs), PNM.T @ Y) - # ... but instead we use an alternative (equivalent) formulation discussed - # in Foster et al. JMLR (2009) - PNM = np.vstack([KNM, PKT.T]) - YP = np.vstack([Y, np.zeros((nrkhs, 1))]) - weights = np.linalg.lstsq(PNM, YP, rcond=None)[0] + # ... but instead we use an alternative (equivalent) formulation using QR + A = np.vstack([ KNM@PKT, np.eye(nrkhs) ]) + b = np.vstack([Y, np.zeros((nrkhs, 1))]) + weights = PKT@np.linalg.lstsq(A, b, rcond=None)[0] - del PKT, PNM + del PKT, eva, eve, A, b model = KRR(weights, kernel, X_sparse, self_contributions) From 076e1fb3d9bcb7660aad956446d8aaccb21a954b Mon Sep 17 00:00:00 2001 From: Michele Ceriotti Date: Thu, 10 Jun 2021 08:30:11 +0200 Subject: [PATCH 09/12] black --- bindings/rascal/models/krr.py | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/bindings/rascal/models/krr.py b/bindings/rascal/models/krr.py index ffd1cc9c7..bab016a12 100644 --- a/bindings/rascal/models/krr.py +++ b/bindings/rascal/models/krr.py @@ -480,11 +480,11 @@ def train_gap_model( weights = np.linalg.lstsq(K, Y, rcond=jitter)[0] del K if solver == "QR": - # Finds the KRR weights solving am extended system, see e.g + # Finds the KRR weights solving am extended system, see e.g # Foster et al. JMLR (2009) - V = np.linalg.cholesky(KMM) + V = np.linalg.cholesky(KMM) A = np.vstack([KNM, V.T]) - b = np.vstack([Y, np.zeros((len(KMM),1))]) + b = np.vstack([Y, np.zeros((len(KMM), 1))]) weights = np.linalg.lstsq(A, b, rcond=jitter)[0] del V, A, b elif solver == "RKHS": @@ -498,16 +498,16 @@ def train_gap_model( nrkhs = len(np.where(eva / eva[0] > jitter)[0]) print("Retaining ", nrkhs, " RKHS components out of ", len(eva)) PKT = eve[:, :nrkhs] @ np.diag(1.0 / np.sqrt(eva[:nrkhs])) - + # This would be the direct LR solution # PKT = eve[:, :nrkhs] @ np.diag(1.0 / np.sqrt(eva[:nrkhs])) # PNM = KNM @ PKT # weights = PKT @ np.linalg.solve(PNM.T @ PNM + np.eye(nrkhs), PNM.T @ Y) # ... but instead we use an alternative (equivalent) formulation using QR - A = np.vstack([ KNM@PKT, np.eye(nrkhs) ]) + A = np.vstack([KNM @ PKT, np.eye(nrkhs)]) b = np.vstack([Y, np.zeros((nrkhs, 1))]) - weights = PKT@np.linalg.lstsq(A, b, rcond=None)[0] + weights = PKT @ np.linalg.lstsq(A, b, rcond=None)[0] del PKT, eva, eve, A, b From 41ce2921edd15e325d5879037be725cf0ca8d100 Mon Sep 17 00:00:00 2001 From: Michele Ceriotti Date: Fri, 11 Jun 2021 10:12:14 +0200 Subject: [PATCH 10/12] Added example file for water monomer --- ...onomers_1k_with_energies_and_gradients.xyz | 5000 +++++++++++++++++ 1 file changed, 5000 insertions(+) create mode 100644 reference_data/inputs/water_monomers_1k_with_energies_and_gradients.xyz diff --git a/reference_data/inputs/water_monomers_1k_with_energies_and_gradients.xyz b/reference_data/inputs/water_monomers_1k_with_energies_and_gradients.xyz new file mode 100644 index 000000000..c6fcc54c2 --- /dev/null +++ b/reference_data/inputs/water_monomers_1k_with_energies_and_gradients.xyz @@ -0,0 +1,5000 @@ +3 +Properties=species:S:1:pos:R:3:force:R:3 mu="-0.734398 -0.0 -0.040971" beta="14.553606 -0.0 0.184257 -0.0 10.77828 -0.0 0.184257 -0.0 5.6182 -0.0 10.77828 -0.0 10.77828 -0.0 0.601308 -0.0 0.601308 -0.0 0.184257 -0.0 5.6182 -0.0 0.601308 -0.0 5.6182 -0.0 0.941105" 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-0.018295217713541922 -0.026927887511955628 0.03759888811961298 +H -0.84883700 0.25218800 0.74218100 0.0215477682470957 0.005256211764310126 0.03241737792334587 +3 +Properties=species:S:1:pos:R:3:force:R:3 mu="0.590648 0.445964 0.128857" beta="-14.182977 -3.863895 2.168367 -3.863895 -3.93609 1.9799 2.168367 1.9799 -9.018322 -3.863895 -3.93609 1.9799 -3.93609 -9.799537 -1.570896 1.9799 -1.570896 -6.577505 2.168367 1.9799 -9.018322 1.9799 -1.570896 -6.577505 -9.018322 -6.577505 -5.413798" potential=-76.3419493878 pbc="T T T" alpha="10.397321 0.367969 -0.619315 0.367969 9.890977 -0.208184 -0.619315 -0.208184 10.693677" energy=-76.4259032890746 electro=-151.92604115880007 +O -1.63334600 0.02504200 0.00966800 -0.04547615021630147 -0.021188414139921452 0.04839840334616774 +H -0.89935200 0.39449500 -0.64957600 0.04729911303536616 0.02380613162750511 -0.042489241721072046 +H -1.37467800 0.39730200 0.85093100 -0.0018231732975793058 -0.0026183824821125468 -0.005907669187956266 +3 +Properties=species:S:1:pos:R:3:force:R:3 mu="0.012748 -0.374083 -0.711168" beta="-0.09538 5.96553 11.005967 5.96553 0.156686 1.096337 11.005967 1.096337 0.086478 5.96553 0.156686 1.096337 0.156686 7.800932 5.111502 1.096337 5.111502 2.584316 11.005967 1.096337 0.086478 1.096337 5.111502 2.584316 0.086478 2.584316 14.825929" potential=-76.3398370336 pbc="T T T" alpha="10.997755 0.265516 0.248533 0.265516 9.98089 0.429765 0.248533 0.429765 10.490348" energy=-76.4238616739529 electro=-151.7611049311329 +O 0.00445400 0.09803000 1.58385900 0.025327541933592768 0.037853820892520096 0.06663945736490984 +H 0.74712000 -0.14695600 0.97121100 0.009081444251046511 -0.01107092461913306 -0.022788316477715842 +H -0.74004900 -0.30723900 0.96510900 -0.03440449816178637 -0.02678307698565685 -0.04385212758492796 From 87a484eb4822e12777e66828897d2358ef1acd58 Mon Sep 17 00:00:00 2001 From: Michele Ceriotti Date: Sat, 12 Jun 2021 01:06:51 +0200 Subject: [PATCH 11/12] A class for sparse GPR solvers that can be also called outside the train_gap_model routines --- bindings/rascal/models/krr.py | 180 ++++++++++++++++++++++++++-------- 1 file changed, 138 insertions(+), 42 deletions(-) diff --git a/bindings/rascal/models/krr.py b/bindings/rascal/models/krr.py index bab016a12..9e8e73669 100644 --- a/bindings/rascal/models/krr.py +++ b/bindings/rascal/models/krr.py @@ -10,10 +10,141 @@ from ..utils import BaseIO from ..lib import compute_sparse_kernel_gradients, compute_sparse_kernel_neg_stress +import scipy import numpy as np import ase +class SparseGPRSolver: + """ + A few quick implementation notes, docs to be done. + + This is meant to solve the sparse GPR problem + b = (KNM.T@KNM + reg*KMM)^-1 @ KNM.T@y + + The inverse needs to be stabilized with application of a numerical jitter, + that is expressed as a fraction of the largest eigenvalue of KMM + + + """ + + def __init__( + self, KMM, regularizer=1, jitter=0, solver="RKHS", relative_jitter=True + ): + + self._solver = solver + + self._nM = len(KMM) + if self._solver == "RKHS" or self._solver == "RKHS-QR": + self._vk, self._Uk = scipy.linalg.eigh(KMM) + self._vk = self._vk[::-1] + self._Uk = self._Uk[:, ::-1] + elif self._solver == "QR" or self._solver == "Normal": + self._KMM = KMM + # gets maximum eigenvalue of KMM to scale the numerical jitter + self._KMM_maxeva = scipy.sparse.linalg.eigsh( + KMM, k=1, return_eigenvectors=False + )[0] + else: + raise ValueError( + "Solver ", + solver, + " not supported. Possible values are [RKHS, RKHS-QR, QR, Normal].", + ) + if relative_jitter: + if self._solver == "RKHS" or self._solver == "RKHS-QR": + self._jitter_scale = self._vk[0] + elif self._solver == "QR" or self._solver == "Normal": + self._jitter_scale = self._KMM_maxeva + else: + self._jitter_scale = 1.0 + self.set_regularizers(regularizer, jitter) + + def set_regularizers(self, regularizer=1.0, jitter=0.0): + self._regularizer = regularizer + self._jitter = jitter + if self._solver == "RKHS" or self._solver == "RKHS-QR": + self._nM = len(np.where(self._vk > self._jitter * self._jitter_scale)[0]) + self._PKPhi = self._Uk[:, : self._nM] * 1 / np.sqrt(self._vk[: self._nM]) + elif self._solver == "QR": + self._VMM = scipy.linalg.cholesky( + self._regularizer * self._KMM + + np.eye(self._nM) * self._jitter_scale * self._jitter + ) + self._Cov = np.zeros((self._nM, self._nM)) + self._KY = None + + def partial_fit(self, KNM, Y, accumulate_only=False): + if len(Y.shape) == 1: + Y = Y[:, np.newaxis] + if self._solver == "RKHS": + Phi = KNM @ self._PKPhi + elif self._solver == "Normal": + Phi = KNM + else: + raise ValueError( + "Partial fit can only be realized with solver = [RKHS, Normal]" + ) + if self._KY is None: + self._KY = np.zeros((self._nM, Y.shape[1])) + + self._Cov += Phi.T @ Phi + self._KY += Phi.T @ Y + + if not accumulate_only: + if self._solver == "RKHS": + self._weights = self._PKPhi @ scipy.linalg.solve( + self._Cov + np.eye(self._nM) * self._regularizer, + self._KY, + assume_a="pos", + ) + elif self._solver == "Normal": + self._weights = scipy.linalg.solve( + self._Cov + + self._regularizer * self._KMM + + np.eye(self._KMM.shape[0]) * self._jitter * self._jitter_scale, + self._KY, + assume_a="pos", + ) + + def fit(self, KNM, Y): + + if len(Y.shape) == 1: + Y = Y[:, np.newaxis] + if self._solver == "RKHS": + Phi = KNM @ self._PKPhi + self._weights = self._PKPhi @ scipy.linalg.solve( + Phi.T @ Phi + np.eye(self._nM) * self._regularizer, + Phi.T @ Y, + assume_a="pos", + ) + elif self._solver == "RKHS-QR": + A = np.vstack( + [KNM @ self._PKPhi, np.sqrt(self._regularizer) * np.eye(self._nM)] + ) + Q, R = np.linalg.qr(A) + self._weights = self._PKPhi @ scipy.linalg.solve_triangular( + R, Q.T @ np.hstack([Y, np.zeros((self._nM, Y.shape[1]))]) + ) + elif self._solver == "QR": + A = np.vstack([KNM, self._VMM]) + Q, R = np.linalg.qr(A) + self._weights = scipy.linalg.solve_triangular( + R, Q.T @ np.vstack([Y, np.zeros((KNM.shape[1], Y.shape[1]))]) + ) + elif self._solver == "Normal": + self._weights = scipy.linalg.solve( + KNM.T @ KNM + + self._regularizer * self._KMM + + np.eye(self._nM) * self._jitter * self._jitter_scale, + KNM.T @ Y, + assume_a="pos", + ) + + def transform(self, KTM): + return KTM @ self._weights + + class KRR(BaseIO): """Kernel Ridge Regression model. Only supports sparse GPR training for the moment. @@ -473,47 +604,12 @@ def train_gap_model( F /= lambdas[1] / delta Y = np.vstack([Y, F]) - if solver == "Normal": - # Finds the KRR weights using the normal equations - K = KMM + np.dot(KNM.T, KNM) - Y = np.dot(KNM.T, Y) - weights = np.linalg.lstsq(K, Y, rcond=jitter)[0] - del K - if solver == "QR": - # Finds the KRR weights solving am extended system, see e.g - # Foster et al. JMLR (2009) - V = np.linalg.cholesky(KMM) - A = np.vstack([KNM, V.T]) - b = np.vstack([Y, np.zeros((len(KMM), 1))]) - weights = np.linalg.lstsq(A, b, rcond=jitter)[0] - del V, A, b - elif solver == "RKHS": - # Finds the weights by computing explicitly the RKHS and - # solving a least-square model - eva, eve = np.linalg.eigh(KMM) - eva = eva[::-1] - eve = eve[:, ::-1] - - # drop eigenvectors smaller than the jitter - nrkhs = len(np.where(eva / eva[0] > jitter)[0]) - print("Retaining ", nrkhs, " RKHS components out of ", len(eva)) - PKT = eve[:, :nrkhs] @ np.diag(1.0 / np.sqrt(eva[:nrkhs])) - - # This would be the direct LR solution - # PKT = eve[:, :nrkhs] @ np.diag(1.0 / np.sqrt(eva[:nrkhs])) - # PNM = KNM @ PKT - # weights = PKT @ np.linalg.solve(PNM.T @ PNM + np.eye(nrkhs), PNM.T @ Y) - - # ... but instead we use an alternative (equivalent) formulation using QR - A = np.vstack([KNM @ PKT, np.eye(nrkhs)]) - b = np.vstack([Y, np.zeros((nrkhs, 1))]) - weights = PKT @ np.linalg.lstsq(A, b, rcond=None)[0] - - del PKT, eva, eve, A, b - - model = KRR(weights, kernel, X_sparse, self_contributions) - - # avoid memory clogging - del KMM + ssolver = SparseGPRSolver( + KMM, regularizer=1, jitter=jitter, solver=solver, relative_jitter=False + ) # in current implementation KMM incorporates regularization so it's better to use an absolute jitter value + ssolver.fit(KNM, Y) + model = KRR(ssolver._weights, kernel, X_sparse, self_contributions) + + del KNM, KMM, solver return model From 4ae721a9b008475b9ba94f9bc7fb5f0903e2f401 Mon Sep 17 00:00:00 2001 From: felixmusil Date: Mon, 4 Oct 2021 13:29:36 +0200 Subject: [PATCH 12/12] Update .gitattributes force restart CI --- .gitattributes | 1 + 1 file changed, 1 insertion(+) diff --git a/.gitattributes b/.gitattributes index 82ebb32a1..ead3f7b43 100644 --- a/.gitattributes +++ b/.gitattributes @@ -3,3 +3,4 @@ examples/zundel_i-PI.ipynb filter= diff= examples/optimized_radial_basis_functions.ipynb filter= diff= +