{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "provenance": [] }, "kernelspec": { "name": "python3", "display_name": "Python 3" }, "language_info": { "name": "python" } }, "cells": [ { "cell_type": "markdown", "source": [ "# Energy Extrapolation\n", "\n", "[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/block-hczhai/block2-preview/blob/master/docs/source/tutorial/energy-extrapolation.ipynb)" ], "metadata": { "id": "gEis3BAAaJLD" } }, { "cell_type": "code", "source": [ "!pip install block2==0.5.2rc13 -qq --progress-bar off --extra-index-url=https://block-hczhai.github.io/block2-preview/pypi/\n", "!pip install pyscf==2.3.0 -qq --progress-bar off" ], "metadata": { "id": "2FXmEVkEaJxX" }, "execution_count": 1, "outputs": [] }, { "cell_type": "markdown", "source": [ "## Introduction\n", "\n", "In this tutorial we explain how to do DMRG energy extrapolation and also get an estimate of the error in the extrapolated energy. First we need to do a normal DMRG calculation, and then a DMRG with a reserve schedule, and then we do the energy extrapolation using the data from the reserve schedule. The DMRG energy is extrapolated using a linear fit for discarded weight vs energies for different bond dimensions. The error is estimated as one fifth of the extrapolation distance, as a convention. It is not recommended to use the normal DMRG data for the extrapolation because the energy for each bond dimension may not be fully converged. For the same reason, the energy at the largest bond dimension may also be excluded from the extrapolation.\n", "\n", "First, we prepare the integrals and the MPO and the initial guess for the MPS." ], "metadata": { "id": "aAO2KvxWaSjo" } }, { "cell_type": "code", "source": [ "import numpy as np\n", "from pyblock2._pyscf.ao2mo import integrals as itg\n", "from pyblock2.driver.core import DMRGDriver, SymmetryTypes\n", "\n", "from pyscf import gto, scf\n", "\n", "mol = gto.M(atom='C 0 0 0; C 0 0 1.2425', basis='ccpvdz', symmetry='d2h')\n", "mf = scf.RHF(mol).run(conv_tol=1E-14)\n", "ncas, n_elec, spin, ecore, h1e, g2e, orb_sym = itg.get_rhf_integrals(mf,\n", " ncore=2, ncas=26, g2e_symm=8)\n", "\n", "print(\"NCAS = %d NCASELEC = %d\" % (ncas, n_elec))\n", "driver = DMRGDriver(scratch=\"./tmp\", symm_type=SymmetryTypes.SU2,\n", " stack_mem=4 << 30, n_threads=4)\n", "driver.initialize_system(n_sites=ncas, n_elec=n_elec, spin=spin, orb_sym=orb_sym)\n", "mpo = driver.get_qc_mpo(h1e=h1e, g2e=g2e, ecore=ecore, iprint=0)\n", "ket = driver.get_random_mps(tag=\"KET\", bond_dim=250, nroots=1)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "XuXZpeFTb5e2", "outputId": "5c43a1cf-edfc-473c-d479-91621c850990" }, "execution_count": 2, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "converged SCF energy = -75.3869023777059\n", "NCAS = 26 NCASELEC = 8\n" ] } ] }, { "cell_type": "markdown", "source": [ "## The Normal Schedule\n", "\n", "First, we do a DMRG with the normal (forward) schedule (namely, the bond dimension increses). We first do 20 2-site sweeps, and then 8 1-site sweeps when it is close to convergence, which is cheaper.\n", "\n", "To prevent optimizing to local minima, it is highly recommended to set the first bond dimension in the forward to be at least 250. If the gap of the system is small or the truncation error is large (for example, for 2D Hubbard model), one may need to do more sweeps for each bond dimension. Sometimes state averaging over multiple states (for example, setting ``nroots=4`` in ``driver.get_random_mps`` above) can help converging the ground state." ], "metadata": { "id": "AoKOfFPEbrHw" } }, { "cell_type": "code", "source": [ "bond_dims = [250] * 4 + [500] * 4 + [750] * 4 + [1000] * 4\n", "noises = [1e-4] * 4 + [1e-5] * 12 + [0]\n", "thrds = [1e-8] * 20\n", "\n", "energy = driver.dmrg(mpo, ket, n_sweeps=28, bond_dims=bond_dims, noises=noises,\n", " thrds=thrds, iprint=1, twosite_to_onesite=20)\n", "print('DMRG energy (variational) = %20.15f' % energy)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "JqphdawZboo9", "outputId": "26dde43a-9f8d-4b7a-81aa-4e1f05c088a4" }, "execution_count": 3, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "\n", "Sweep = 0 | Direction = forward | Bond dimension = 250 | Noise = 1.00e-04 | Dav threshold = 1.00e-08\n", "Time elapsed = 48.206 | E = -75.6988045936 | DW = 4.92e-07\n", "\n", "Sweep = 1 | Direction = backward | Bond dimension = 250 | Noise = 1.00e-04 | Dav threshold = 1.00e-08\n", "Time elapsed = 61.355 | E = -75.7234052111 | DE = -2.46e-02 | DW = 4.32e-05\n", "\n", "Sweep = 2 | Direction = forward | Bond dimension = 250 | Noise = 1.00e-04 | Dav threshold = 1.00e-08\n", "Time elapsed = 74.078 | E = -75.7249238917 | DE = -1.52e-03 | DW = 6.80e-05\n", "\n", "Sweep = 3 | Direction = backward | Bond dimension = 250 | Noise = 1.00e-04 | Dav threshold = 1.00e-08\n", "Time elapsed = 87.346 | E = -75.7254307257 | DE = -5.07e-04 | DW = 6.87e-05\n", "\n", "Sweep = 4 | Direction = forward | Bond dimension = 500 | Noise = 1.00e-05 | Dav threshold = 1.00e-08\n", "Time elapsed = 110.212 | E = -75.7273558056 | DE = -1.93e-03 | DW = 3.97e-06\n", "\n", "Sweep = 5 | Direction = backward | Bond dimension = 500 | Noise = 1.00e-05 | Dav threshold = 1.00e-08\n", "Time elapsed = 142.710 | E = -75.7278860763 | DE = -5.30e-04 | DW = 1.58e-05\n", "\n", "Sweep = 6 | Direction = forward | Bond dimension = 500 | Noise = 1.00e-05 | Dav threshold = 1.00e-08\n", "Time elapsed = 173.278 | E = -75.7278862359 | DE = -1.60e-07 | DW = 1.67e-05\n", "\n", "Sweep = 7 | Direction = backward | Bond dimension = 500 | Noise = 1.00e-05 | Dav threshold = 1.00e-08\n", "Time elapsed = 203.646 | E = -75.7279905032 | DE = -1.04e-04 | DW = 1.65e-05\n", "\n", "Sweep = 8 | Direction = forward | Bond dimension = 750 | Noise = 1.00e-05 | Dav threshold = 1.00e-08\n", "Time elapsed = 249.619 | E = -75.7282187494 | DE = -2.28e-04 | DW = 1.40e-06\n", "\n", "Sweep = 9 | Direction = backward | Bond dimension = 750 | Noise = 1.00e-05 | Dav threshold = 1.00e-08\n", "Time elapsed = 308.157 | E = -75.7283283738 | DE = -1.10e-04 | DW = 2.39e-06\n", "\n", "Sweep = 10 | Direction = forward | Bond dimension = 750 | Noise = 1.00e-05 | Dav threshold = 1.00e-08\n", "Time elapsed = 368.993 | E = -75.7283309384 | DE = -2.56e-06 | DW = 3.28e-06\n", "\n", "Sweep = 11 | Direction = backward | Bond dimension = 750 | Noise = 1.00e-05 | Dav threshold = 1.00e-08\n", "Time elapsed = 426.670 | E = -75.7283513281 | DE = -2.04e-05 | DW = 2.59e-06\n", "\n", "Sweep = 12 | Direction = forward | Bond dimension = 1000 | Noise = 1.00e-05 | Dav threshold = 1.00e-08\n", "Time elapsed = 502.719 | E = -75.7284190450 | DE = -6.77e-05 | DW = 1.18e-06\n", "\n", "Sweep = 13 | Direction = backward | Bond dimension = 1000 | Noise = 1.00e-05 | Dav threshold = 1.00e-08\n", "Time elapsed = 592.335 | E = -75.7284581391 | DE = -3.91e-05 | DW = 1.11e-06\n", "\n", "Sweep = 14 | Direction = forward | Bond dimension = 1000 | Noise = 1.00e-05 | Dav threshold = 1.00e-08\n", "Time elapsed = 681.041 | E = -75.7284587601 | DE = -6.21e-07 | DW = 1.80e-06\n", "\n", "Sweep = 15 | Direction = backward | Bond dimension = 1000 | Noise = 1.00e-05 | Dav threshold = 1.00e-08\n", "Time elapsed = 769.707 | E = -75.7284677459 | DE = -8.99e-06 | DW = 1.16e-06\n", "\n", "Sweep = 16 | Direction = forward | Bond dimension = 1000 | Noise = 0.00e+00 | Dav threshold = 1.00e-08\n", "Time elapsed = 854.210 | E = -75.7284682379 | DE = -4.92e-07 | DW = 1.14e-06\n", "\n", "Sweep = 17 | Direction = backward | Bond dimension = 1000 | Noise = 0.00e+00 | Dav threshold = 1.00e-08\n", "Time elapsed = 934.636 | E = -75.7284724835 | DE = -4.25e-06 | DW = 1.16e-06\n", "\n", "Sweep = 18 | Direction = forward | Bond dimension = 1000 | Noise = 0.00e+00 | Dav threshold = 1.00e-08\n", "Time elapsed = 1019.953 | E = -75.7284724841 | DE = -6.41e-10 | DW = 1.16e-06\n", "\n", "Sweep = 19 | Direction = backward | Bond dimension = 1000 | Noise = 0.00e+00 | Dav threshold = 1.00e-08\n", "Time elapsed = 1099.196 | E = -75.7284733044 | DE = -8.20e-07 | DW = 1.17e-06\n", "\n", "\n", "Sweep = 20 | Direction = forward | Bond dimension = 1000 | Noise = 0.00e+00 | Dav threshold = 1.00e-09\n", "Time elapsed = 44.519 | E = -75.7284670047 | DE = 6.30e-06 | DW = 4.75e-17\n", "\n", "Sweep = 21 | Direction = backward | Bond dimension = 1000 | Noise = 0.00e+00 | Dav threshold = 1.00e-09\n", "Time elapsed = 113.701 | E = -75.7284673359 | DE = -3.31e-07 | DW = 6.22e-19\n", "\n", "Sweep = 22 | Direction = forward | Bond dimension = 1000 | Noise = 0.00e+00 | Dav threshold = 1.00e-09\n", "Time elapsed = 157.729 | E = -75.7284677042 | DE = -3.68e-07 | DW = 4.78e-17\n", "\n", "Sweep = 23 | Direction = backward | Bond dimension = 1000 | Noise = 0.00e+00 | Dav threshold = 1.00e-09\n", "Time elapsed = 224.673 | E = -75.7284679694 | DE = -2.65e-07 | DW = 5.68e-19\n", "\n", "Sweep = 24 | Direction = forward | Bond dimension = 1000 | Noise = 0.00e+00 | Dav threshold = 1.00e-09\n", "Time elapsed = 268.982 | E = -75.7284681140 | DE = -1.45e-07 | DW = 5.17e-17\n", "\n", "Sweep = 25 | Direction = backward | Bond dimension = 1000 | Noise = 0.00e+00 | Dav threshold = 1.00e-09\n", "Time elapsed = 334.809 | E = -75.7284681905 | DE = -7.64e-08 | DW = 5.74e-19\n", "\n", "Sweep = 26 | Direction = forward | Bond dimension = 1000 | Noise = 0.00e+00 | Dav threshold = 1.00e-09\n", "Time elapsed = 378.814 | E = -75.7284682377 | DE = -4.72e-08 | DW = 1.32e-17\n", "\n", "Sweep = 27 | Direction = backward | Bond dimension = 1000 | Noise = 0.00e+00 | Dav threshold = 1.00e-09\n", "Time elapsed = 444.799 | E = -75.7284682709 | DE = -3.32e-08 | DW = 6.42e-19\n", "\n", "ATTENTION: DMRG is not converged to desired tolerance of 1.00e-08\n", "DMRG energy (variational) = -75.728468270883781\n" ] } ] }, { "cell_type": "markdown", "source": [ "## The Reverse Schedule\n", "\n", "For the reverse schedule, we decrease the bond dimension to make the energy at each bond dimension fully converged. The noise should be zero. The MPS is first changed from the 1-site format to the 2-site format. And the reverse schedule has to be done fully using the 2-site DMRG (since 1-site DMRG with zero noise will generate close-to-zero discarded weights). The energy convergence tolerance is set to zero to prevent early stop.\n", "\n", "Note that the reverse schedule will destroy the data in the optimized MPS. We can first backup the MPS by copying it to another tag ``KET-ORIG``. If you want to later compute the properties on the optimized MPS, the ``ket_orig`` MPS should be used. If you want to restart a calculation from the MPS (automatically) stored in the scratch foloder, you can load it using its tag (for example, using ``ket = driver.load_mps(tag='KET-ORIG')``).\n", "\n", "In practice, it is recommended to perform an even number of sweeps for each reverse schedule bond dimension, to prevent DW difference for odd/even sweeps. The first reverse schedule bond dimension should be slightly smaller than the last forward schedule bond dimension, to make sure that the energy obatined in reverse schedule is fully converged. One can also discard the energy from the first bond dimension to ensure this. The last bond dimension in reverse schedule should not be too small, since it is hard to obtain a stable energy of a very low bond dimension MPS." ], "metadata": { "id": "rLUKdqQ6d13V" } }, { "cell_type": "code", "source": [ "bond_dims = [800] * 4 + [700] * 4 + [600] * 4 + [500] * 4\n", "noises = [0] * 16\n", "thrds = [1e-10] * 16\n", "\n", "ket_orig = driver.copy_mps(ket, tag='KET-ORIG')\n", "ket = driver.adjust_mps(ket, dot=2)[0]\n", "energy = driver.dmrg(mpo, ket, n_sweeps=16, bond_dims=bond_dims, noises=noises,\n", " tol=0, thrds=thrds, iprint=1)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "dOr3oMovfiS1", "outputId": "48a81eb2-0bb2-44ee-a76e-f5eedf019521" }, "execution_count": 4, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "\n", "Sweep = 0 | Direction = forward | Bond dimension = 800 | Noise = 0.00e+00 | Dav threshold = 1.00e-10\n", "Time elapsed = 75.765 | E = -75.7284682749 | DW = 6.89e-06\n", "\n", "Sweep = 1 | Direction = backward | Bond dimension = 800 | Noise = 0.00e+00 | Dav threshold = 1.00e-10\n", "Time elapsed = 138.033 | E = -75.7284033759 | DE = 6.49e-05 | DW = 2.47e-06\n", "\n", "Sweep = 2 | Direction = forward | Bond dimension = 800 | Noise = 0.00e+00 | Dav threshold = 1.00e-10\n", "Time elapsed = 205.532 | E = -75.7284034664 | DE = -9.04e-08 | DW = 2.42e-06\n", "\n", "Sweep = 3 | Direction = backward | Bond dimension = 800 | Noise = 0.00e+00 | Dav threshold = 1.00e-10\n", "Time elapsed = 310.035 | E = -75.7284040381 | DE = -5.72e-07 | DW = 2.40e-06\n", "\n", "Sweep = 4 | Direction = forward | Bond dimension = 700 | Noise = 0.00e+00 | Dav threshold = 1.00e-10\n", "Time elapsed = 388.303 | E = -75.7283965259 | DE = 7.51e-06 | DW = 8.05e-06\n", "\n", "Sweep = 5 | Direction = backward | Bond dimension = 700 | Noise = 0.00e+00 | Dav threshold = 1.00e-10\n", "Time elapsed = 435.992 | E = -75.7283294371 | DE = 6.71e-05 | DW = 3.42e-06\n", "\n", "Sweep = 6 | Direction = forward | Bond dimension = 700 | Noise = 0.00e+00 | Dav threshold = 1.00e-10\n", "Time elapsed = 483.591 | E = -75.7283294384 | DE = -1.30e-09 | DW = 3.42e-06\n", "\n", "Sweep = 7 | Direction = backward | Bond dimension = 700 | Noise = 0.00e+00 | Dav threshold = 1.00e-10\n", "Time elapsed = 531.150 | E = -75.7283301970 | DE = -7.59e-07 | DW = 3.40e-06\n", "\n", "Sweep = 8 | Direction = forward | Bond dimension = 600 | Noise = 0.00e+00 | Dav threshold = 1.00e-10\n", "Time elapsed = 574.284 | E = -75.7283301973 | DE = -2.32e-10 | DW = 1.29e-05\n", "\n", "Sweep = 9 | Direction = backward | Bond dimension = 600 | Noise = 0.00e+00 | Dav threshold = 1.00e-10\n", "Time elapsed = 610.012 | E = -75.7282237067 | DE = 1.06e-04 | DW = 8.58e-06\n", "\n", "Sweep = 10 | Direction = forward | Bond dimension = 600 | Noise = 0.00e+00 | Dav threshold = 1.00e-10\n", "Time elapsed = 646.755 | E = -75.7282237089 | DE = -2.27e-09 | DW = 8.58e-06\n", "\n", "Sweep = 11 | Direction = backward | Bond dimension = 600 | Noise = 0.00e+00 | Dav threshold = 1.00e-10\n", "Time elapsed = 683.397 | E = -75.7282244369 | DE = -7.28e-07 | DW = 8.41e-06\n", "\n", "Sweep = 12 | Direction = forward | Bond dimension = 500 | Noise = 0.00e+00 | Dav threshold = 1.00e-10\n", "Time elapsed = 714.398 | E = -75.7282244373 | DE = -3.28e-10 | DW = 2.34e-05\n", "\n", "Sweep = 13 | Direction = backward | Bond dimension = 500 | Noise = 0.00e+00 | Dav threshold = 1.00e-10\n", "Time elapsed = 741.278 | E = -75.7280407981 | DE = 1.84e-04 | DW = 1.76e-05\n", "\n", "Sweep = 14 | Direction = forward | Bond dimension = 500 | Noise = 0.00e+00 | Dav threshold = 1.00e-10\n", "Time elapsed = 768.488 | E = -75.7280408085 | DE = -1.04e-08 | DW = 1.76e-05\n", "\n", "Sweep = 15 | Direction = backward | Bond dimension = 500 | Noise = 0.00e+00 | Dav threshold = 1.00e-10\n", "Time elapsed = 795.707 | E = -75.7280421420 | DE = -1.33e-06 | DW = 1.74e-05\n", "\n" ] } ] }, { "cell_type": "markdown", "source": [ "## Energy Extrapolation" ], "metadata": { "id": "93XI4zDZgnHZ" } }, { "cell_type": "markdown", "source": [ "We can get the extrapolated energy using linear fitting." ], "metadata": { "id": "51Cdjar2ifvG" } }, { "cell_type": "code", "source": [ "import scipy.stats\n", "\n", "ds, dws, eners = driver.get_dmrg_results()\n", "print('BOND DIMS = ', ds[3::4])\n", "print('Discarded Weights = ', dws[3::4])\n", "print('Energies = ', eners[3::4, 0])\n", "reg = scipy.stats.linregress(dws[3::4], eners[3::4, 0])\n", "emin, emax = min(eners[3::4, 0]), max(eners[3::4, 0])\n", "print('DMRG energy (extrapolated) = %20.15f +/- %15.10f' %\n", " (reg.intercept, abs(reg.intercept - emin) / 5))" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "kRgOZpp2gv1P", "outputId": "bfc24b03-e696-4abb-afee-e07efa0f9b72" }, "execution_count": 5, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "BOND DIMS = [800 700 600 500]\n", "Discarded Weights = [2.39910258e-06 3.39687452e-06 8.41354132e-06 1.74228067e-05]\n", "Energies = [-75.72840404 -75.7283302 -75.72822444 -75.72804214]\n", "DMRG energy (extrapolated) = -75.728429118584003 +/- 0.0000050161\n" ] } ] }, { "cell_type": "markdown", "source": [ "Finally, we plot the energy extrapolation.\n", "\n", "If you see a non-linear behavior, for example, the actual energy at larger bond dimension is higher than the linear fitting, it can be a signal of local minima. One may need to use increase the largest bond dimension used in the forward sweep, change the orbital ordering, or use a stricter Davidson convergence threshold (such as 1E-10)." ], "metadata": { "id": "bx4acBALijEc" } }, { "cell_type": "code", "source": [ "import matplotlib.pyplot as plt\n", "from matplotlib import ticker\n", "de = emax - emin\n", "x_reg = np.array([0, dws[-1] + dws[3]])\n", "ax = plt.gca()\n", "ax.xaxis.set_major_formatter(ticker.StrMethodFormatter(\"{x:.1E}\"))\n", "plt.plot(x_reg, reg.intercept + reg.slope * x_reg, '--', linewidth=1, color='#426A5A')\n", "plt.plot(dws[3::4], eners[3::4, 0], ' ', marker='s', mfc='white', mec='#426A5A', color='#426A5A', markersize=5)\n", "plt.text(dws[3] * 0.25, emax + de * 0.1, \"$E(M=\\\\infty) = %.6f \\\\pm %.6f \\\\mathrm{\\\\ Hartree}$\" %\n", " (reg.intercept, abs(reg.intercept - emin) / 5), color='#426A5A', fontsize=12)\n", "plt.text(dws[3] * 0.25, emax - de * 0.0, \"$R^2 = %.6f$\" % (reg.rvalue ** 2),\n", " color='#426A5A', fontsize=12)\n", "plt.xlim((0, dws[-1] + dws[3]))\n", "plt.ylim((reg.intercept - de * 0.1, emax + de * 0.2))\n", "plt.xlabel(\"Largest Discarded Weight\")\n", "plt.ylabel(\"Sweep Energy (Hartree)\")\n", "plt.subplots_adjust(left=0.17, bottom=0.1, right=0.95, top=0.95)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 503 }, "id": "03Zq1W_VinsW", "outputId": "f4298084-4f66-4065-f951-36f160a2131e" }, "execution_count": 6, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" 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