{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "P3PtqZkfwBPQ" }, "source": [ "# Partial Differential Equations\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/dmrg-pde.ipynb)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "id": "ESv9UfhG2KmT" }, "outputs": [], "source": [ "!pip install block2==0.5.4rc10 -qq --progress-bar off --extra-index-url=https://block-hczhai.github.io/block2-preview/pypi/" ] }, { "cell_type": "markdown", "metadata": { "id": "1dy3Xb5H3vA8" }, "source": [ "## Prepration" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "id": "QmOlQM4i3xd1" }, "outputs": [], "source": [ "import numpy as np\n", "from pyblock2.algebra.io import MPSTools, MPOTools\n", "from pyblock2.algebra.pde import PDETools1D" ] }, { "cell_type": "markdown", "metadata": { "id": "Kwk9Rw062XXZ" }, "source": [ "## Diffusion Equation (TD-DMRG)\n", "\n", "In this example, we solve the following diffusion equation\n", "\n", "$$\\frac{\\mathrm{d} f(x,t)}{\\mathrm{d} t} = \\nu \\ \\frac{\\mathrm{d}^2 f(x,t)}{\\mathrm{d} x^2}\n", "+ \\alpha\\ g(x)$$\n", "\n", "on the interval $x\\in [-1,1]$ using the QTT grid with $2^8$ grid points along the $x$ direction. We propagate $nt = 50$ steps with the time step size $dt = 0.002$. $\\nu = 0.1$.\n", "\n", "**Kernels:** With ``kernel_a``, we have $\\alpha = 0$, and with ``kernel_b``, we have $\\alpha = 1$.\n", "\n", "**Boundary condition and parameters:** $$ f(x,t=0) = \\begin{cases}1 & -0.2\\le x \\le 0.2 \\\\ 0 & \\text{otherwise}\\end{cases} \\\\ g(x) = \\begin{cases}1 & 0.3\\le x \\le 0.5 \\\\ 0 & \\text{otherwise}\\end{cases}$$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "6Bb5jW712SHn", "outputId": "7eb50087-e4fb-4d0f-ebe0-bf7e353a9803" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sigma = 3.2768\n", "it = 0 ( 0 %)\n", "it = 12 ( 24 %)\n", "it = 24 ( 48 %)\n", "it = 36 ( 72 %)\n", "it = 48 ( 96 %)\n", "it = 0 ( 0 %)\n", "it = 12 ( 24 %)\n", "it = 24 ( 48 %)\n", "it = 36 ( 72 %)\n", "it = 48 ( 96 %)\n" ] } ], "source": [ "pde = PDETools1D(8, xi=-1, xf=1, bases=2)\n", "pde.init_dmrg_driver(scratch=\"./tmp\")\n", "driver = pde.driver\n", "\n", "nu = 0.1\n", "dt = 0.002\n", "nt = 50\n", "\n", "sigma = nu * dt / pde.dx ** 2\n", "print('sigma = ', sigma)\n", "\n", "# H = nu * d^2/dx^2\n", "pympo = pde.pympo_from_differential([0, 0, 1], pbc=True) * nu\n", "mpo = MPOTools.to_block2(pympo, driver.basis, add_ident=True)\n", "\n", "pyket = pde.pymps_from_range(-0.2, 0.2, 1.0)\n", "ket = MPSTools.to_block2(pyket, driver.basis, tag='KET')\n", "ket = driver.adjust_mps(ket, dot=2)[0]\n", "\n", "pygket = pde.pymps_from_range(0.3, 0.5, 1.0)\n", "gket = MPSTools.to_block2(pygket, driver.basis, tag='GKET')\n", "gket = driver.adjust_mps(gket, dot=2)[0]\n", "\n", "# df/dt = nu * d^2 f / dx^2\n", "def kernel_a(beta, hop, a, b, xs):\n", " hop(a, b, beta) # b = beta * H * a\n", "\n", "# df/dt = nu * d^2 f / dx^2 + g\n", "def kernel_b(beta, hop, a, b, xs):\n", " hop(a, b, beta)\n", " b += beta * xs[0]\n", "\n", "def run_td(mpo, ket, kernel, ext_mpss=None):\n", " tket = driver.copy_mps(ket, tag='TKET')\n", " for it in range(nt):\n", " if it % (nt // 4) == 0:\n", " print(\"it = %5d (%4.0f %%)\" % (it, it * 100 / nt))\n", " tket = driver.td_dmrg(mpo, tket, -dt, -dt, final_mps_tag='TKET',\n", " n_sub_sweeps=2, te_type='rk4', kernel=kernel, ext_mpss=ext_mpss,\n", " cutoff=1E-24, hermitian=False, normalize_mps=False, bond_dims=[50], iprint=0)\n", " tket = driver.adjust_mps(tket, dot=1)[0]\n", " return MPSTools.from_block2(tket)\n", "\n", "pytket_a = run_td(mpo, ket, kernel_a)\n", "pytket_b = run_td(mpo, ket, kernel_b, [gket])" ] }, { "cell_type": "markdown", "metadata": { "id": "13N1RVYU46F1" }, "source": [ "### Plot results" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 635 }, "id": "7yF8a7OO47QH", "outputId": "705020f8-fc6b-48c7-a04b-963896551581" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fx, fy = pde.pymps_rasterize(pyket)\n", "gx, gy = pde.pymps_rasterize(pytket_a)\n", "hx, hy = pde.pymps_rasterize(pytket_b)\n", "jx, jy = pde.pymps_rasterize(pygket)\n", "\n", "import matplotlib.pyplot as plt\n", "\n", "plt.grid(which='both', axis='both')\n", "\n", "plt.plot(fx, fy, '--', label='$f(x,t=0)$')\n", "plt.plot(gx, gy, '-', label='$f(x,t=t_f)$ kernel-a')\n", "plt.plot(hx, hy, '-', label='$f(x,t=t_f)$ kernel-b')\n", "plt.plot(jx, jy, '--', label='$g(x)$')\n", "plt.legend(loc='upper left')\n", "plt.gcf().set_dpi(150)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "CIL8vLlD5RCV" }, "source": [ "## Time-Independent Schrödinger Equation (Ground and Excited State DMRG)\n", "\n", "In this example, we solve the following time-independent schrödinger equation\n", "\n", "$$ \\left( -\\frac{\\hbar^2}{2\\mu} \\frac{\\mathrm{d}^2}{\\mathrm{d} x^2}+V(x) \\right) \\psi(x) = E\\ \\psi(x) $$\n", "\n", "on the interval $x\\in[-2,7]$ using the QTT grid with $2^{12}$ grid points along the $x$ direction. We use the Morse potential\n", "$$V(x) = D_e \\big(\\mathrm{e}^{-2\\beta x} - 2\\mathrm{e}^{-\\beta x} \\big)$$\n", "\n", "The analytical solution is given by\n", "$$E_n = -D_e + \\left( n+\\frac{1}{2}\\right) \\hbar\\omega - \\left( n+\\frac{1}{2}\\right)^2 \\frac{\\hbar^2\\omega^2}{4D_e},\\quad\\left(\\omega = \\sqrt{\\frac{2D_e\\beta^2}{\\mu}}\\right)$$\n", "\n", "**Parameters:** $\\beta = 0.5, \\mu=6, D_e=12, \\hbar=1$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "hI960nux5IqA", "outputId": "4dc44e17-c7e4-4f0f-830a-1cda3276e8c8" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Sweep = 0 | Direction = forward | Bond dimension = 50 | Noise = 0.00e+00 | Dav threshold = 0.00e+00\n", "Time elapsed = 0.018 | E = -7.0114287425 | DW = 0.00000e+00\n", "\n", "Sweep = 1 | Direction = backward | Bond dimension = 50 | Noise = 0.00e+00 | Dav threshold = 0.00e+00\n", "Time elapsed = 0.185 | E = -11.5051563140 | DE = -4.49e+00 | DW = 1.57547e-30\n", "\n", "Sweep = 2 | Direction = forward | Bond dimension = 50 | Noise = 0.00e+00 | Dav threshold = 0.00e+00\n", "Time elapsed = 0.244 | E = -11.5052092135 | DE = -5.29e-05 | DW = 4.76125e-31\n", "\n", "Sweep = 3 | Direction = backward | Bond dimension = 50 | Noise = 0.00e+00 | Dav threshold = 0.00e+00\n", "Time elapsed = 0.290 | E = -11.5052092135 | DE = 3.59e-13 | DW = 3.16122e-31\n", "\n", "\n", "Sweep = 0 | Direction = forward | Bond dimension = 50 | Noise = 0.00e+00 | Dav threshold = 0.00e+00\n", "Time elapsed = 0.031 | E = -6.6026598014 | DW = 0.00000e+00\n", "\n", "Sweep = 1 | Direction = backward | Bond dimension = 50 | Noise = 0.00e+00 | Dav threshold = 0.00e+00\n", "Time elapsed = 0.354 | E = -10.5468390226 | DE = -3.94e+00 | DW = 4.27018e-31\n", "\n", "Sweep = 2 | Direction = forward | Bond dimension = 50 | Noise = 0.00e+00 | Dav threshold = 0.00e+00\n", "Time elapsed = 0.423 | E = -10.5468790843 | DE = -4.01e-05 | DW = 4.86237e-31\n", "\n", "Sweep = 3 | Direction = backward | Bond dimension = 50 | Noise = 0.00e+00 | Dav threshold = 0.00e+00\n", "Time elapsed = 0.463 | E = -10.5468790843 | DE = 1.98e-12 | DW = 4.78202e-31\n", "\n", "\n", "Sweep = 0 | Direction = forward | Bond dimension = 50 | Noise = 0.00e+00 | Dav threshold = 0.00e+00\n", "Time elapsed = 0.073 | E = -2.0014809622 | DW = 0.00000e+00\n", "\n", "Sweep = 1 | Direction = backward | Bond dimension = 50 | Noise = 0.00e+00 | Dav threshold = 0.00e+00\n", "Time elapsed = 0.534 | E = -9.6302181085 | DE = -7.63e+00 | DW = 6.51780e-31\n", "\n", "Sweep = 2 | Direction = forward | Bond dimension = 50 | Noise = 0.00e+00 | Dav threshold = 0.00e+00\n", "Time elapsed = 0.594 | E = -9.6302181718 | DE = -6.33e-08 | DW = 1.04214e-30\n", "\n", "Sweep = 3 | Direction = backward | Bond dimension = 50 | Noise = 0.00e+00 | Dav threshold = 0.00e+00\n", "Time elapsed = 0.638 | E = -9.6302181718 | DE = 1.44e-13 | DW = 6.28101e-31\n", "\n", "E[ 0] = -11.50520921 Error = -8.80e-07\n", "E[ 1] = -10.54687908 Error = -4.08e-06\n", "E[ 2] = -9.63021817 Error = -9.84e-06\n" ] } ], "source": [ "pde = PDETools1D(12, xi=-2, xf=7, bases=2)\n", "pde.init_dmrg_driver(scratch=\"./tmp\")\n", "driver = pde.driver\n", "\n", "beta = 0.5\n", "mu = 6\n", "de = 12\n", "\n", "# V(x) = de * exp(-2 beta x) - 2 * exp(-beta x)\n", "pymps = de * (pde.pymps_from_exponential(np.e, -2 * beta) - 2 * pde.pymps_from_exponential(np.e, -beta))\n", "\n", "# H = (-1/2mu) * d^2/dx^2 + V(x)\n", "pympo = (-1 / (2 * mu)) * pde.pympo_from_differential([0, 0, 1], pbc=True) + pymps.diag()\n", "\n", "mpo = MPOTools.to_block2(pympo, driver.basis, add_ident=True)\n", "\n", "nroots = 3\n", "kets = [driver.get_random_mps(tag=\"KET%d\" % x, bond_dim=1) for x in range(nroots)]\n", "energies = []\n", "for ir in range(nroots):\n", " energy = driver.dmrg(mpo, kets[ir], n_sweeps=12, bond_dims=[50] * 12,\n", " noises=[0] * 12, thrds=[0] * 12, dav_max_iter=500, iprint=1,\n", " proj_mpss=kets[:ir], proj_weights=[10.0] * ir,\n", " dav_rel_conv_thrd=1E-5, tol=1E-8, cutoff=1E-30)\n", " energies.append(energy)\n", "\n", "omega = (2 * de * beta ** 2 / mu) ** 0.5\n", "exact = [-de + (n + 0.5) * omega - (n + 0.5) ** 2 * omega ** 2 / (4 * de) for n in range(nroots)]\n", "\n", "for ir in range(nroots):\n", " print(\"E[%2d] = %15.8f Error = %9.2e\" % (ir, energies[ir], energies[ir] - exact[ir]))\n", "\n", "pykets = []\n", "for ir in range(nroots):\n", " kets[ir] = driver.adjust_mps(kets[ir], dot=1)[0]\n", " pykets.append(MPSTools.from_block2(kets[ir]))" ] }, { "cell_type": "markdown", "metadata": { "id": "pZB8VrRU9JMz" }, "source": [ "### Plot results" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 641 }, "id": "6amGkNVS9FZe", "outputId": "93dbdeb1-5b2b-4098-eec2-9dfddbb7a3e3" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "plt.grid(which='both', axis='both')\n", "\n", "fx, fy = pde.pymps_rasterize(pymps / 100)\n", "plt.plot(fx, fy, '--', label='$V(x)$ / 100')\n", "\n", "for ir, pyket in enumerate(pykets):\n", " fx, fy = pde.pymps_rasterize(pyket)\n", " plt.plot(fx, fy, '-', label='$\\\\psi_%d(x)$' % ir)\n", "plt.legend(loc='upper right')\n", "plt.gcf().set_dpi(150)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "ia8q40qW9arj" }, "source": [ "## Poisson Equation (Dynamical DMRG)\n", "\n", "In this example, we solve the following Poisson equation\n", "\n", "$$ \\frac{\\mathrm{d}^2}{\\mathrm{d}x^2}\\ f(x) = g(x) $$\n", "\n", "on the interval $x\\in [0,1]$ (periodic) using the QTT grid with $2^8$ grid points along the $x$ direction. We set\n", "\n", "$$g(x) = \\delta(x - 0.35) + \\delta(x - 0.60) $$\n", "\n", "and $f(x=0) = f(x=1) = 0$ as the boundary condition." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "EYW8tZaV9Nwk", "outputId": "5e2af5ac-6e48-4697-e0c5-3d629692fb86" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Sweep = 0 | Direction = forward | BRA bond dimension = 5 | Noise = 0.00e+00 | Linear threshold = 0.00e+00\n", "Time elapsed = 0.024 | F = -1.1776266e-04 | DW = 1.82162e-25\n", "\n", "Sweep = 1 | Direction = backward | BRA bond dimension = 5 | Noise = 0.00e+00 | Linear threshold = 0.00e+00\n", "Time elapsed = 0.055 | F = -0.0026878715 | DF = -2.57e-03 | DW = 6.78374e-22\n", "\n", "Sweep = 2 | Direction = forward | BRA bond dimension = 5 | Noise = 0.00e+00 | Linear threshold = 0.00e+00\n", "Time elapsed = 0.083 | F = -0.0026878715 | DF = -1.15e-14 | DW = 9.16664e-25\n", "\n", "Sweep = 3 | Direction = backward | BRA bond dimension = 5 | Noise = 0.00e+00 | Linear threshold = 0.00e+00\n", "Time elapsed = 0.106 | F = -0.0026878715 | DF = 2.80e-13 | DW = 1.32988e-22\n", "\n", "Sweep = 4 | Direction = forward | BRA bond dimension = 5 | Noise = 0.00e+00 | Linear threshold = 0.00e+00\n", "Time elapsed = 0.129 | F = -0.0026878715 | DF = -3.50e-15 | DW = 6.72943e-25\n", "\n", "Sweep = 5 | Direction = backward | BRA bond dimension = 5 | Noise = 0.00e+00 | Linear threshold = 0.00e+00\n", "Time elapsed = 0.159 | F = -0.0026878715 | DF = 8.64e-15 | DW = 4.93266e-22\n", "\n", "Sweep = 6 | Direction = forward | BRA bond dimension = 5 | Noise = 0.00e+00 | Linear threshold = 0.00e+00\n", "Time elapsed = 0.184 | F = -0.0026878715 | DF = -2.39e-15 | DW = 3.33131e-23\n", "\n", "Sweep = 7 | Direction = backward | BRA bond dimension = 5 | Noise = 0.00e+00 | Linear threshold = 0.00e+00\n", "Time elapsed = 0.209 | F = -0.0026878715 | DF = -1.17e-15 | DW = 2.74649e-22\n", "\n", "Sweep = 8 | Direction = forward | BRA bond dimension = 5 | Noise = 0.00e+00 | Linear threshold = 0.00e+00\n", "Time elapsed = 0.236 | F = -0.0026878715 | DF = -1.64e-15 | DW = 2.38289e-25\n", "\n", "Sweep = 9 | Direction = backward | BRA bond dimension = 5 | Noise = 0.00e+00 | Linear threshold = 0.00e+00\n", "Time elapsed = 0.269 | F = -0.0026878715 | DF = -2.36e-15 | DW = 9.86052e-25\n", "\n", "Sweep = 10 | Direction = forward | BRA bond dimension = 5 | Noise = 0.00e+00 | Linear threshold = 0.00e+00\n", "Time elapsed = 0.294 | F = -0.0026878715 | DF = -2.28e-15 | DW = 8.74449e-24\n", "\n", "Sweep = 11 | Direction = backward | BRA bond dimension = 5 | Noise = 0.00e+00 | Linear threshold = 0.00e+00\n", "Time elapsed = 0.320 | F = -0.0026878715 | DF = -3.83e-15 | DW = 2.10892e-22\n", "\n" ] } ], "source": [ "pde = PDETools1D(8, xi=0, xf=1, bases=2)\n", "pde.init_dmrg_driver(scratch=\"./tmp\")\n", "driver = pde.driver\n", "\n", "# H = d^2/dx^2\n", "pympo = pde.pympo_from_differential([0, 0, 1], pbc=True)\n", "mpo = MPOTools.to_block2(pympo, driver.basis, add_ident=True)\n", "\n", "# g(x) = delta(x - 0.35) + delta(x - 0.60)\n", "pyket = pde.pymps_from_range(0.3, 0.3, 1.0) + pde.pymps_from_range(0.60, 0.60, 1.0)\n", "ket = MPSTools.to_block2(pyket, driver.basis, tag='KET')\n", "ket = driver.adjust_mps(ket, dot=2)[0]\n", "\n", "# p(x) = delta(x - 0.0) (boundary condition)\n", "pypket = pde.pymps_from_range(0.0, 0.0, 1.0)\n", "pket = MPSTools.to_block2(pypket, driver.basis, tag='PKET')\n", "pket = driver.adjust_mps(pket, dot=2)[0]\n", "\n", "impo = driver.get_identity_mpo()\n", "\n", "bra = driver.get_random_mps(tag=\"BRA\", bond_dim=5, nroots=1)\n", "\n", "# solve d^2 f(x) /dx^2 = g(x) with boundary condition f(0) = 0\n", "driver.multiply(bra, impo, ket, n_sweeps=12, bond_dims=[50] * 12,\n", " noises=[0] * 12, thrds=[0] * 12, tol=0.0, left_mpo=mpo,\n", " linear_max_iter=500, linear_rel_conv_thrd=1E-5, cutoff=1E-24, solver_type='CG',\n", " proj_mpss=[pket], proj_weights=[1.0], proj_bond_dim=100,\n", " iprint=1)\n", "\n", "bra = driver.adjust_mps(bra, dot=1)[0]\n", "pybra = MPSTools.from_block2(bra)" ] }, { "cell_type": "markdown", "metadata": { "id": "MDj-2g8q-xIH" }, "source": [ "### Plot results" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 635 }, "id": "1H_hBsEY-udm", "outputId": "fdc8e655-43cb-4a15-d8d9-5b5b27daca03" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "plt.grid(which='both', axis='both')\n", "\n", "fx, fy = pde.pymps_rasterize(pybra)\n", "gx, gy = pde.pymps_rasterize(pyket)\n", "px, py = pde.pymps_rasterize(pypket)\n", "plt.plot(fx, -fy, '-', label='$-f(x)$')\n", "plt.plot(gx, gy * max(abs(fy)), '--', label='$g(x)$')\n", "plt.plot(px, py * max(abs(fy)), '--', label='$p(x)$')\n", "\n", "plt.legend(loc='upper right')\n", "plt.gcf().set_dpi(150)\n", "plt.show()" ] } ], "metadata": { "colab": { "provenance": [] }, "kernelspec": { "display_name": "Python 3", "name": "python3" }, "language_info": { "name": "python" } }, "nbformat": 4, "nbformat_minor": 0 }