From 54e1a985b5d208fa6f24953c538c7cd90505bec6 Mon Sep 17 00:00:00 2001 From: Hatem Helal Date: Fri, 26 Apr 2024 15:08:34 +0000 Subject: [PATCH] add autodiff in optim --- docs/optim.ipynb | 34 ++++++++++++++++++++++++---------- 1 file changed, 24 insertions(+), 10 deletions(-) diff --git a/docs/optim.ipynb b/docs/optim.ipynb index 1af1a09..2c29636 100644 --- a/docs/optim.ipynb +++ b/docs/optim.ipynb @@ -17,7 +17,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Energy Minimisation\n", + "# Electronic Energy Minimisation\n", "\n", "A central problem of electronic structure simulations is finding the ground state \n", "configuration of many interacting electrons. Within MESS this is handled by:\n", @@ -35,7 +35,11 @@ { "cell_type": "code", "execution_count": 2, - "metadata": {}, + "metadata": { + "tags": [ + "hide-cell" + ] + }, "outputs": [ { "name": "stderr", @@ -56,8 +60,15 @@ "from mess import Hamiltonian, basisset, molecule\n", "from mess.structure import nuclear_energy\n", "\n", - "sns.set_theme(style=\"whitegrid\")\n", - "\n", + "sns.set_theme(style=\"whitegrid\")" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ "mol = molecule(\"water\")\n", "basis = basisset(mol, \"6-31g\")\n", "H = Hamiltonian(basis, xc_method=\"lda\")\n", @@ -75,7 +86,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -94,18 +105,21 @@ "metadata": {}, "source": [ "We use a somewhat arbitrary initial guess and use the Adam optimiser to minimise\n", - "the total energy" + "the total energy. The function transformation\n", + "[jax.value_and_grad](https://jax.readthedocs.io/en/latest/_autosummary/jax.value_and_grad.html)\n", + "uses automatic differentiation to evaluate both the energy and the gradient of the\n", + "energy with respect to the trial matrix $Z$." ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "fa079b0017194f83a0582509f15799a9", + "model_id": "8a43134ddb704605bd039d816026672b", "version_major": 2, "version_minor": 0 }, @@ -139,12 +153,12 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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