diff --git a/day_2/01-IntroductionDay2.ipynb b/day_2/01-IntroductionDay2.ipynb new file mode 100644 index 0000000000000000000000000000000000000000..b0eb7f2eb9609571f3b539f4a348c094e99d76fe --- /dev/null +++ b/day_2/01-IntroductionDay2.ipynb @@ -0,0 +1,137 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Day 2 - Parameterization of interatomic potentials" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this tutorial we will do simple fits for three different interatomic potentials.\n", + "* Embedded Atom Method Potential\n", + "* Neural Network Potential\n", + "* Atomic Cluster Expansion\n", + "\n", + "Some details of these potentials will be summarized in the following." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Embedded Atom Method Potential" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* Atomic descriptors: pair functions\n", + "\n", + "$\\rho_i = \\sum_j \\phi(r_{ij})$ (density)\n", + "\n", + "$V_i = \\sum_j V(r_{ij})$ (pair repulsion)\n", + " \n", + "* Atomic energy\n", + "\n", + "$E_i = F( \\rho_i ) + V_i$ \n", + "\n", + "with non-linear embedding function $F$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Neural Network Potential" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* Atomic descriptors: pair and three-body symmetry functions\n", + "\n", + "$G_i = \\sum_j \\phi(r_{ij})$\n", + "\n", + "$G_i = \\sum_{jk} \\phi(r_{ij},r_{ik}, \\cos_{jik})$\n", + " \n", + "* Atomic energy\n", + "\n", + "$E_i = NN(G_i)$ \n", + "\n", + "with neural network $NN$. Various different $G_i$ are the inputs to the $NN$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Atomic Cluster Expansion" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* Atomic descriptors: pair, three-body, ... many-body basis functions\n", + "\n", + "$A_i = \\sum_j \\phi(\\pmb{r}_{ij})$ (many different basis functions that depend on direction and length of $r_{ij}$)\n", + "\n", + "$\\varphi_i = c_1 A_i + c_2 A_i A_i + c_3 A_i A_i A_i + ...$\n", + " \n", + "* Atomic energy\n", + "\n", + "$E_i = F(\\varphi_i)$ \n", + "\n", + "with general non-linear function $F$ and several $\\varphi_i$. In the tutorial we will use $E_i = \\sqrt{\\varphi^{(1)}_i} + \\varphi^{(2)}_i$ to make contact to the Embedded Atom Method.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Reference data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The potentials are parameterized by fitting to reference data. Here we use DFT data for Cu that we generated with the FHI-aims code. In the following we summarize key properties of the dataset." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}