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Lesson4_DeepPot.ipynb

@@ -181,7 +181,7 @@
     {
       "cell_type": "markdown",
       "source": [
-        "First, we build the environment matrix for each atom $\\mathcal{R}_i$\n",
+        "First, we build the environment matrix for each atom $\\tilde{\\mathcal{R}}_i$\n",
         "\n",
         "$$\\begin{eqnarray}\n",
         "{\\tilde{\\mathcal{R}}^i} = \\begin{pmatrix}\n",
@@ -259,7 +259,7 @@
     {
       "cell_type": "markdown",
       "source": [
-        "Now we use embedding neural networks to transform each of the $s$ values into $M_1$ numbers. This gives us the local embedding matrix $\\mathcal{G}$. Note the embedding neural network parameters depend on the chemical species of atom $i$ and atom $j$.  \n",
+        "Now we use embedding neural networks to transform each of the $s$ values into $m_1$ numbers. This gives us the local embedding matrix $g_i$. Note the embedding neural network parameters depend on the chemical species of atom $i$ and atom $j$.  \n",
         "\n",
         "$$\\begin{eqnarray}\n",
         "g_i\n",
@@ -275,15 +275,15 @@
         "\\end{pmatrix}\n",
         "\\end{eqnarray}$$\n",
         "\n",
-        "Two local embedding matrices are used: $g_{i}^{1}$ is $n\\times M_1$ dimensions, while $g_{i}^{2}$ is $n\\times M_2$ dimensions. The dimensions $M_1$ and $M_2$ represent the number of neural network parameters, where $M_1$ is larger than $M_2$.\n",
+        "Two local embedding matrices are used: $g_{i}^{1}$ is $n\\times m_1$ dimensions, while $g_{i}^{2}$ is $n\\times m_2$ dimensions. The dimensions $m_1$ and $m_2$ represent the number of neural network parameters, where $m_1$ is larger than $m_2$.\n",
         "\n",
         "By multiplying our local embedding matrices and environment matrices, we can preserve the translational, rotational, and permutational symmetry in the form of the encoded feature matrix $D_i$  \n",
         "\n",
         "$$\\begin{eqnarray}\n",
         "D_i = \\left( g_i^1   \\right)^T \\tilde{\\mathcal{R}}^i (\\tilde{\\mathcal{R}}^i)^T g_i^2\n",
         "\\end{eqnarray}$$\n",
         "\n",
-        "The local feature matrix is then mapped to the atomic energy using the fitting neural network. Finally, the atomic energies are summed to yield the total energy of the molecule."
+        "The local feature matrix is then mapped to the atomic energy ($E_i$) using the fitting neural network. Finally, the atomic energies are summed to yield the total energy of the molecule."
       ],
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