latex works with ipynb

docs/tutorials/notebooks/adapt_pce.ipynb

@@ -51,25 +51,37 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a1305580",
+   "id": "5d8da914",
+   "metadata": {},
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "33090c17",
    "metadata": {},
    "source": [
     "### Define Forward model\n",
     "\n",
-    "The model in this example is a 1D laplacian ODE.  See the [`laplace_ode_1d` method](../models.html) or `UncertainSCI/model_examples.py` for details.\n",
+    "The model in this example is a 1D laplacian ODE.  See the `laplace_ode_1d` [method](../models.html) or `UncertainSCI/model_examples.py` for details.\n",
     "\n",
-    "  -d/dx a(x,p) d/dx u(x,p) = f(x)\n",
+    "$$\n",
+    "-\\frac{d}{dx} a(x,p) \\cdot \\frac{d}{dx} u(x,p) = f(x)\n",
+    "$$\n",
     "\n",
-    "over x in \\[-1,1\\], where a(x,p) is a parameterized diffusion model:\n",
+    "over $x$ in $[-1,1]$, where $a(x,p)$ is a parameterized diffusion model:\n",
     "\n",
-    "  a(x,p) = abar(x) + sum_{j=1}^d lambda_j p_j phi_j(x),\n",
+    "$$\n",
+    "a(x,p) = \\bar{x} + \\sum_{j=1}^d \\lambda_j p_j \\phi_j(x)\n",
+    "$$\n",
     "\n",
-    "where d = dimension, (lambda_j, phi_j) are eigenpairs of the exponential\n",
+    "where $d$ is the dimension, ($\\lambda_j$, $\\phi_j$) are eigenpairs of the exponential\n",
     "covariance kernel,\n",
     "\n",
-    "  K(s,t) = exp(-|s-t|/a).\n",
+    "$$\n",
+    "K(s,t) = e^{-|s-t|/a}.\n",
+    "$$\n",
     "\n",
-    "The p_j are modeled as iid random variables.\n",
+    "The $p_j$ are modeled as random variables.\n",
     "\n"
    ]
   },
@@ -101,7 +113,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "54ded9e5",
+   "id": "8f5ef04c",
    "metadata": {},
    "source": [
     "### Parameter Distributions\n",
@@ -126,7 +138,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0bbaba88",
+   "id": "15c692e9",
    "metadata": {},
    "source": [
     "### Initial Expressivity of the PCE\n",
@@ -163,7 +175,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ee464b72",
+   "id": "766761af",
    "metadata": {},
    "source": [
     "## Running Adaptive PCE\n",
@@ -266,7 +278,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9f0ee07f",
+   "id": "b6b27e09",
    "metadata": {},
    "source": [
     "## Output Statistics\n",
@@ -324,7 +336,7 @@
   {
    "cell_type": "code",
    "execution_count": 44,
-   "id": "09929b42",
+   "id": "4945132c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -339,7 +351,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ac56a966",
+   "id": "fa30c3f4",
    "metadata": {},
    "source": [
     "## Monte Carlo Statistics\n",
@@ -350,7 +362,7 @@
   {
    "cell_type": "code",
    "execution_count": 45,
-   "id": "3e1fdf8b",
+   "id": "eb408ce7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -374,7 +386,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "de9fc48c",
+   "id": "cac47460",
    "metadata": {},
    "source": [
     "## Visualize Statistics\n",
@@ -400,7 +412,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8a06e89e",
+   "id": "7a7c4b2f",
    "metadata": {},
    "source": [
     "### Single Domain Plot Comparison\n",
@@ -447,7 +459,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "142aa563",
+   "id": "769884ea",
    "metadata": {},
    "source": [
     "### Side-by-Side Domain Plot Comparison\n",
@@ -1497,7 +1509,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fc97f583",
+   "id": "83847911",
    "metadata": {},
    "source": [
     "### Parameter Sensitivity Estimated with PCE\n",
@@ -2515,7 +2527,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "274ce2d2",
+   "id": "2db64d2e",
    "metadata": {},
    "source": [
     "### Regression Plots\n",
@@ -3573,7 +3585,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ffa960d5",
+   "id": "83750574",
    "metadata": {},
    "outputs": [],
    "source": []