update tutorials

Author: GiovanniCanali

tutorials/tutorial1/tutorial.ipynb

@@ -34,7 +34,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -71,21 +71,18 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "# define the burger equation\n",
-    "def burger_equation(input_, output_):\n",
-    "    du = fast_grad(output_, input_, components=[\"u\"], d=[\"x\"])\n",
-    "    ddu = grad(du, input_, components=[\"dudx\"])\n",
+    "# define the burgers equation\n",
+    "def burgers_equation(input_, output_):\n",
+    "    du = grad(output_, input_)\n",
+    "    ddu = laplacian(output_, input_, components=\"x\")\n",
     "    return (\n",
-    "        du.extract([\"dudt\"])\n",
-    "        + output_.extract([\"u\"]) * du.extract([\"dudx\"])\n",
-    "        - (0.01 / torch.pi) * ddu.extract([\"ddudxdx\"])\n",
+    "        du[\"dudt\"] + output_[\"u\"] * du[\"dudx\"] - (0.01 / torch.pi) * ddu\n",
     "    )\n",
     "\n",
-    "\n",
     "# define initial condition\n",
     "def initial_condition(input_, output_):\n",
-    "    u_expected = -torch.sin(torch.pi * input_.extract([\"x\"]))\n",
-    "    return output_.extract([\"u\"]) - u_expected"
+    "    u_expected = -torch.sin(torch.pi * input_[\"x\"])\n",
+    "    return output_[\"u\"] - u_expected"
    ]
   },
   {
@@ -107,7 +104,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -119,24 +116,18 @@
     "    temporal_domain = CartesianDomain({\"t\": [0, 1]})\n",
     "\n",
     "    domains = {\n",
-    "        \"bound_cond1\": CartesianDomain({\"x\": -1, \"t\": [0, 1]}),\n",
-    "        \"bound_cond2\": CartesianDomain({\"x\": 1, \"t\": [0, 1]}),\n",
-    "        \"time_cond\": CartesianDomain({\"x\": [-1, 1], \"t\": 0}),\n",
-    "        \"phys_cond\": CartesianDomain({\"x\": [-1, 1], \"t\": [0, 1]}),\n",
+    "        \"bound_cond\": spatial_domain.partial().update(temporal_domain),\n",
+    "        \"time_cond\": spatial_domain.update(CartesianDomain({\"t\": 0.0})),\n",
+    "        \"phys_cond\": spatial_domain.update(temporal_domain),\n",
     "    }\n",
     "    # problem condition statement\n",
     "    conditions = {\n",
-    "        \"bound_cond1\": Condition(\n",
-    "            domain=\"bound_cond1\", equation=FixedValue(0.0)\n",
-    "        ),\n",
-    "        \"bound_cond2\": Condition(\n",
-    "            domain=\"bound_cond2\", equation=FixedValue(0.0)\n",
-    "        ),\n",
+    "        \"bound_cond\": Condition(domain=\"bound_cond\", equation=FixedValue(0.0)),\n",
     "        \"time_cond\": Condition(\n",
     "            domain=\"time_cond\", equation=Equation(initial_condition)\n",
     "        ),\n",
     "        \"phys_cond\": Condition(\n",
-    "            domain=\"phys_cond\", equation=Equation(burger_equation)\n",
+    "            domain=\"phys_cond\", equation=Equation(burgers_equation)\n",
     "        ),\n",
     "    }"
    ]
@@ -145,7 +136,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The `Equation` class takes as input a function (in this case it happens twice, with `initial_condition` and `burger_equation`) which computes a residual of an equation, such as a PDE. In a problem class such as the one above, the `Equation` class with such a given input is passed as a parameter in the specified `Condition`. \n",
+    "The `Equation` class takes as input a function (in this case it happens twice, with `initial_condition` and `burgers_equation`) which computes a residual of an equation, such as a PDE. In a problem class such as the one above, the `Equation` class with such a given input is passed as a parameter in the specified `Condition`. \n",
     "\n",
     "The `FixedValue` class takes as input a value of the same dimensions as the output functions. This class can be used to enforce a fixed value for a specific condition, such as Dirichlet boundary conditions, as demonstrated in our example.\n",
     "\n",
@@ -172,7 +163,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -206,7 +197,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -223,19 +214,13 @@
     "    temporal_domain = CartesianDomain({\"t\": [0, 1]})\n",
     "\n",
     "    domains = {\n",
-    "        \"bound_cond1\": CartesianDomain({\"x\": -1, \"t\": [0, 1]}),\n",
-    "        \"bound_cond2\": CartesianDomain({\"x\": 1, \"t\": [0, 1]}),\n",
-    "        \"time_cond\": CartesianDomain({\"x\": [-1, 1], \"t\": 0}),\n",
-    "        \"phys_cond\": CartesianDomain({\"x\": [-1, 1], \"t\": [0, 1]}),\n",
+    "        \"bound_cond\": spatial_domain.partial().update(temporal_domain),\n",
+    "        \"time_cond\": spatial_domain.update(CartesianDomain({\"t\": 0.0})),\n",
+    "        \"phys_cond\": spatial_domain.update(temporal_domain),\n",
     "    }\n",
     "    # problem condition statement\n",
     "    conditions = {\n",
-    "        \"bound_cond1\": Condition(\n",
-    "            domain=\"bound_cond1\", equation=FixedValue(0.0)\n",
-    "        ),\n",
-    "        \"bound_cond2\": Condition(\n",
-    "            domain=\"bound_cond2\", equation=FixedValue(0.0)\n",
-    "        ),\n",
+    "        \"bound_cond\": Condition(domain=\"bound_cond\", equation=FixedValue(0.0)),\n",
     "        \"time_cond\": Condition(\n",
     "            domain=\"time_cond\", equation=Equation(initial_condition)\n",
     "        ),\n",
@@ -266,7 +251,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "pina",
+   "display_name": "deep",
    "language": "python",
    "name": "python3"
   },
@@ -280,7 +265,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.21"
+   "version": "3.12.11"
   },
   "orig_nbformat": 4
  },