export tutorials changed in dd88513 (#559)
Co-authored-by: dario-coscia <dario-coscia@users.noreply.github.com>
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Dario Coscia
Dario Coscia
parent
228f807d92
commit
d10c525e74
72
tutorials/tutorial17/tutorial.ipynb
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72
tutorials/tutorial17/tutorial.ipynb
vendored
@@ -97,12 +97,13 @@
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"source": [
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"## routine needed to run the notebook on Google Colab\n",
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"try:\n",
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" import google.colab\n",
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" IN_COLAB = True\n",
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" import google.colab\n",
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"\n",
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" IN_COLAB = True\n",
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"except:\n",
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" IN_COLAB = False\n",
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" IN_COLAB = False\n",
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"if IN_COLAB:\n",
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" !pip install \"pina-mathlab[tutorial]\"\n",
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" !pip install \"pina-mathlab[tutorial]\"\n",
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"\n",
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"import warnings\n",
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"import torch\n",
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@@ -140,16 +141,18 @@
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"outputs": [],
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"source": [
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"# (a) Data generation and plot\n",
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"domain = CartesianDomain({'x' : [-3, 3]})\n",
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"domain = CartesianDomain({\"x\": [-3, 3]})\n",
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"x = domain.sample(n=20, mode=\"random\")\n",
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"y = LabelTensor(x.pow(3) + 3*torch.randn_like(x), 'y')\n",
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"y = LabelTensor(x.pow(3) + 3 * torch.randn_like(x), \"y\")\n",
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"\n",
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"\n",
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"# (b) PINA Problem formulation\n",
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"class BayesianProblem(AbstractProblem):\n",
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"\n",
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" output_variables = ['y']\n",
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" input_variables = ['x']\n",
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" conditions = {'data': Condition(input_points=x, output_points=y)}\n",
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" output_variables = [\"y\"]\n",
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" input_variables = [\"x\"]\n",
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" conditions = {\"data\": Condition(input_points=x, output_points=y)}\n",
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"\n",
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"\n",
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"problem = BayesianProblem()\n",
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"\n",
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@@ -309,32 +312,35 @@
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}
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],
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"source": [
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"from pina.solver import SupervisedSolver \n",
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"from pina.solver import SupervisedSolver\n",
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"from pina.trainer import Trainer\n",
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"\n",
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"\n",
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"# define problem & data (step 1)\n",
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"class BayesianModel(torch.nn.Module):\n",
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" def __init__(self):\n",
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" super().__init__()\n",
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" self.layers = torch.nn.Sequential(\n",
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" torch.nn.Linear(1, 100),\n",
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" torch.nn.ReLU(),\n",
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" torch.nn.Dropout(0.5),\n",
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" torch.nn.Linear(100, 1)\n",
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" )\n",
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" torch.nn.Linear(1, 100),\n",
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" torch.nn.ReLU(),\n",
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" torch.nn.Dropout(0.5),\n",
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" torch.nn.Linear(100, 1),\n",
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" )\n",
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"\n",
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" def forward(self, x):\n",
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" return self.layers(x)\n",
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"\n",
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"\n",
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"problem = BayesianProblem()\n",
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"\n",
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"# model design (step 2)\n",
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"model = BayesianModel()\n",
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"model = BayesianModel()\n",
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"\n",
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"# solver selection (step 3)\n",
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"solver = SupervisedSolver(problem, model)\n",
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"solver = SupervisedSolver(problem, model)\n",
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"\n",
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"# training (step 4)\n",
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"trainer = Trainer(solver=solver, max_epochs=2000, accelerator='cpu')\n",
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"trainer = Trainer(solver=solver, max_epochs=2000, accelerator=\"cpu\")\n",
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"trainer.train()"
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]
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},
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@@ -374,17 +380,23 @@
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}
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],
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"source": [
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"x_test = LabelTensor(torch.linspace(-4, 4, 100).reshape(-1, 1), 'x')\n",
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"x_test = LabelTensor(torch.linspace(-4, 4, 100).reshape(-1, 1), \"x\")\n",
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"y_test = torch.stack([solver(x_test) for _ in range(1000)], dim=0)\n",
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"y_mean, y_std = y_test.mean(0).detach(), y_test.std(0).detach()\n",
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"# plot\n",
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"x_test = x_test.flatten()\n",
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"y_mean = y_mean.flatten()\n",
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"y_std = y_std.flatten()\n",
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"plt.plot(x_test, y_mean, label=r'$\\mu_{\\theta}$')\n",
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"plt.fill_between(x_test, y_mean-3*y_std, y_mean+3*y_std, alpha=0.3, label=r'3$\\sigma_{\\theta}$')\n",
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"plt.plot(x_test, x_test.pow(3), label='true')\n",
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"plt.scatter(x, y, label='train data')\n",
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"y_std = y_std.flatten()\n",
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"plt.plot(x_test, y_mean, label=r\"$\\mu_{\\theta}$\")\n",
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"plt.fill_between(\n",
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" x_test,\n",
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" y_mean - 3 * y_std,\n",
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" y_mean + 3 * y_std,\n",
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" alpha=0.3,\n",
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" label=r\"3$\\sigma_{\\theta}$\",\n",
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")\n",
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"plt.plot(x_test, x_test.pow(3), label=\"true\")\n",
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"plt.scatter(x, y, label=\"train data\")\n",
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"plt.legend()\n",
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"plt.show()"
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]
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@@ -598,10 +610,10 @@
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}
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],
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"source": [
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"print('Points are not automatically sampled, you can see this by:')\n",
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"print(\"Points are not automatically sampled, you can see this by:\")\n",
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"print(f\" {poisson_problem.are_all_domains_discretised=}\\n\")\n",
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"print('But you can easily sample by running .discretise_domain:')\n",
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"poisson_problem.discretise_domain(n=1000, domains=['interior'])\n",
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"print(\"But you can easily sample by running .discretise_domain:\")\n",
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"poisson_problem.discretise_domain(n=1000, domains=[\"interior\"])\n",
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"poisson_problem.discretise_domain(n=100, domains=[\"border\"])\n",
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"print(f\" {poisson_problem.are_all_domains_discretised=}\")"
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]
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@@ -632,10 +644,10 @@
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"from pina.model import FeedForward\n",
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"\n",
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"model = FeedForward(\n",
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" func = torch.nn.Tanh,\n",
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" layers=[120]*2,\n",
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" func=torch.nn.Tanh,\n",
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" layers=[120] * 2,\n",
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" output_dimensions=len(poisson_problem.output_variables),\n",
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" input_dimensions=len(poisson_problem.input_variables)\n",
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" input_dimensions=len(poisson_problem.input_variables),\n",
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")"
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]
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},
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