update tutorial3
This commit is contained in:
Dario Coscia
committed by
Nicola Demo
Nicola Demo
parent
dc71d328cf
commit
7ef39f1e3b
304
tutorials/tutorial3/tutorial.ipynb
vendored
304
tutorials/tutorial3/tutorial.ipynb
vendored
@@ -32,16 +32,19 @@
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" \n",
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"import torch\n",
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"import matplotlib.pyplot as plt\n",
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"plt.style.use('tableau-colorblind10')\n",
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"import warnings\n",
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"\n",
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"from pina import Condition, LabelTensor\n",
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"from pina.problem import SpatialProblem, TimeDependentProblem\n",
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"from pina.operator import laplacian, grad\n",
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"from pina.domain import CartesianDomain\n",
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"from pina.solver import PINN\n",
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"from pina.trainer import Trainer\n",
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"from pina.equation import Equation\n",
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"from pina.equation.equation_factory import FixedValue\n",
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"from pina import Condition, LabelTensor"
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"from pina.equation import Equation, FixedValue\n",
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"\n",
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"from lightning.pytorch.loggers import TensorBoardLogger\n",
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"\n",
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"warnings.filterwarnings('ignore')"
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]
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},
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{
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@@ -86,37 +89,61 @@
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"outputs": [],
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"source": [
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"class Wave(TimeDependentProblem, SpatialProblem):\n",
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" output_variables = ['u']\n",
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" spatial_domain = CartesianDomain({'x': [0, 1], 'y': [0, 1]})\n",
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" temporal_domain = CartesianDomain({'t': [0, 1]})\n",
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" output_variables = [\"u\"]\n",
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" spatial_domain = CartesianDomain({\"x\": [0, 1], \"y\": [0, 1]})\n",
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" temporal_domain = CartesianDomain({\"t\": [0, 1]})\n",
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"\n",
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" def wave_equation(input_, output_):\n",
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" u_t = grad(output_, input_, components=['u'], d=['t'])\n",
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" u_tt = grad(u_t, input_, components=['dudt'], d=['t'])\n",
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" nabla_u = laplacian(output_, input_, components=['u'], d=['x', 'y'])\n",
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" u_t = grad(output_, input_, components=[\"u\"], d=[\"t\"])\n",
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" u_tt = grad(u_t, input_, components=[\"dudt\"], d=[\"t\"])\n",
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" nabla_u = laplacian(output_, input_, components=[\"u\"], d=[\"x\", \"y\"])\n",
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" return nabla_u - u_tt\n",
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"\n",
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" def initial_condition(input_, output_):\n",
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" u_expected = (torch.sin(torch.pi*input_.extract(['x'])) *\n",
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" torch.sin(torch.pi*input_.extract(['y'])))\n",
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" return output_.extract(['u']) - u_expected\n",
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" u_expected = torch.sin(torch.pi * input_.extract([\"x\"])) * torch.sin(\n",
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" torch.pi * input_.extract([\"y\"])\n",
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" )\n",
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" return output_.extract([\"u\"]) - u_expected\n",
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"\n",
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" conditions = {\n",
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" 'bound_cond1': Condition(domain=CartesianDomain({'x': [0, 1], 'y': 1, 't': [0, 1]}), equation=FixedValue(0.)),\n",
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" 'bound_cond2': Condition(domain=CartesianDomain({'x': [0, 1], 'y': 0, 't': [0, 1]}), equation=FixedValue(0.)),\n",
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" 'bound_cond3': Condition(domain=CartesianDomain({'x': 1, 'y': [0, 1], 't': [0, 1]}), equation=FixedValue(0.)),\n",
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" 'bound_cond4': Condition(domain=CartesianDomain({'x': 0, 'y': [0, 1], 't': [0, 1]}), equation=FixedValue(0.)),\n",
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" 'time_cond': Condition(domain=CartesianDomain({'x': [0, 1], 'y': [0, 1], 't': 0}), equation=Equation(initial_condition)),\n",
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" 'phys_cond': Condition(domain=CartesianDomain({'x': [0, 1], 'y': [0, 1], 't': [0, 1]}), equation=Equation(wave_equation)),\n",
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" \"bound_cond1\": Condition(\n",
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" domain=CartesianDomain({\"x\": [0, 1], \"y\": 1, \"t\": [0, 1]}),\n",
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" equation=FixedValue(0.0),\n",
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" ),\n",
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" \"bound_cond2\": Condition(\n",
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" domain=CartesianDomain({\"x\": [0, 1], \"y\": 0, \"t\": [0, 1]}),\n",
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" equation=FixedValue(0.0),\n",
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" ),\n",
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" \"bound_cond3\": Condition(\n",
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" domain=CartesianDomain({\"x\": 1, \"y\": [0, 1], \"t\": [0, 1]}),\n",
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" equation=FixedValue(0.0),\n",
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" ),\n",
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" \"bound_cond4\": Condition(\n",
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" domain=CartesianDomain({\"x\": 0, \"y\": [0, 1], \"t\": [0, 1]}),\n",
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" equation=FixedValue(0.0),\n",
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" ),\n",
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" \"time_cond\": Condition(\n",
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" domain=CartesianDomain({\"x\": [0, 1], \"y\": [0, 1], \"t\": 0}),\n",
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" equation=Equation(initial_condition),\n",
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" ),\n",
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" \"phys_cond\": Condition(\n",
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" domain=CartesianDomain({\"x\": [0, 1], \"y\": [0, 1], \"t\": [0, 1]}),\n",
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" equation=Equation(wave_equation),\n",
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" ),\n",
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" }\n",
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"\n",
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" def wave_sol(self, pts):\n",
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" return (torch.sin(torch.pi*pts.extract(['x'])) *\n",
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" torch.sin(torch.pi*pts.extract(['y'])) *\n",
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" torch.cos(torch.sqrt(torch.tensor(2.))*torch.pi*pts.extract(['t'])))\n",
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" def truth_solution(self, pts):\n",
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" f = (\n",
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" torch.sin(torch.pi * pts.extract([\"x\"]))\n",
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" * torch.sin(torch.pi * pts.extract([\"y\"]))\n",
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" * torch.cos(\n",
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" torch.sqrt(torch.tensor(2.0)) * torch.pi * pts.extract([\"t\"])\n",
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" )\n",
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" )\n",
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" return LabelTensor(f, self.output_variables)\n",
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"\n",
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" truth_solution = wave_sol\n",
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"\n",
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"# define problem\n",
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"problem = Wave()"
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]
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},
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@@ -152,16 +179,23 @@
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" def __init__(self, input_dim, output_dim):\n",
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" super().__init__()\n",
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"\n",
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" self.layers = torch.nn.Sequential(torch.nn.Linear(input_dim, 40),\n",
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" torch.nn.ReLU(),\n",
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" torch.nn.Linear(40, 40),\n",
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" torch.nn.ReLU(),\n",
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" torch.nn.Linear(40, output_dim))\n",
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" \n",
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" self.layers = torch.nn.Sequential(\n",
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" torch.nn.Linear(input_dim, 40),\n",
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" torch.nn.ReLU(),\n",
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" torch.nn.Linear(40, 40),\n",
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" torch.nn.ReLU(),\n",
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" torch.nn.Linear(40, output_dim),\n",
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" )\n",
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"\n",
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" # here in the foward we implement the hard constraints\n",
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" def forward(self, x):\n",
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" hard = x.extract(['x'])*(1-x.extract(['x']))*x.extract(['y'])*(1-x.extract(['y']))\n",
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" return hard*self.layers(x)"
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" hard = (\n",
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" x.extract([\"x\"])\n",
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" * (1 - x.extract([\"x\"]))\n",
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" * x.extract([\"y\"])\n",
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" * (1 - x.extract([\"y\"]))\n",
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" )\n",
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" return hard * self.layers(x)"
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]
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},
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{
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@@ -177,7 +211,7 @@
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"id": "b465bebd",
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"metadata": {},
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"source": [
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"In this tutorial, the neural network is trained for 1000 epochs with a learning rate of 0.001 (default in `PINN`). Training takes approximately 3 minutes."
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"In this tutorial, the neural network is trained for 1000 epochs with a learning rate of 0.001 (default in `PINN`). As always, we will log using `Tensorboard`."
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]
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},
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{
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@@ -188,22 +222,66 @@
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"outputs": [],
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"source": [
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"# generate the data\n",
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"problem.discretise_domain(1000, 'random', domains=['phys_cond', 'time_cond', 'bound_cond1', 'bound_cond2', 'bound_cond3', 'bound_cond4'])\n",
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"problem.discretise_domain(\n",
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" 1000,\n",
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" \"random\",\n",
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" domains=[\n",
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" \"phys_cond\",\n",
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" \"time_cond\",\n",
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" \"bound_cond1\",\n",
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" \"bound_cond2\",\n",
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" \"bound_cond3\",\n",
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" \"bound_cond4\",\n",
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" ],\n",
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")\n",
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"\n",
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"# create the solver\n",
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"pinn = PINN(problem, HardMLP(len(problem.input_variables), len(problem.output_variables)))\n",
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"# define model\n",
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"model = HardMLP(len(problem.input_variables), len(problem.output_variables))\n",
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"\n",
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"# crete the solver\n",
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"pinn = PINN(problem=problem, model=model)\n",
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"\n",
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"# create trainer and train\n",
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"trainer = Trainer(pinn, max_epochs=1000, accelerator='cpu', enable_model_summary=False) # we train on CPU and avoid model summary at beginning of training (optional)\n",
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"trainer = Trainer(\n",
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" solver=pinn,\n",
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" max_epochs=1000,\n",
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" accelerator=\"cpu\",\n",
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" enable_model_summary=False,\n",
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" train_size=1.0,\n",
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" val_size=0.0,\n",
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" test_size=0.0,\n",
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" logger=TensorBoardLogger(\"tutorial_logs\"),\n",
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" enable_progress_bar=False,\n",
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")\n",
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"trainer.train()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "4c6dbfac",
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"metadata": {},
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"source": [
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"Let's now plot the logging to see how the losses vary during training. For this, we will use `TensorBoard`."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "77bfcb6e",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Load the TensorBoard extension\n",
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"%load_ext tensorboard\n",
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"%tensorboard --logdir 'tutorial_logs'\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "c2a5c405",
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"metadata": {},
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"source": [
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"Notice that the loss on the boundaries of the spatial domain is exactly zero, as expected! After the training is completed one can now plot some results using the `matplotlib`. We plot the predicted output on the left side, the true solution at the center and the difference on the right side."
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"Notice that the loss on the boundaries of the spatial domain is exactly zero, as expected! After the training is completed one can now plot some results using the `matplotlib`. We plot the predicted output on the left side, the true solution at the center and the difference on the right side using the `plot_solution` function."
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]
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},
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{
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@@ -213,32 +291,35 @@
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"metadata": {},
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"outputs": [],
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"source": [
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"def fixed_time_plot(fixed_variables, pinn):\n",
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" #sample domain points and get values corresponding to fixed variables\n",
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" pts = pinn.problem.spatial_domain.sample(256, 'grid', variables=['x','y'])\n",
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" grids = [p_.reshape(256, 256) for p_ in pts.extract(['x','y']).T]\n",
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" fixed_pts = torch.ones(pts.shape[0], len(fixed_variables))\n",
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" fixed_pts *= torch.tensor(list(fixed_variables.values()))\n",
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" fixed_pts = fixed_pts.as_subclass(LabelTensor)\n",
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" fixed_pts.labels = list(fixed_variables.keys())\n",
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" pts = pts.append(fixed_pts).to(device=pinn.device)\n",
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" predicted_output = pinn.forward(pts).extract('u').as_subclass(torch.Tensor).cpu().detach().reshape(256,256)\n",
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" #get true solution\n",
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" true_output = pinn.problem.truth_solution(pts).cpu().detach().reshape(256,256)\n",
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" pts = pts.cpu()\n",
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" #plot prediction, true solution and difference\n",
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" grids = [p_.reshape(256, 256) for p_ in pts.extract(['x','y']).T]\n",
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" fig, ax = plt.subplots(nrows=1, ncols=3, figsize=(16, 6))\n",
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" cb = getattr(ax[0], 'contourf')(*grids, predicted_output)\n",
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" fig.colorbar(cb, ax=ax[0])\n",
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" ax[0].title.set_text('Neural Network prediction')\n",
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" cb = getattr(ax[1], 'contourf')(*grids, true_output)\n",
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" fig.colorbar(cb, ax=ax[1])\n",
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" ax[1].title.set_text('True solution')\n",
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" cb = getattr(ax[2],'contourf')(*grids,(true_output - predicted_output))\n",
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" fig.colorbar(cb, ax=ax[2])\n",
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" ax[2].title.set_text('Residual')\n",
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" plt.show(block=True)"
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"@torch.no_grad()\n",
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"def plot_solution(solver, time):\n",
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" # get the problem\n",
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" problem = solver.problem\n",
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" # get spatial points\n",
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" spatial_samples = problem.spatial_domain.sample(30, \"grid\")\n",
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" # get temporal value\n",
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" time = LabelTensor(torch.tensor([[time]]), \"t\")\n",
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" # cross data\n",
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" points = spatial_samples.append(time, mode=\"cross\")\n",
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" # compute pinn solution, true solution and absolute difference\n",
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" data = {\n",
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" \"PINN solution\": solver(points),\n",
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" \"True solution\": problem.truth_solution(points),\n",
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" \"Absolute Difference\": torch.abs(\n",
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" solver(points) - problem.truth_solution(points)\n",
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" )\n",
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" }\n",
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" # plot the solution\n",
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" plt.suptitle(f'Solution for time {time.item()}')\n",
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" for idx, (title, field) in enumerate(data.items()):\n",
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" plt.subplot(1, 3, idx + 1)\n",
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" plt.title(title)\n",
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" plt.tricontourf( # convert to torch tensor + flatten\n",
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" points.extract(\"x\").tensor.flatten(),\n",
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" points.extract(\"y\").tensor.flatten(),\n",
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" field.tensor.flatten(),\n",
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" )\n",
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" plt.colorbar(), plt.tight_layout()"
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]
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},
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{
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@@ -256,12 +337,14 @@
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"metadata": {},
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"outputs": [],
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"source": [
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"print('Plotting at t=0')\n",
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"fixed_time_plot(fixed_variables={'t':0.0},pinn=pinn)\n",
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"print('Plotting at t=0.5')\n",
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"fixed_time_plot(fixed_variables={'t':0.5},pinn=pinn)\n",
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"print('Plotting at t=1.0')\n",
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"fixed_time_plot(fixed_variables={'t':1.0},pinn=pinn)"
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"plt.figure(figsize=(12, 6))\n",
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"plot_solution(solver=pinn, time=0)\n",
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"\n",
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"plt.figure(figsize=(12, 6))\n",
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"plot_solution(solver=pinn, time=0.5)\n",
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"\n",
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"plt.figure(figsize=(12, 6))\n",
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"plot_solution(solver=pinn, time=1)"
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]
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},
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{
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@@ -290,17 +373,30 @@
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" def __init__(self, input_dim, output_dim):\n",
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" super().__init__()\n",
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"\n",
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" self.layers = torch.nn.Sequential(torch.nn.Linear(input_dim, 40),\n",
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" torch.nn.ReLU(),\n",
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" torch.nn.Linear(40, 40),\n",
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" torch.nn.ReLU(),\n",
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" torch.nn.Linear(40, output_dim))\n",
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" \n",
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" self.layers = torch.nn.Sequential(\n",
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" torch.nn.Linear(input_dim, 40),\n",
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" torch.nn.ReLU(),\n",
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" torch.nn.Linear(40, 40),\n",
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" torch.nn.ReLU(),\n",
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" torch.nn.Linear(40, output_dim),\n",
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" )\n",
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"\n",
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" # here in the foward we implement the hard constraints\n",
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" def forward(self, x):\n",
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" hard_space = x.extract(['x'])*(1-x.extract(['x']))*x.extract(['y'])*(1-x.extract(['y']))\n",
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" hard_t = torch.sin(torch.pi*x.extract(['x'])) * torch.sin(torch.pi*x.extract(['y'])) * torch.cos(torch.sqrt(torch.tensor(2.))*torch.pi*x.extract(['t']))\n",
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" return hard_space * self.layers(x) * x.extract(['t']) + hard_t"
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" hard_space = (\n",
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" x.extract([\"x\"])\n",
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" * (1 - x.extract([\"x\"]))\n",
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" * x.extract([\"y\"])\n",
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" * (1 - x.extract([\"y\"]))\n",
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" )\n",
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" hard_t = (\n",
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" torch.sin(torch.pi * x.extract([\"x\"]))\n",
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" * torch.sin(torch.pi * x.extract([\"y\"]))\n",
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" * torch.cos(\n",
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" torch.sqrt(torch.tensor(2.0)) * torch.pi * x.extract([\"t\"])\n",
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" )\n",
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" )\n",
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" return hard_space * self.layers(x) * x.extract([\"t\"]) + hard_t"
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]
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},
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{
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@@ -308,7 +404,7 @@
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"id": "5d3dc67b",
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"metadata": {},
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"source": [
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"Now let's train with the same configuration as thre previous test"
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"Now let's train with the same configuration as the previous test"
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]
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},
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{
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@@ -318,14 +414,24 @@
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"metadata": {},
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"outputs": [],
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"source": [
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"# generate the data\n",
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"problem.discretise_domain(1000, 'random', domains=['phys_cond', 'time_cond', 'bound_cond1', 'bound_cond2', 'bound_cond3', 'bound_cond4'])\n",
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"# define model\n",
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"model = HardMLPtime(len(problem.input_variables), len(problem.output_variables))\n",
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"\n",
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"# crete the solver\n",
|
||||
"pinn = PINN(problem, HardMLPtime(len(problem.input_variables), len(problem.output_variables)))\n",
|
||||
"pinn = PINN(problem=problem, model=model)\n",
|
||||
"\n",
|
||||
"# create trainer and train\n",
|
||||
"trainer = Trainer(pinn, max_epochs=1000, accelerator='cpu', enable_model_summary=False) # we train on CPU and avoid model summary at beginning of training (optional)\n",
|
||||
"trainer = Trainer(\n",
|
||||
" solver=pinn,\n",
|
||||
" max_epochs=1000,\n",
|
||||
" accelerator=\"cpu\",\n",
|
||||
" enable_model_summary=False,\n",
|
||||
" train_size=1.0,\n",
|
||||
" val_size=0.0,\n",
|
||||
" test_size=0.0,\n",
|
||||
" logger=TensorBoardLogger(\"tutorial_logs\"),\n",
|
||||
" enable_progress_bar=False,\n",
|
||||
")\n",
|
||||
"trainer.train()"
|
||||
]
|
||||
},
|
||||
@@ -344,12 +450,14 @@
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"print('Plotting at t=0')\n",
|
||||
"fixed_time_plot(fixed_variables={'t':0.0},pinn=pinn)\n",
|
||||
"print('Plotting at t=0.5')\n",
|
||||
"fixed_time_plot(fixed_variables={'t':0.5},pinn=pinn)\n",
|
||||
"print('Plotting at t=1.0')\n",
|
||||
"fixed_time_plot(fixed_variables={'t':1.0},pinn=pinn)\n"
|
||||
"plt.figure(figsize=(12, 6))\n",
|
||||
"plot_solution(solver=pinn, time=0)\n",
|
||||
"\n",
|
||||
"plt.figure(figsize=(12, 6))\n",
|
||||
"plot_solution(solver=pinn, time=0.5)\n",
|
||||
"\n",
|
||||
"plt.figure(figsize=(12, 6))\n",
|
||||
"plot_solution(solver=pinn, time=1)"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -357,7 +465,17 @@
|
||||
"id": "b7338109",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"We can see now that the results are way better! This is due to the fact that previously the network was not learning correctly the initial conditon, leading to a poor solution when time evolved. By imposing the initial condition the network is able to correctly solve the problem."
|
||||
"We can see now that the results are way better! This is due to the fact that previously the network was not learning correctly the initial conditon, leading to a poor solution when time evolved. By imposing the initial condition the network is able to correctly solve the problem. We can also see using Tensorboard how the two losses decreased:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "7ce34dac",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"%tensorboard --logdir 'tutorial_logs'"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -381,7 +499,7 @@
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3",
|
||||
"display_name": "pina",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
@@ -395,7 +513,7 @@
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.12.7"
|
||||
"version": "3.9.21"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
||||
Reference in New Issue
Block a user