Update Tutorials 0.2 (#490)
This commit is contained in:
Dario Coscia
committed by
Nicola Demo
Nicola Demo
parent
beee4cdc0b
commit
6ce0bafc2b
100
tutorials/tutorial12/tutorial.ipynb
vendored
100
tutorials/tutorial12/tutorial.ipynb
vendored
@@ -63,11 +63,11 @@
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"import torch\n",
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"\n",
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"#useful imports\n",
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"from pina import Condition\n",
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"from pina.problem import SpatialProblem, TimeDependentProblem\n",
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"from pina.equation import Equation, FixedValue\n",
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"from pina.domain import CartesianDomain\n",
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"from pina.operator import grad, laplacian\n",
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"from pina import Condition"
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"from pina.operator import grad, laplacian"
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]
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},
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{
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@@ -76,34 +76,50 @@
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"metadata": {},
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"outputs": [],
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"source": [
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"# define the burger equation\n",
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"def burger_equation(input_, output_):\n",
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" du = grad(output_, input_)\n",
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" ddu = grad(du, input_, components=[\"dudx\"])\n",
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" return (\n",
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" du.extract([\"dudt\"])\n",
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" + output_.extract([\"u\"]) * du.extract([\"dudx\"])\n",
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" - (0.01 / torch.pi) * ddu.extract([\"ddudxdx\"])\n",
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" )\n",
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"\n",
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"\n",
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"# define initial condition\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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" return output_.extract([\"u\"]) - u_expected\n",
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"\n",
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"\n",
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"class Burgers1D(TimeDependentProblem, SpatialProblem):\n",
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"\n",
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" # define the burger equation\n",
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" def burger_equation(input_, output_):\n",
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" du = grad(output_, input_)\n",
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" ddu = grad(du, input_, components=['dudx'])\n",
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" return (\n",
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" du.extract(['dudt']) +\n",
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" output_.extract(['u'])*du.extract(['dudx']) -\n",
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" (0.01/torch.pi)*ddu.extract(['ddudxdx'])\n",
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" )\n",
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"\n",
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" # define initial condition\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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" return output_.extract(['u']) - u_expected\n",
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"\n",
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" # assign output/ spatial and temporal variables\n",
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" output_variables = ['u']\n",
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" spatial_domain = CartesianDomain({'x': [-1, 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\": [-1, 1]})\n",
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" temporal_domain = CartesianDomain({\"t\": [0, 1]})\n",
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"\n",
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" domains = {\n",
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" \"bound_cond1\": CartesianDomain({\"x\": -1, \"t\": [0, 1]}),\n",
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" \"bound_cond2\": CartesianDomain({\"x\": 1, \"t\": [0, 1]}),\n",
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" \"time_cond\": CartesianDomain({\"x\": [-1, 1], \"t\": 0}),\n",
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" \"phys_cond\": CartesianDomain({\"x\": [-1, 1], \"t\": [0, 1]}),\n",
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" }\n",
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" # problem condition statement\n",
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" conditions = {\n",
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" 'bound_cond1': Condition(domain=CartesianDomain({'x': -1, 't': [0, 1]}), equation=FixedValue(0.)),\n",
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" 'bound_cond2': Condition(domain=CartesianDomain({'x': 1, 't': [0, 1]}), equation=FixedValue(0.)),\n",
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" 'time_cond': Condition(domain=CartesianDomain({'x': [-1, 1], 't': 0}), equation=Equation(initial_condition)),\n",
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" 'phys_cond': Condition(domain=CartesianDomain({'x': [-1, 1], 't': [0, 1]}), equation=Equation(burger_equation)),\n",
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" \"bound_cond1\": Condition(\n",
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" domain=\"bound_cond1\", equation=FixedValue(0.0)\n",
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" ),\n",
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" \"bound_cond2\": Condition(\n",
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" domain=\"bound_cond2\", equation=FixedValue(0.0)\n",
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" ),\n",
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" \"time_cond\": Condition(\n",
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" domain=\"time_cond\", equation=Equation(initial_condition)\n",
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" ),\n",
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" \"phys_cond\": Condition(\n",
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" domain=\"phys_cond\", equation=Equation(burger_equation)\n",
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" ),\n",
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" }"
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]
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},
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@@ -186,20 +202,34 @@
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"\n",
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" # define initial condition\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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" return output_.extract(['u']) - u_expected\n",
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" u_expected = -torch.sin(torch.pi * input_.extract([\"x\"]))\n",
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" return output_.extract([\"u\"]) - u_expected\n",
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"\n",
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" # assign output/ spatial and temporal variables\n",
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" output_variables = ['u']\n",
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" spatial_domain = CartesianDomain({'x': [-1, 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\": [-1, 1]})\n",
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" temporal_domain = CartesianDomain({\"t\": [0, 1]})\n",
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"\n",
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" domains = {\n",
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" \"bound_cond1\": CartesianDomain({\"x\": -1, \"t\": [0, 1]}),\n",
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" \"bound_cond2\": CartesianDomain({\"x\": 1, \"t\": [0, 1]}),\n",
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" \"time_cond\": CartesianDomain({\"x\": [-1, 1], \"t\": 0}),\n",
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" \"phys_cond\": CartesianDomain({\"x\": [-1, 1], \"t\": [0, 1]}),\n",
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" }\n",
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" # problem condition statement\n",
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" conditions = {\n",
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" 'bound_cond1': Condition(domain=CartesianDomain({'x': -1, 't': [0, 1]}), equation=FixedValue(0.)),\n",
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" 'bound_cond2': Condition(domain=CartesianDomain({'x': 1, 't': [0, 1]}), equation=FixedValue(0.)),\n",
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" 'time_cond': Condition(domain=CartesianDomain({'x': [-1, 1], 't': 0}), equation=Equation(initial_condition)),\n",
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" 'phys_cond': Condition(domain=CartesianDomain({'x': [-1, 1], 't': [0, 1]}), equation=Burgers1DEquation(0.01/torch.pi)),\n",
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" \"bound_cond1\": Condition(\n",
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" domain=\"bound_cond1\", equation=FixedValue(0.0)\n",
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" ),\n",
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" \"bound_cond2\": Condition(\n",
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" domain=\"bound_cond2\", equation=FixedValue(0.0)\n",
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" ),\n",
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" \"time_cond\": Condition(\n",
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" domain=\"time_cond\", equation=Equation(initial_condition)\n",
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" ),\n",
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" \"phys_cond\": Condition(\n",
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" domain=\"phys_cond\", equation=Burgers1DEquation(nu=0.01 / torch.pi)\n",
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" ),\n",
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" }"
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]
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},
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@@ -223,7 +253,7 @@
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"display_name": "pina",
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"language": "python",
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"name": "python3"
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},
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@@ -237,7 +267,7 @@
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.3"
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"version": "3.9.21"
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},
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"orig_nbformat": 4
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},
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156
tutorials/tutorial12/tutorial.py
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156
tutorials/tutorial12/tutorial.py
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@@ -1,156 +0,0 @@
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#!/usr/bin/env python
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# coding: utf-8
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# # Tutorial: The `Equation` Class
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#
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# [](https://colab.research.google.com/github/mathLab/PINA/blob/master/tutorials/tutorial12/tutorial.ipynb)
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# In this tutorial, we will show how to use the `Equation` Class in PINA. Specifically, we will see how use the Class and its inherited classes to enforce residuals minimization in PINNs.
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# # Example: The Burgers 1D equation
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# We will start implementing the viscous Burgers 1D problem Class, described as follows:
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#
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#
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# $$
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# \begin{equation}
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# \begin{cases}
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# \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} &= \nu \frac{\partial^2 u}{ \partial x^2}, \quad x\in(0,1), \quad t>0\\
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# u(x,0) &= -\sin (\pi x)\\
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# u(x,t) &= 0 \quad x = \pm 1\\
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# \end{cases}
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# \end{equation}
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# $$
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#
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# where we set $ \nu = \frac{0.01}{\pi}$.
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#
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# In the class that models this problem we will see in action the `Equation` class and one of its inherited classes, the `FixedValue` class.
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# In[1]:
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## routine needed to run the notebook on Google Colab
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try:
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import google.colab
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IN_COLAB = True
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except:
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IN_COLAB = False
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if IN_COLAB:
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get_ipython().system('pip install "pina-mathlab"')
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import torch
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#useful imports
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from pina.problem import SpatialProblem, TimeDependentProblem
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from pina.equation import Equation, FixedValue
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from pina.domain import CartesianDomain
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from pina.operator import grad, laplacian
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from pina import Condition
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# In[2]:
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class Burgers1D(TimeDependentProblem, SpatialProblem):
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# define the burger equation
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def burger_equation(input_, output_):
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du = grad(output_, input_)
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ddu = grad(du, input_, components=['dudx'])
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return (
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du.extract(['dudt']) +
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output_.extract(['u'])*du.extract(['dudx']) -
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(0.01/torch.pi)*ddu.extract(['ddudxdx'])
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)
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# define initial condition
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def initial_condition(input_, output_):
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u_expected = -torch.sin(torch.pi*input_.extract(['x']))
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return output_.extract(['u']) - u_expected
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# assign output/ spatial and temporal variables
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output_variables = ['u']
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spatial_domain = CartesianDomain({'x': [-1, 1]})
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temporal_domain = CartesianDomain({'t': [0, 1]})
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# problem condition statement
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conditions = {
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'bound_cond1': Condition(domain=CartesianDomain({'x': -1, 't': [0, 1]}), equation=FixedValue(0.)),
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'bound_cond2': Condition(domain=CartesianDomain({'x': 1, 't': [0, 1]}), equation=FixedValue(0.)),
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'time_cond': Condition(domain=CartesianDomain({'x': [-1, 1], 't': 0}), equation=Equation(initial_condition)),
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'phys_cond': Condition(domain=CartesianDomain({'x': [-1, 1], 't': [0, 1]}), equation=Equation(burger_equation)),
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}
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#
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# 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`.
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#
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# The `FixedValue` class takes as input a value of same dimensions of the output functions; this class can be used to enforce a fixed value for a specific condition, e.g. Dirichlet boundary conditions, as it happens for instance in our example.
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#
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# Once the equations are set as above in the problem conditions, the PINN solver will aim to minimize the residuals described in each equation in the training phase.
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# Available classes of equations include also:
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# - `FixedGradient` and `FixedFlux`: they work analogously to `FixedValue` class, where we can require a constant value to be enforced, respectively, on the gradient of the solution or the divergence of the solution;
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# - `Laplace`: it can be used to enforce the laplacian of the solution to be zero;
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# - `SystemEquation`: we can enforce multiple conditions on the same subdomain through this class, passing a list of residual equations defined in the problem.
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#
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# # Defining a new Equation class
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# `Equation` classes can be also inherited to define a new class. As example, we can see how to rewrite the above problem introducing a new class `Burgers1D`; during the class call, we can pass the viscosity parameter $\nu$:
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# In[3]:
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class Burgers1DEquation(Equation):
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def __init__(self, nu = 0.):
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"""
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Burgers1D class. This class can be
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used to enforce the solution u to solve the viscous Burgers 1D Equation.
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:param torch.float32 nu: the viscosity coefficient. Default value is set to 0.
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"""
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self.nu = nu
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def equation(input_, output_):
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return grad(output_, input_, d='t') +\
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output_*grad(output_, input_, d='x') -\
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self.nu*laplacian(output_, input_, d='x')
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super().__init__(equation)
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# Now we can just pass the above class as input for the last condition, setting $\nu= \frac{0.01}{\pi}$:
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# In[4]:
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class Burgers1D(TimeDependentProblem, SpatialProblem):
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# define initial condition
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def initial_condition(input_, output_):
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u_expected = -torch.sin(torch.pi*input_.extract(['x']))
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return output_.extract(['u']) - u_expected
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# assign output/ spatial and temporal variables
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output_variables = ['u']
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spatial_domain = CartesianDomain({'x': [-1, 1]})
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temporal_domain = CartesianDomain({'t': [0, 1]})
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# problem condition statement
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conditions = {
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'bound_cond1': Condition(domain=CartesianDomain({'x': -1, 't': [0, 1]}), equation=FixedValue(0.)),
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'bound_cond2': Condition(domain=CartesianDomain({'x': 1, 't': [0, 1]}), equation=FixedValue(0.)),
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'time_cond': Condition(domain=CartesianDomain({'x': [-1, 1], 't': 0}), equation=Equation(initial_condition)),
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'phys_cond': Condition(domain=CartesianDomain({'x': [-1, 1], 't': [0, 1]}), equation=Burgers1DEquation(0.01/torch.pi)),
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}
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# # What's next?
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# Congratulations on completing the `Equation` class tutorial of **PINA**! As we have seen, you can build new classes that inherit `Equation` to store more complex equations, as the Burgers 1D equation, only requiring to pass the characteristic coefficients of the problem.
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# From now on, you can:
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# - define additional complex equation classes (e.g. `SchrodingerEquation`, `NavierStokeEquation`..)
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# - define more `FixedOperator` (e.g. `FixedCurl`)
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