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Fixing tutorials grammar (#242)

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* grammar check and sparse rephrasing
* rst created
* meta copyright adjusted
This commit is contained in:
Giuseppe Alessio D'Inverno
2024-03-05 10:43:34 +01:00
committed by GitHub
parent 15136e13f8
commit b10e02103b
23 changed files with 272 additions and 237 deletions
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32
tutorials/tutorial9/tutorial.py vendored
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@@ -1,11 +1,11 @@
#!/usr/bin/env python
# coding: utf-8
# # Tutorial: One dimensional Helmotz equation using Periodic Boundary Conditions
# # Tutorial: One dimensional Helmholtz equation using Periodic Boundary Conditions
# This tutorial presents how to solve with Physics-Informed Neural Networks (PINNs)
# a one dimensional Helmotz equation with periodic boundary conditions (PBC).
# a one dimensional Helmholtz equation with periodic boundary conditions (PBC).
# We will train with standard PINN's training by augmenting the input with
# periodic expasion as presented in [*An expert’s guide to training
# periodic expansion as presented in [*An expert’s guide to training
# physics-informed neural networks*](
# https://arxiv.org/abs/2308.08468).
#
@@ -30,7 +30,7 @@ from pina.equation import Equation
# ## The problem definition
#
# The one-dimensional Helmotz problem is mathematically written as:
# The one-dimensional Helmholtz problem is mathematically written as:
# $$
# \begin{cases}
# \frac{d^2}{dx^2}u(x) - \lambda u(x) -f(x) &= 0 \quad x\in(0,2)\\
@@ -38,9 +38,9 @@ from pina.equation import Equation
# \end{cases}
# $$
# In this case we are asking the solution to be $C^{\infty}$ periodic with
# period $2$, on the inifite domain $x\in(-\infty, \infty)$. Notice that the
# classical PINN would need inifinite conditions to evaluate the PBC loss function,
# one for each derivative, which is of course infeasable...
# period $2$, on the infinite domain $x\in(-\infty, \infty)$. Notice that the
# classical PINN would need infinite conditions to evaluate the PBC loss function,
# one for each derivative, which is of course infeasible...
# A possible solution, diverging from the original PINN formulation,
# is to use *coordinates augmentation*. In coordinates augmentation you seek for
# a coordinates transformation $v$ such that $x\rightarrow v(x)$ such that
@@ -54,11 +54,11 @@ from pina.equation import Equation
# In[2]:
class Helmotz(SpatialProblem):
class Helmholtz(SpatialProblem):
output_variables = ['u']
spatial_domain = CartesianDomain({'x': [0, 2]})
def helmotz_equation(input_, output_):
def Helmholtz_equation(input_, output_):
x = input_.extract('x')
u_xx = laplacian(output_, input_, components=['u'], d=['x'])
f = - 6.*torch.pi**2 * torch.sin(3*torch.pi*x)*torch.cos(torch.pi*x)
@@ -68,21 +68,21 @@ class Helmotz(SpatialProblem):
# here we write the problem conditions
conditions = {
'D': Condition(location=spatial_domain,
equation=Equation(helmotz_equation)),
equation=Equation(Helmholtz_equation)),
}
def helmotz_sol(self, pts):
def Helmholtz_sol(self, pts):
return torch.sin(torch.pi * pts) * torch.cos(3. * torch.pi * pts)
truth_solution = helmotz_sol
truth_solution = Helmholtz_sol
problem = Helmotz()
problem = Helmholtz()
# let's discretise the domain
problem.discretise_domain(200, 'grid', locations=['D'])
# As usual the Helmotz problem is written in **PINA** code as a class.
# As usual the Helmholtz problem is written in **PINA** code as a class.
# The equations are written as `conditions` that should be satisfied in the
# corresponding domains. The `truth_solution`
# is the exact solution which will be compared with the predicted one. We used
@@ -129,7 +129,7 @@ model = torch.nn.Sequential(PeriodicBoundaryEmbedding(input_dimension=1,
#
# We will now sole the problem as usually with the `PINN` and `Trainer` class.
# In[5]:
# In[ ]:
pinn = PINN(problem=problem, model=model)
@@ -180,7 +180,7 @@ with torch.no_grad():
#
# ## What's next?
#
# Nice you have completed the one dimensional Helmotz tutorial of **PINA**! There are multiple directions you can go now:
# Nice you have completed the one dimensional Helmholtz tutorial of **PINA**! There are multiple directions you can go now:
#
# 1. Train the network for longer or with different layer sizes and assert the finaly accuracy
#