Examples update for v0.1 (#206)
* modify examples/problems * modify tutorials --------- Co-authored-by: Dario Coscia <dariocoscia@dhcp-235.eduroam.sissa.it> Co-authored-by: Dario Coscia <dariocoscia@dhcp-015.eduroam.sissa.it>
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Dario Coscia
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Nicola Demo
Nicola Demo
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@@ -1,52 +1,80 @@
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import numpy as np
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import torch
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from pina.segment import Segment
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from pina.cube import Cube
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from pina.problem2d import Problem2D
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xmin, xmax, ymin, ymax = -1, 1, -1, 1
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class ParametricEllipticOptimalControl(Problem2D):
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def __init__(self, alpha=1):
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def term1(input_, param_, output_):
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grad_p = self.grad(output_['p'], input_)
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gradgrad_p_x1 = self.grad(grad_p['x1'], input_)
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gradgrad_p_x2 = self.grad(grad_p['x2'], input_)
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return output_['y'] - param_ - (gradgrad_p_x1['x1'] + gradgrad_p_x2['x2'])
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def term2(input_, param_, output_):
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grad_y = self.grad(output_['y'], input_)
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gradgrad_y_x1 = self.grad(grad_y['x1'], input_)
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gradgrad_y_x2 = self.grad(grad_y['x2'], input_)
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return - (gradgrad_y_x1['x1'] + gradgrad_y_x2['x2']) - output_['u_param']
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def term3(input_, param_, output_):
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return output_['p'] - output_['u_param']*alpha
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""" Poisson OCP problem. """
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def term(input_, param_, output_):
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return term1( input_, param_, output_) +term2( input_, param_, output_) + term3( input_, param_, output_)
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from pina import Condition
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from pina.geometry import CartesianDomain
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from pina.equation import SystemEquation, FixedValue
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from pina.problem import SpatialProblem, ParametricProblem
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from pina.operators import laplacian
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def nil_dirichlet(input_, param_, output_):
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y_value = 0.0
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p_value = 0.0
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return torch.abs(output_['y'] - y_value) + torch.abs(output_['p'] - p_value)
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# ===================================================== #
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# #
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# This script implements the two dimensional #
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# Parametric Elliptic Optimal Control problem. #
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# The ParametricEllipticOptimalControl class is #
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# inherited from TimeDependentProblem, SpatialProblem #
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# and we denote: #
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# u --> field variable #
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# p --> field variable #
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# y --> field variable #
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# x1, x2 --> spatial variables #
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# mu, alpha --> problem parameters #
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# #
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# More info in https://arxiv.org/pdf/2110.13530.pdf #
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# Section 4.2 of the article #
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# ===================================================== #
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self.conditions = {
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'gamma1': {'location': Segment((xmin, ymin), (xmax, ymin)), 'func': nil_dirichlet},
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'gamma2': {'location': Segment((xmax, ymin), (xmax, ymax)), 'func': nil_dirichlet},
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'gamma3': {'location': Segment((xmax, ymax), (xmin, ymax)), 'func': nil_dirichlet},
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'gamma4': {'location': Segment((xmin, ymax), (xmin, ymin)), 'func': nil_dirichlet},
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'D1': {'location': Cube([[xmin, xmax], [ymin, ymax]]), 'func': term},
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#'D2': {'location': Cube([[0, 1], [0, 1]]), 'func': term2},
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#'D3': {'location': Cube([[0, 1], [0, 1]]), 'func': term3}
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}
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self.input_variables = ['x1', 'x2']
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self.output_variables = ['u', 'p', 'y']
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self.parameters = ['mu']
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self.spatial_domain = Cube([[xmin, xmax], [xmin, xmax]])
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self.parameter_domain = np.array([[0.5, 3]])
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class ParametricEllipticOptimalControl(SpatialProblem, ParametricProblem):
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# setting spatial variables ranges
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xmin, xmax, ymin, ymax = -1, 1, -1, 1
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x_range = [xmin, xmax]
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y_range = [ymin, ymax]
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# setting parameters range
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amin, amax = 0.0001, 1
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mumin, mumax = 0.5, 3
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mu_range = [mumin, mumax]
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a_range = [amin, amax]
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# setting field variables
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output_variables = ['u', 'p', 'y']
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# setting spatial and parameter domain
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spatial_domain = CartesianDomain({'x1': x_range, 'x2': y_range})
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parameter_domain = CartesianDomain({'mu': mu_range, 'alpha': a_range})
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# equation terms as in https://arxiv.org/pdf/2110.13530.pdf
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def term1(input_, output_):
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laplace_p = laplacian(output_, input_, components=['p'], d=['x1', 'x2'])
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return output_.extract(['y']) - input_.extract(['mu']) - laplace_p
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def term2(input_, output_):
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laplace_y = laplacian(output_, input_, components=['y'], d=['x1', 'x2'])
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return - laplace_y - output_.extract(['u'])
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def fixed_y(input_, output_):
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return output_.extract(['y'])
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def fixed_p(input_, output_):
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return output_.extract(['p'])
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# setting problem condition formulation
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conditions = {
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'gamma1': Condition(
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location=CartesianDomain({'x1': x_range, 'x2': 1, 'mu': mu_range, 'alpha': a_range}),
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equation=SystemEquation([fixed_y, fixed_p])),
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'gamma2': Condition(
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location=CartesianDomain({'x1': x_range, 'x2': -1, 'mu': mu_range, 'alpha': a_range}),
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equation=SystemEquation([fixed_y, fixed_p])),
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'gamma3': Condition(
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location=CartesianDomain({'x1': 1, 'x2': y_range, 'mu': mu_range, 'alpha': a_range}),
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equation=SystemEquation([fixed_y, fixed_p])),
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'gamma4': Condition(
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location=CartesianDomain({'x1': -1, 'x2': y_range, 'mu': mu_range, 'alpha': a_range}),
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equation=SystemEquation([fixed_y, fixed_p])),
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'D': Condition(
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location=CartesianDomain(
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{'x1': x_range, 'x2': y_range,
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'mu': mu_range, 'alpha': a_range
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}),
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equation=SystemEquation([term1, term2])),
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}
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