78 lines
3.2 KiB
Python
78 lines
3.2 KiB
Python
import numpy as np
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import torch
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from pina import Span, Condition
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from pina.problem import SpatialProblem, ParametricProblem
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from pina.operators import grad, nabla
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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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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 = Span({'x1': x_range, 'x2': y_range})
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parameter_domain = Span({'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 = nabla(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 = nabla(output_, input_, components=['y'], d=['x1', 'x2'])
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return - laplace_y - output_.extract(['u_param'])
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def state_dirichlet(input_, output_):
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y_exp = 0.0
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return output_.extract(['y']) - y_exp
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def adj_dirichlet(input_, output_):
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p_exp = 0.0
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return output_.extract(['p']) - p_exp
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# setting problem condition formulation
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conditions = {
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'gamma1': Condition(
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location=Span({'x1': x_range, 'x2': 1, 'mu': mu_range, 'alpha': a_range}),
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function=[state_dirichlet, adj_dirichlet]),
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'gamma2': Condition(
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location=Span({'x1': x_range, 'x2': -1, 'mu': mu_range, 'alpha': a_range}),
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function=[state_dirichlet, adj_dirichlet]),
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'gamma3': Condition(
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location=Span({'x1': 1, 'x2': y_range, 'mu': mu_range, 'alpha': a_range}),
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function=[state_dirichlet, adj_dirichlet]),
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'gamma4': Condition(
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location=Span({'x1': -1, 'x2': y_range, 'mu': mu_range, 'alpha': a_range}),
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function=[state_dirichlet, adj_dirichlet]),
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'D': Condition(
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location=Span({'x1': x_range, 'x2': y_range,
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'mu': mu_range, 'alpha': a_range}),
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function=[term1, term2]),
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} |