9cae9a438f
* Enable DDP training with batch_size=None and add validity check for split sizes * Refactoring SolverInterfaces (#435) * Solver update + weighting * Updating PINN for 0.2 * Modify GAROM + tests * Adding more versatile loggers * Disable compilation when running on Windows * Fix tests --------- Co-authored-by: giovanni <giovanni.canali98@yahoo.it> Co-authored-by: FilippoOlivo <filippo@filippoolivo.com>
51 lines
2.1 KiB
Python
51 lines
2.1 KiB
Python
""" Definition of the inverse Poisson problem on a square domain."""
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import torch
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from pina import Condition, LabelTensor
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from pina.problem import SpatialProblem, InverseProblem
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from pina.operators import laplacian
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from pina.domain import CartesianDomain
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from pina.equation.equation import Equation
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from pina.equation.equation_factory import FixedValue
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def laplace_equation(input_, output_, params_):
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"""
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Implementation of the laplace equation.
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"""
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force_term = torch.exp(- 2*(input_.extract(['x']) - params_['mu1'])**2
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- 2*(input_.extract(['y']) - params_['mu2'])**2)
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delta_u = laplacian(output_, input_, components=['u'], d=['x', 'y'])
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return delta_u - force_term
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class InversePoisson2DSquareProblem(SpatialProblem, InverseProblem):
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"""
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Implementation of the inverse 2-dimensional Poisson problem
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on a square domain, with parameter domain [-1, 1] x [-1, 1].
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"""
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output_variables = ['u']
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x_min, x_max = -2, 2
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y_min, y_max = -2, 2
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data_input = LabelTensor(torch.rand(10, 2), ['x', 'y'])
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data_output = LabelTensor(torch.rand(10, 1), ['u'])
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spatial_domain = CartesianDomain({'x': [x_min, x_max], 'y': [y_min, y_max]})
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unknown_parameter_domain = CartesianDomain({'mu1': [-1, 1], 'mu2': [-1, 1]})
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domains = {
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'g1': CartesianDomain({'x': [x_min, x_max], 'y': y_max}),
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'g2': CartesianDomain({'x': [x_min, x_max], 'y': y_min}),
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'g3': CartesianDomain({'x': x_max, 'y': [y_min, y_max]}),
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'g4': CartesianDomain({'x': x_min, 'y': [y_min, y_max]}),
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'D': CartesianDomain({'x': [x_min, x_max], 'y': [y_min, y_max]}),
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}
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conditions = {
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'nil_g1': Condition(domain='g1', equation=FixedValue(0.0)),
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'nil_g2': Condition(domain='g2', equation=FixedValue(0.0)),
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'nil_g3': Condition(domain='g3', equation=FixedValue(0.0)),
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'nil_g4': Condition(domain='g4', equation=FixedValue(0.0)),
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'laplace_D': Condition(domain='D', equation=Equation(laplace_equation)),
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'data': Condition(
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input_points=data_input.extract(['x', 'y']),
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output_points=data_output)
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}
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