df673cad4e
* solvers -> solver * adaptive_functions -> adaptive_function * callbacks -> callback * operators -> operator * pinns -> physics_informed_solver * layers -> block
52 lines
1.9 KiB
Python
52 lines
1.9 KiB
Python
""" Definition of the diffusion-reaction problem."""
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import torch
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from pina import Condition, LabelTensor
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from pina.problem import SpatialProblem, TimeDependentProblem, InverseProblem
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from pina.equation.equation import Equation
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from pina.domain import CartesianDomain
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from pina.operator import grad
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def diffusion_reaction(input_, output_):
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"""
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Implementation of the diffusion-reaction equation.
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"""
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x = input_.extract('x')
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t = input_.extract('t')
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u_t = grad(output_, input_, d='t')
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u_x = grad(output_, input_, d='x')
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u_xx = grad(u_x, input_, d='x')
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r = torch.exp(-t) * (1.5 * torch.sin(2*x) + (8/3) * torch.sin(3*x) +
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(15/4) * torch.sin(4*x) + (63/8) * torch.sin(8*x))
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return u_t - u_xx - r
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class InverseDiffusionReactionProblem(TimeDependentProblem,
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SpatialProblem,
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InverseProblem):
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"""
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Implementation of the diffusion-reaction inverse problem on the spatial
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interval [-pi, pi] and temporal interval [0,1], with unknown parameters
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in the interval [-1,1].
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"""
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output_variables = ['u']
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spatial_domain = CartesianDomain({'x': [-torch.pi, torch.pi]})
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temporal_domain = CartesianDomain({'t': [0, 1]})
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unknown_parameter_domain = CartesianDomain({'mu': [-1, 1]})
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conditions = {
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'D': Condition(
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domain=CartesianDomain({'x': [-torch.pi, torch.pi], 't': [0, 1]}),
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equation=Equation(diffusion_reaction)),
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'data' : Condition(
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input_points=LabelTensor(torch.randn(10, 2), ['x', 't']),
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output_points=LabelTensor(torch.randn(10, 1), ['u'])),
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}
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def _solution(self, pts):
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t = pts.extract('t')
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x = pts.extract('x')
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return torch.exp(-t) * (
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torch.sin(x) + (1/2)*torch.sin(2*x) + (1/3)*torch.sin(3*x) +
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(1/4)*torch.sin(4*x) + (1/8)*torch.sin(8*x)
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)
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