forked from p94628173/idrlnet
40 lines
1.3 KiB
Markdown
40 lines
1.3 KiB
Markdown
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# Parameterized Poisson
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We consider an extended problem of [Simple Poisson](1_simple_poisson.md).
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$$
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\begin{array}{l}
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-\Delta u=1\\
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\frac{\partial u(x, -1)}{\partial n}=\frac{\partial u(x, 1)}{\partial n}=0 \\
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u(-1,y)=T_l\\
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u(1, y)=0,
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\end{array}
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$$
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where $T_l$ is a design parameter ranging in $(-0.2,0.2)$.
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The target is to train a surrogate that $u_\theta(x,y,T_l)$ gives the temperature at $(x,y)$ when $T_l$ is provided.
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## Train A Surrogate
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In addition, we define the parameter
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```python
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temp = sp.Symbol('temp')
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temp_range = {temp: (-0.2, 0.2)}
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```
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The usage of `temp` is similar to the time variable in [Burgers' Equation](3_burgers_equation.md).
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`temp_range` should be passed to the argument `param_ranges` in sampling domains.
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The left bound value condition is
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```python
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@sc.datanode
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class Left(sc.SampleDomain):
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# Due to `name` is not specified, Left will be the name of datanode automatically
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def sampling(self, *args, **kwargs):
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points = rec.sample_boundary(1000, sieve=(sp.Eq(x, -1.)), param_ranges=temp_range)
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constraints = sc.Variables({'T': temp})
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return points, constraints
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```
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The result is shown as follows:
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See `examples/parameterized_poisson`.
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