forked from idrl/idrlnet
87 lines
2.4 KiB
Python
87 lines
2.4 KiB
Python
import matplotlib.pyplot as plt
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import sympy as sp
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import numpy as np
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import idrlnet.shortcut as sc
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x = sp.symbols("x")
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Line = sc.Line1D(0, 1)
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y = sp.Function("y")(x)
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@sc.datanode(name="interior")
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class Interior(sc.SampleDomain):
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def sampling(self, *args, **kwargs):
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return Line.sample_interior(1000), {"dddd_y": 0}
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@sc.datanode(name="left_boundary1")
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class LeftBoundary1(sc.SampleDomain):
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def sampling(self, *args, **kwargs):
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return Line.sample_boundary(100, sieve=(sp.Eq(x, 0))), {"y": 0}
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@sc.datanode(name="left_boundary2")
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class LeftBoundary2(sc.SampleDomain):
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def sampling(self, *args, **kwargs):
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return Line.sample_boundary(100, sieve=(sp.Eq(x, 0))), {"d_y": 0}
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@sc.datanode(name="right_boundary1")
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class RightBoundary1(sc.SampleDomain):
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def sampling(self, *args, **kwargs):
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return Line.sample_boundary(100, sieve=(sp.Eq(x, 1))), {"dd_y": 0}
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@sc.datanode(name="right_boundary2")
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class RightBoundary2(sc.SampleDomain):
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def sampling(self, *args, **kwargs):
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return Line.sample_boundary(100, sieve=(sp.Eq(x, 1))), {"ddd_y": 0}
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@sc.datanode(name="infer")
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class Infer(sc.SampleDomain):
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def sampling(self, *args, **kwargs):
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return {"x": np.linspace(0, 1, 1000).reshape(-1, 1)}, {}
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net = sc.get_net_node(inputs=("x",), outputs=("y",), name="net", arch=sc.Arch.mlp)
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pde1 = sc.ExpressionNode(
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name="dddd_y", expression=y.diff(x).diff(x).diff(x).diff(x) + 1
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)
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pde2 = sc.ExpressionNode(name="d_y", expression=y.diff(x))
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pde3 = sc.ExpressionNode(name="dd_y", expression=y.diff(x).diff(x))
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pde4 = sc.ExpressionNode(name="ddd_y", expression=y.diff(x).diff(x).diff(x))
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solver = sc.Solver(
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sample_domains=(
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Interior(),
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LeftBoundary1(),
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LeftBoundary2(),
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RightBoundary1(),
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RightBoundary2(),
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),
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netnodes=[net],
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pdes=[pde1, pde2, pde3, pde4],
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max_iter=2000)
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solver.solve()
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# inference
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def exact(x):
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return -(x ** 4) / 24 + x ** 3 / 6 - x ** 2 / 4
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solver.sample_domains = (Infer(),)
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points = solver.infer_step({"infer": ["x", "y"]})
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xs = points["infer"]["x"].detach().cpu().numpy().ravel()
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y_pred = points["infer"]["y"].detach().cpu().numpy().ravel()
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plt.plot(xs, y_pred, label="Pred")
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y_exact = exact(xs)
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plt.plot(xs, y_exact, label="Exact", linestyle="--")
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plt.legend()
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plt.xlabel("x")
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plt.ylabel("w")
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plt.savefig("Euler_beam.png", dpi=300, bbox_inches="tight")
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plt.show()
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