add unit test for biharmonic

Signed-off-by: jjyaoao <jjyaoao@126.com>

test/equation/test_biharmonic.py

@@ -0,0 +1,75 @@
+import paddle
+import pytest
+from paddle import nn
+
+from ppsci import equation
+
+__all__ = []
+
+
+@pytest.mark.parametrize("dim", (2, 3))
+def test_biharmonic(dim):
+    """Test for biharmonic equation."""
+    batch_size = 13
+    input_dims = ("x", "y", "z")[:dim]
+    output_dims = ("u",)
+
+    q = -1.0
+    D = 1.0
+
+    # generate input data
+    x = paddle.randn([batch_size, 1])
+    y = paddle.randn([batch_size, 1])
+    x.stop_gradient = False
+    y.stop_gradient = False
+    input_data = paddle.concat([x, y], axis=1)
+    if dim == 3:
+        z = paddle.randn([batch_size, 1])
+        z.stop_gradient = False
+        input_data = paddle.concat([x, y, z], axis=1)
+
+    # build NN model
+    model = nn.Sequential(
+        nn.Linear(len(input_dims), len(output_dims)),
+        nn.Tanh(),
+    )
+
+    # manually generate output
+    u = model(input_data)
+
+    # use self-defined jacobian and hessian
+    def jacobian(y: "paddle.Tensor", x: "paddle.Tensor") -> "paddle.Tensor":
+        return paddle.grad(y, x, create_graph=True)[0]
+
+    def hessian(y: "paddle.Tensor", x: "paddle.Tensor") -> "paddle.Tensor":
+        return jacobian(jacobian(y, x), x)
+
+    # compute expected result
+    expected_result = -q / D
+
+    # compute fourth order derivative
+    for var_i in (x, y):
+        for var_j in (x, y):
+            expected_result += hessian(hessian(u, var_i), var_j)
+    if dim == 3:
+        for var_i in (x, y, z):
+            for var_j in (x, y, z):
+                expected_result += hessian(hessian(u, var_i), var_j)
+
+    # compute result using built-in Biharmonic module
+    biharmonic_equation = equation.Biharmonic(dim=dim, q=q, D=D)
+    data_dict = {
+        "x": x,
+        "y": y,
+        "u": u,
+    }
+    if dim == 3:
+        data_dict["z"] = z
+    test_result = biharmonic_equation.equations["biharmonic"](data_dict)
+
+    # check result whether is equal
+    assert paddle.allclose(expected_result, test_result)
+
+
+if __name__ == "__main__":
+    pytest.main()