Add an example of Poisson-like 2D problem for multioutput DeepONet Add the example

examples/operator/poisson_aligned_multioutput_pideeponet_2d.py

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+"""
+Poisson-like 2D problem
+Supported backend: tensorflow.compat.v1, tensorflow
+"""
+import numpy as np
+
+import deepxde as dde
+
+
+# Two target variables: A and B
+# Equations: dA_xx = f, dB_tt = f
+def equation(x, y, f):
+    # A = y[:, 0:1] and B = y[:, 1:2]
+    dA_xx = dde.grad.hessian(y, x, component=0, i=0, j=0)
+    dB_tt = dde.grad.hessian(y, x, component=1, i=1, j=1)
+    return [dA_xx - f, dB_tt - f]
+
+
+# Define space/time geometry
+geomtime = dde.geometry.GeometryXTime(
+    dde.geometry.Interval(0, 1), dde.geometry.TimeDomain(0, 1)
+)
+
+# Boundary conditions for A and B
+A_bc = dde.icbc.DirichletBC(
+    geomtime,
+    lambda _: 0,
+    lambda _, on_boundary: on_boundary and np.isclose(_[0], 0),
+    component=0,
+)
+B_bc = dde.icbc.DirichletBC(
+    geomtime,
+    lambda _: 0,
+    lambda _, on_boundary: on_boundary and np.isclose(_[0], 1),
+    component=1,
+)
+
+space = dde.data.GRF2D()
+evaluation_points = geomtime.uniform_points(10)
+
+data = dde.data.PDEOperatorCartesianProd(
+    dde.data.TimePDE(
+        geomtime, equation, [A_bc, B_bc], num_domain=1000, num_boundary=10
+    ),
+    space,
+    evaluation_points,
+    num_function=10,
+)
+
+# Define DeepONet with two outputs.
+# Use `split_branch` strategy. The output size of the trunk net is equal
+# to the output size of the branch net divided by the number of outputs.
+net = dde.nn.DeepONetCartesianProd(
+    [evaluation_points.shape[0], 100, 100],
+    [geomtime.dim, 100, 50],
+    activation="tanh",
+    kernel_initializer="Glorot normal",
+    num_outputs=2,
+    multi_output_strategy="split_branch",
+)
+
+# Train model
+model = dde.Model(data, net)
+model.compile("adam", lr=0.001)
+model.train(iterations=5000)